Mitigating retail rice price volatility for sustainable supply chains:&nbsp;an optimization and regression-based approach

Lucia Diawati; Arif Shafwan Rasyid

doi:10.12688/f1000research.161723.2

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Research Article

Revised

Mitigating retail rice price volatility for sustainable supply chains: an optimization and regression-based approach

[version 2; peer review: 2 approved]

Lucia Diawati¹, Arif Shafwan Rasyid ²

PUBLISHED 05 Jun 2025

Author details Author details

¹ Industrial Engineering and Management, Bandung Institute of Technology, Bandung, West Java, 40132, Indonesia
² Industrial Engineering and Management, Bandung Institute of Technology, Bandung, West Java, 40132, Indonesia

Lucia Diawati
Roles: Conceptualization, Formal Analysis, Investigation, Project Administration, Resources, Supervision, Validation, Writing – Review & Editing

Arif Shafwan Rasyid
Roles: Data Curation, Methodology, Software, Visualization, Writing – Original Draft Preparation

OPEN PEER REVIEW

REVIEWER STATUS

This article is included in the Agriculture, Food and Nutrition gateway.

Abstract

Background

This study addresses the challenge of stabilizing rice retail prices in Indonesia, where rice is a critical staple food, as in many Asian countries. The government prioritizes price stability to prevent sharp increases that could trigger social unrest during shortages. Price control approaches are categorized as direct or indirect. Direct controls involve immediate interventions, such as boosting rice stocks through imports to quickly influence market prices. Indirect controls consist of longer-term measures, like enhancing domestic production capacity for gradual stabilization. This study proposes an optimization model to determine the optimal rice import volume to minimize bi-monthly retail price fluctuations.

Methods

A linear programming model is formulated to minimize bimonthly price changes, subject to constraints including local production capacity, import limits, rice flow balance, and demand fulfillment. The monthly retail price is modeled using a compound linear regression approach with seven explanatory variables: the rupiah exchange rate against the US dollar, GDP per capita, the price of ground dry rice (GKG) per kilogram, domestic rice procurement, rice imports, rice distribution, and government-managed rice stock aimed at ensuring domestic availability and price stability. The explanatory variable is forecasted using methods best suited to its historical pattern.

Results

The model was tested using data from 2020 to 2023. The results indicate that bimonthly rice prices increases can be effectively controlled, with maximum price change rates maintained between 0.75% and 1.14% and a standard deviation ranging from 0.20% to 0.34%. These values are significantly lower than the anticipated inflation rate of 2–3%.

Conclusions

The optimization model effectively determines the required volume of rice imports to minimize bimonthly retail price fluctuations. By regulating import volumes, excessive price increases can be prevented. Enhanced data-driven forecasting with granular historical data may further improve the accuracy of retail rice price predictions and strengthen price stabilization initiatives.

Keywords

Rice supply chain, Rice import, Increasing rate of rice price, Hybrid optimization-regression model.

Corresponding author: Arif Shafwan Rasyid

Competing interests: No competing interests were disclosed.

Grant information: The author(s) declared that no grants were involved in supporting this work.

Copyright: © 2025 Diawati L and Rasyid AS. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

How to cite: Diawati L and Rasyid AS. Mitigating retail rice price volatility for sustainable supply chains: an optimization and regression-based approach [version 2; peer review: 2 approved]. F1000Research 2025, 14:311 (https://doi.org/10.12688/f1000research.161723.2) First published: 20 Mar 2025, 14:311 (https://doi.org/10.12688/f1000research.161723.1) Latest published: 05 Jun 2025, 14:311 (https://doi.org/10.12688/f1000research.161723.2)

Revised Amendments from Version 1

The revised version of the article incorporates an enhanced compound linear regression model that includes seven independent variables, offering improved accuracy in estimating optimal rice import volumes aimed at minimizing fluctuations in the monthly rice price change rate. To validate the model, a behavioral evaluation was conducted to assess the extent to which the model accurately replicates the real-world dynamics of the system. This evaluation followed a standard procedure involving the comparison of simulated outputs with historical data over time, along with calculating the average deviation between simulated and observed values. The primary performance metric used in this assessment was the Mean Squared Error (MSE), supplemented by its decomposition into bias (UM), variance inequality (US), and covariance inequality (UC) components. Ultimately, the model's application in determining monthly rice import quantities is presented, with simulations conducted over 12 months for four consecutive years: January–December of 2020, 2021, 2022, and 2023.

Additionally, a sensitivity analysis was performed by varying the lower limit of the strategic inventory to examine the effect of parameter changes on the model’s outcomes. The sensitivity analysis results indicate that, from 2020 to 2023, changes in the strategic inventory threshold had minimal impact on the monthly rice price change rate between consecutive months, with maximum monthly fluctuations ranging from 0.42% to 1.14%. In 2022 and 2023, the model produced more stable price change rates compared to the actual historical data. Conversely, in 2020 and 2021, the model-generated price change rates exhibited greater volatility than observed in reality. This discrepancy is likely attributable to the COVID-19 pandemic, which led to a decline in rice demand and subsequently reduced rice prices.

See the authors' detailed response to the review by Katsuhiko Takahashi
See the authors' detailed response to the review by Amelia Santoso

1. Introduction

Rice is a staple food with a high level of consumption in Indonesia. In 2017, the average national per capita rice consumption reached 97.6 kg per year, significantly exceeding the average consumption of meat (2.5 kg per capita per year) and poultry (7.5 kg per capita per year). Corn, often considered an alternative carbohydrate source, was consumed at an average of only 2 kg per capita per year (Arifin, et al., 2018). Given Indonesia's growing population, rice demand is projected to rise in the coming years. From a population of approximately 275 million in 2022, Indonesia is expected to see an increase to 294 million in 2030 and 319 million in 2045 (BPS-Statistics Indonesia, 2018). This population growth will likely lead to greater demand for staple foods, particularly rice. Arifin et al. (2018) forecasted that per capita rice consumption in Indonesia will increase by 14% to 101.5 kg per year by 2025 and by an additional 1% to 102 kg per year by 2045.

Such trends highlight rice's critical role in national economic stability, food security, and political stability. Ensuring a stable rice supply, characterized by consistent availability and affordable prices, is essential. However, recent trends indicate a decline in rice production. According to estimates from the Area Sample Framework (Kerangka Sampel Area, KSA) conducted by the National Statistics Bureau (BPS-Statistics Indonesia), national rice production decreased from 59.2 million tonnes in 2018 to 54.6 million tonnes in 2019. This figure remained relatively unchanged in 2020 at 54.6 million tonnes but further declined to 54.4 million tonnes in 2021 (BPS-Statistics Indonesia, 2022b).

The combination of increasing demand and declining production has disrupted the balance of rice supply and demand, leading to scarcity and rising prices. Typically, rice prices are lower during the harvest period (February to September) but increase toward the year's end due to reduced supply. However, between September 2022 and September 2023, rice prices in traditional markets displayed a consistent increasing trend.

In response to these challenges, the government has implemented policies to stabilize rice prices, including the minimum purchase price for farmers and the highest retail price (Harga Eceran Tertinggi, HET) for consumers (Hermanto, 2017). With rising inflation, rice prices have continued to climb, prompting the National Food Agency (Badan Pangan Nasional) to issue updated regulations on HET based on rice quality and trade location, as outlined in the National Food Agency Regulation No. 7 Year 2023.

To manage national rice stocks, ensure food security, and stabilize prices (Bappenas, 2019), the Indonesian government has appointed a state-owned enterprise responsible for these objectives. When retail rice prices exceed the HET, this entity intervenes by importing rice. This study aims to develop a model to determine the required quantity of rice imports to minimize the rate of increase in retail rice prices between consecutive months.

Over the years, research on commodity distribution, price prediction, and price stabilization has evolved significantly. Early studies primarily focused on supply chain network design and optimization. Melo et al. (2006) explored dynamic supply chain network design, focusing on relocating, adding, or reducing distribution center capacity. This study sought to optimize facility operations, capacity movement, and the quantity of goods produced, stored, or delivered. Min et al. (2007) and Li & Bing (2007) studied supply chain equilibrium under varying demand conditions, examining how product distribution among factories, retailers, and customers affects overall network performance. Wu & Zhang (2014) further investigated multi-commodity supply chains, focusing on cost reduction through optimized distribution center locations and retailer allocations. Teng et al. (2007) focus on developing a multi-commodity flow supply chain network equilibrium model that accounts for random demand. Afterwards, Xu and Zhu (2007), and Dellaert et al. (2021) extend the multi-commodity flow supply chain network equilibrium model by incorporating stochastic choice.

Athanasiou et al. (2008) focused on price stabilization in commodity markets through a nonlinear Cobweb model. The study showed that government interventions, such as adjusting stock levels, could stabilize prices. Paksoy et al. (2012) presented a fuzzy multi-objective linear programming model to minimize transportation costs for commodity distribution across multiple stages in the supply chain. Gouel (2013) and Dawe & Timmer (2012) further explored government policies aimed at stabilizing food prices, highlighting the role of subsidies, stock management, and trade regulations in minimizing price volatility.

Other studies concentrated on supply chain optimization under specific conditions. Serra & Gil (2012) found that blending biodiesel with diesel could mitigate fuel price fluctuations in Spain. Dorosh & Rashid (2013) examined rice price stabilization in Bangladesh, finding that stock management and trade interventions were key to price stabilization during crises. Similarly, Possamai et al. (2015) used a spatial-temporal network framework to model price stabilization for agricultural commodities, emphasizing the importance of interseasonal storage.

Several studies, such as Mogale et al. (2017), Gholamian and Taghanzadeh (2017), and Cheraghalipour et al. (2019), focused on minimizing logistics costs, but did not explore the interaction between product distribution quantities and market prices, an important factor for controlling price inflation. In contrast, Fitrawaty et al. (2023) investigated how domestic production levels, exchange rates, international prices, and GDP affect rice prices in Indonesia, providing policy insights but not actionable strategies for price control.

Research also examined various computational models for optimizing supply chain performance. Zhou et al. (2018) and Boccia et al. (2018) explored vehicle route optimization and facility location for multi-commodity distribution. Gu et al. (2021) and Guimaraes et al. (2019) combined inventory policies with route optimization to minimize distribution costs. Studies by Mohamed et al. (2023) and Zhang et al. (2022) addressed the complexities of stochastic demand in e-commerce, using algorithms to optimize facility locations and vehicle routes.

In terms of price prediction and stabilization, several studies have developed models to forecast commodity prices and mitigate fluctuations (Lin and Xu, 2019; Kwas et al., 2022; Elyasi & Teimoury, 2022). Ohyver & Pudjihastuti (2018) employed an ARIMA model to forecast rice prices in Indonesia, while Mele et al. (2020) explored suboptimal price stabilization as central banks influence market expectations. Anggraeni et al. (2019) combined hybrid neural network and ARIMA models to predict rice prices, Fitrawaty et al. (2023) developed a regression model that takes into account various factors influencing rice market prices. Menawhile, Maulana et al. (2023) created a model to optimize the equilibrium within the rice supply chain network using the Method of Successive Average (MSA).

While existing studies have made significant contributions to supply chain optimization and the analysis of price fluctuations, there remains a notable shortcoming in research that integrates rice distribution quantities with price control mechanisms capable of generating immediate effects. To address this shortcoming, the present study aims to develop a quantitative model for determining the optimal monthly volume of rice imports necessary to balance supply and demand, thereby minimizing increases in retail rice market prices. By optimizing import volumes, the GE authorized for rice imports can ensure a stable rice supply while maintaining its affordability as a staple food, particularly in developing economies where rice is a primary dietary component.

2. Methods

2.1 Model development

The primary model to be developed is an optimization model aimed at minimizing monthly changes in rice retail prices over two consecutive months. This is achieved by determining the quantity of rice imports necessary to control fluctuations in monthly rice retail prices, subject to 10 constraints governing the rice supply chain mechanism from sources to markets. To support the development of this optimization model, several auxiliary models are required.

Variables
${PP}_{t}$	Rice production rate in month t (tonnes/month)
${NT}_{t}$	The rupiah exchange rate against the dollar in the month of t (rupiah)
${PDB}_{t}$	Gross Domestic Product (GDP) per capita in month t (rupiah)
${LL}_{t}$	Agricultural land area in month t (ha)
${GKP}_{t}$	Harvested Dry Rice price per kg in month t (rupiah per kg)
${GKG}_{t}$	Ground Dry Rice price per kg in month t (rupiah per kg)
$X_{t}$	Domestic rice procurement in month t (tonnes)
$Y_{t}$	Rice imports in month t (tonnes)
$O_{t}$	Rice distribution in month t (tonnes)
$I_{t}$	Rice stocks at the end of month t (tonnes)
$Z_{t}$	The rate of increase in rice prices between month t and the preceding month (percent)
$P_{t}$	Rice price per kg in month t (rupiah per kg)
Parameters
$X_{bT}$	Domestic rice procurement in month b year T (tonnes)
${PCT}_{b 2017}$	Percentage of domestic rice procurement to national rice production in month b of 2017
${PB}_{bT}$	Domestic rice production in b year T (tonnes)
$Prop$	Proportion of rice distribution to consumers relative to national rice consumption
$\bar{D_{T}}$	Average rice consumption per month in year T (tonnes)
$s_{month}$	Standard deviation of rice consumption per month (tonnes)
$s_{year}^{2}$	Variation in rice consumption per year (tonnes)
$D_{t}$	National rice consumption in month t (tonnes)
$β_{0}$	Parameter intercept of compound linear regression model
$β_{n}$	The parameter of the coefficient of factor n that affects the price of rice per kg in month t. The value of n ranges from 1–10, representing factors that affect the price of rice per kg in month t.
$d_{t}$	Consumer demand for rice in month t (tonnes)
$ss$	Lower limit of strategic inventory (tonnes)
$h$	Rice storage capacity (tonnes)
$p_{t}$	Production capacity of domestic rice mills in month t (tonnes)
$s$	The export capacity of rice from source countries to Indonesia (tonnes)
${PB}_{t 2018 - 2022}$	Maximum rice production of domestic mills in month t 2018–2022 (tonnes)
$F_{t}$	Intercept value for month t
${Tr}_{t}$	Slope factor value for month t
$B_{t}$	Seasonal factor value in month t
$F_{T}$	Intercept value for year T
${Tr}_{T}$	Slope factor value for year T
MSE	Mean Squared Error
U^M	Bias, represents the difference between mean of actual data and mean of model outputs
U^S	Variance inequality, measures the difference between standar deviation of actual data and that of model outputs
U^C	Covariance inequality, represents unexplained variation between actual data and model outputs.
r	Correlation coefficient

2.2 Review System: government enterprise rice supply chain network

The rice supply chain in Indonesia commences with farmers who cultivate rice during the harvest season, producing Harvested Dry Rice and Ground Dry Rice. The harvested rice is subsequently sold to intermediaries, who then distribute it to domestic rice mills. These mills process the rice using GKG as the primary raw material. The processed rice is acquired by private distributors and government enterprises for domestic rice procurement. Private distributors then sell the rice to retail traders, including supermarkets and traditional markets, which serve as the primary purchase points for rice consumers in Indonesia.

In procuring rice, government enterprises have two sources: domestic rice mills and rice imports. The rice supplied by government enterprises is stored and subsequently distributed to consumers to meet their demand. When the retail price of rice in the market is high, government enterprises conduct market operations by increasing the distribution of rice to the market or importing rice from source countries to enhance rice availability. Consumers purchase rice from government enterprises through traditional markets. This study models the rice supply chain network, which includes domestic rice mills, import source countries, national rice warehouses owned by government enterprises, and traditional markets as points of purchase for consumers. Figure 1 illustrates the rice supply chain network in Indonesia and the scope of the modelled rice supply chain network in this study.

Figure 1. Rice supply chain network in Indonesia.

2.3 Factors affecting rice prices

Fitrawaty et al. (2023) stated that rice prices are influenced by several factors, including the followings.

1. Rice production rate
2. Rupiah exchange rate against dollar
3. Gross Domestic Product per capita

In addition, according to Rusono (2019), rice prices in Indonesia are also influenced by the availability of rice, which includes rice stocks as well as the mechanism for its procurement and distribution of rice. Some of the activities carried out by government enterprise to maintain rice price stabilization in Indonesia include (Rusono, 2019):

1. Procuring domestic rice
2. Importing rice
3. Distributing rice to consumers
4. Managing rice stocks

The increase in rice supplies in Indonesia, encompassing domestic procurement, rice imports, distribution to consumers, and stocks managed by government enterprises, can lead to a reduction in rice prices. The availability of rice in Indonesia is also significantly influenced by the extent of agricultural land; larger areas of rice farming correspond to higher production levels, thereby increasing rice availability for consumption. According to Makbul & Ratnaningtyas (2017), the prices of Harvested Dry Rice (GKP) and Ground Dry Rice (GKG) per kilogram also play a critical role in determining the retail market price of rice. An increase in GKP and GKG prices per kilogram directly leads to a rise in retail rice prices.

Based on the aforementioned factors, a compound linear regression model with 10 independent variables, representing these determinants, can be used to predict rice prices for a given month. The model parameters, specifically the intercept and slope coefficients, were estimated using the Ordinary Least Squares (OLS) method. To develop this predictive model, historical data on rice prices and the factors influencing them are required, as outlined in Appendix A.

2.4 Estimating unavailable data

The variables of GDP per capita per month, domestic rice procurement, rice imports, and rice distribution are readily available, but require estimation. The monthly GDP per capita for Indonesia is estimated by dividing the annual GDP per capita (at current prices) by 12 (BPS-Statistics Indonesia; 2022a). Monthly domestic rice procurement by government enterprises for the period January 2018–December 2022 is approximated using historical data on the monthly proportion of domestic rice procurement to national rice production from January to December 2017 (Rusono, 2019) and historical data on monthly rice production for the same period from the National Statistics Bureau (BPS-Statistics Indonesia; 2022b).

Table 1 summarizes the national rice production, rice procurement, and the proportion of rice procurement to national production for January–December 2017. Historical data on monthly rice production for January 2018–December 2022 is provided in Table 2.

Table 1. National rice production, rice procurement, and proportion of rice procurement to national production January-December 2017.

Month	Rice production (tonnes)	Rice procurement (tonnes)	Rice procurement proportion
January	2,203,250	641	0.0003
February	4,419,219	4,194	0.0009
March	8,844,298	167,810	0.0190
April	6,664,739	649,780	0.0975
May	3,213,603	572,387	0.1781
June	3,328,442	407,724	0.1225
July	4,264,106	162,222	0.0380
August	5,141,666	250,000	0.0486
September	4,769,844	200,000	0.0419
October	2,769,836	200,000	0.0722
November	1,919,833	200,000	0.1042
December	2,113,599	200,000	0.0946
Total	9,652,435	3,014,758

Table 2. Historical data on rice production for the period January 2018 – December 2022 (Tonnes).

Month	2018	2019	2020	2021	2022
January	1,595,000	1,168,000	934,000	1,200,000	1,420,000
February	3,289,000	2,083,000	1,328,000	2,337,000	2,350,000
March	5,547,000	5,255,000	3,632,000	5,570,000	5,490,000
April	4,358,000	5,121,000	5,626,000	4,476,000	4,450,000
May	2,812,000	2,505,000	3,586,000	2,277,000	2,380,000
June	2,574,000	2,475,000	2,059,000	2,326,000	2,510,000
July	3,117,000	2,663,000	2,578,000	3,175,000	2,710,000
August	3,083,000	3,214,000	3,345,000	2,402,000	2,350,000
September	2,972,000	2,430,000	3,161,000	2,464,000	2,500,000
October	1,907,000	1,899,000	2,455,000	2,302,000	2,380,000
November	1,606,000	1,522,000	1,858,000	1,653,000	1,880,000
December	1,084,000	979,000	935,000	1,174,000	1,110,000

The monthly proportion of rice procurement to national rice production from 2017 is applied to estimate domestic rice procurement for January 2018–December 2022 using Equation (1). Similarly, monthly rice import data (BPS-Statistics Indonesia, 2022c) for the same period is estimated using Equation (2)

(1)

X_{bT} = {PCT}_{b 2017} ∙ {PB}_{bT}

(2)

Y_{t} = I_{t} + O_{t} - X_{t} - I_{t - 1}

To estimate the monthly rice distribution by government enterprises for the period January 2018–December 2022, the 2018 rice distribution data (BPS-Statistics Indonesia, 2022d), totaling 1,449,000 tonnes, was used as a baseline. Additionally, national rice consumption data for the 2018–2022 period, obtained from the National Statistics Bureau (BPS-Statistics Indonesia, 2022e), is presented in Table 3.

Table 3. National rice consumption in 2018-2022 (BPS-Statistics Indonesia, 2022b).

Year	National rice consumption (tonnes)
2018	25,792,716
2019	25,214,232
2020	25,348,135
2021	25,596,828
2022	25,941,627

Based on rice distribution and national rice consumption data for 2018, the proportion of rice distribution to consumers relative to national rice consumption was calculated using Equation (3), yielding a value of 0.056. After determining this proportion, monthly national rice consumption data for the period January 2018–December 2022 was required. However, actual monthly data for this period was unavailable.

To estimate the required data, the average monthly rice consumption for the 2018–2022 period was first calculated using Equation (4). The results, including the average monthly rice consumption and the annual standard deviation for the 2018–2022 period, are presented in Table 4. To derive the standard deviation of monthly rice consumption, Equation (5) was applied under the assumption that the standard deviation remains constant throughout the 2018–2022 period.

(3)

Prop = \frac{Rice Distribution 2018}{National Rice Consumption 2018}

(4)

\bar{D_{T}} = \frac{National rice consumption year T}{12 months}

(5)

s_{month} = \sqrt{\frac{s_{year}^{2}}{12 month}}

Table 4. Average national rice consumption per month in the period 2018–2022.

Year	Average National Rice Consumption per Month (tonnes)
2018	2,149,393
2019	2,101,186
2020	2,112,345
2021	2,133,069
2022	2,161,802
Standard Deviation	25,133.1

With the estimated average monthly rice consumption and its standard deviation, the monthly national rice consumption data for January 2018–December 2022 was generated, assuming the data follows a normal distribution. The estimated monthly national rice consumption values for this period are presented in Table 5.

Table 5. Estimated Monthly National Rice Consumption (in tonnes) from January 2018 to December 2022 (tonnes).

Month	2018	2019	2020	2021	2022
January	2,155,188	2,152,242	2,113,239	2,143,044	2,146,314
February	2,156,587	2,153,263	2,114,297	2,142,936	2,150,026
March	2,152,556	2,114,180	2,115,544	2,141,930	2,147,570
April	2,152,262	2,113,031	2,116,266	2,140,064	2,153,803
May	2,148,060	2,100,766	2,111,001	2,139,379	2,149,595
June	2,147,766	2,108,933	2,110,559	2,137,999	2,148,297
July	2,144,845	2,110,405	2,111,921	2,136,923	2,142,464
August	2,141,968	2,107,593	2,109,595	2,135,643	2,149,353
September	2,142,694	2,108,725	2,108,502	2,134,404	2,152,868
October	2,144,837	2,109,777	2,107,129	2,132,286	2,154,979
November	2,147,717	2,110,372	2,106,314	2,131,539	2,158,980
December	2,148,155	2,112,568	2,103,921	2,134,242	2,161,367

Once the monthly national rice consumption data for the period January 2018–December 2022 is obtained, the monthly rice distribution data for the same period can be estimated using Equation (6). For months without rice imports, the rice distribution data is estimated using Equation (7)

(6)

O_{t} = Prop ∙ D_{t}

(7)

O_{t} = I_{t - 1} + X_{t} - I_{t}

2.5 Rice price prediction model

The compound linear regression model was built using 60 training data, namely time series data in the period January 2018 - December 2022. The dataset used in developing the model is available from the authors upon request. The rice price prediction model formed is shown by Equation (8)

(8)

P_{t} = 10.437,47 - 0.000004 ∙ {PP}_{t} + 0,0016 ∙ {NT}_{t} - 0, 00006 ∙ {PDB}_{t} + 0, 0001 ∙ {LL}_{t} + 0, 1592 ∙ {GKP}_{t} + 0, 1742 ∙ {GKG}_{t} + 0, 0001 ∙ X_{t} - 0, 00004 ∙ Y_{t} - 0, 00007 ∙ O_{t} - 0, 00009 ∙ I_{t}

The coefficient value, t-statistic, and p-value of each variable can be seen in Table 6.

Table 6. The coefficient value, t-statistic, and p-value of each independent variable of the first model.

Independent variable	Coefficient symbol	Coefficient value	t-statistic	p-value	VIF
	β₀	10,437.37	39.141	<0.001
PP_t	β₁	-0.000004	-0.111	0.912	139.368
NT_t	β₂	0.0016	0.093	0.926	1.457
PDB_t	β₃	-0.00006	-2.767	0.008	1.843
LL_t	β₄	0.0001	0.457	0.650	151.194
GKP_t	β₅	0.1592	2.011	0.050	11.229
GKG_t	β₆	0.1742	2.649	0.011	7.154
X_t	β₇	0.0001	1.759	0.085	2.618
Y_t	β₈	-0.00004	-0.651	0.518	1.305
O_t	β₉	-0.00007	-0.413	0.682	2.028
I_t	β₁₀	-0.00009	-5.281	<0.001	1.791

The calculated F-statistic of this compound linear regression model is 17.66 which is greater than the critical F-value = 1.99 for 60 training data and 10 independent variables. The p-value of the resulting calculation of F-statistic is <0.001 which is less than α = 0.05, indicating that the 10 independent variables together significantly affect the price of rice in a month. The R-squared value obtained from this model is 0.783. This indicates that the ten independent variables collectively explain 78.3% of the variance in the dependent variable. As three independent variables has Variance Inflation Factor (VIF) higher than 10, the model was revised by eliminating the variables and re-calculate the statistics of the revised model.

The new compound linear regression model is as follow

(9)

P_{t} = 10.576,43 + 0.0105 \cdot {NT}_{t} - 0,00006 \cdot {PDB}_{t} + 0,2848 \cdot {GKG}_{t} + 0,0001 \cdot X_{t} - 0,000001 \cdot Y_{t} - 0,00008 \cdot O_{t} - 0,00009 \cdot I_{t}

The coefficient value, t count, p-value, and VIF value of each independent variable of the revised model can be seen in Table 7.

Table 7. The coefficient value, t-statistic, and p-value of each independent variable of the revised model.

Independent variable	Coefficient symbol	Coefficient value	t-statistic	p-value	VIF
	β₀	10,576.43	38.807	<0.001
NT_t	β₁	0.0105	0.604	0.548	1.393
PDB_t	β₂	-0.00006	-2.861	0.006	1.785
GKG_t	β₃	0.2848	9.136	<0.001	1.472
X_t	β₄	0.0001	1.880	0.066	1.896
Y_t	β₅	-0.000001	-0.012	0.690	1.235
O_t	β₆	-0.00008	-0.757	0.453	2.000
I_t	β₇	-0.00009	-5.730	<0.001	1.565

By using the significance value of α = 0.05, the critical t value is obtained = 1.671. If the calculated t value of each variable is compared with the critical t value, it can be seen that the independent variables that significantly affect the price of rice are:

1. Gross Domestic Product per capita in month t (PDB_t)
2. Ground Dry Rice price per kg in month t (GKG_t)
3. Rice stock at the end of month t.

In alignment with the research objective of stabilizing rice price fluctuations through import mechanisms, this study emphasizes the overall validity of the model rather than the marginal contributions of individual independent variables. The model's validity is demonstrated as follows: The computed F-statistic for this compound linear regression model is 22.07, exceeding the critical F-value of 2.17 for a sample size of 60 training observations and 7 independent variables. The p-value associated with the F-statistic is less than 0.001, which is below the significance threshold of α = 0.05, indicating that the combined effect of the 7 independent variables significantly influences monthly rice prices. Furthermore, the model exhibits an R-squared value of 0.748, suggesting a strong explanatory power. Additionally, the Variance Inflation Factor (VIF) values for all independent variables are below 5.0, confirming the absence of multicollinearity in the developed rice price prediction model.

2.6 The objective function for rice import quantity model

The objective function aims to minimize the rate of increase in rice prices between consecutive months, specifically between the current month (t) and the previous month (t−1), as expressed in Equation (9). The rice price for month is predicted using a compound linear regression model with 10 independent variables, as represented in Equation (8)

(10)

Min Z_{t} = (P_{t} - P_{t - 1}) / P_{t - 1}

2.7 Rice flow constraints in the rice supply chain network

The set of constraints that define the flow of rice in the rice supply chain network of government enterprise can be described as follows

(11)

X_{t} \leq p_{t}, \forall t \in T

(12)

Y_{t} \leq s, \forall t \in T

(13)

O_{t} = X_{t} + Y_{t} + I_{t - 1} - ss, \forall t \in T

(14)

I_{t} = I_{t - 1} + X_{t} + Y_{t} - O_{t}, \forall t \in T

(15)

ss \leq I_{t} \leq h, \forall t \in T

(16)

O_{t} = d_{t}, \forall t \in T

(17)

X_{t} \geq 0, \forall t \in T

(18)

Y_{t} \geq 0, \forall t \in T

(19)

O_{t} \geq 0, \forall t \in T

(20)

I_{t} \geq 0, \forall t \in T

Constraint (11) ensures that the quantity of rice procured by government enterprise from domestic rice mills in month t does not exceed the production capacity of domestic mills in month t. Constraint (12) guarantees that the quantity of rice imported from all import source countries in month t does not exceed the total rice export capacity of all import source countries to Indonesia.

Constraint (13) ensures that the rice distributed by government enterprise in month t comes from the procurement of domestic rice in month of t, the import of rice in month t, as well as the difference between the rice stock at the end of the previous month (t-1) and the lower limit of the strategic inventory. Constraint (14) represents the balance of rice flow in the rice warehouse of a government enterprise. Rice stocks at the end of month t are rice stocks at the end of the previous month (t-1) plus domestic rice procurement in month t plus rice imports in month t minus rice distribution by government enterprise in month t.

Constraint (15) states that the quantity of rice stored in the national rice warehouse at the end of month t is not less than the lower limit of the strategic inventory of rice in a month and does not exceed its storage capacity. Constraint (16) ensures that the amount of rice distributed by government enterprise in month t is equal to consumer demand for rice in month t. Finally, Constraints (17) to (20) ensure non-negativity for the variables representing domestic rice procurement, rice imports, rice distribution, and rice stock at the end of month t.

2.8 Parameter estimation

The value of consumer rice demand parameters is estimated using the triple exponential smoothing method, based on monthly rice distribution data for the period January 2018 - December 2022. The procedure is outlined as follows:

1. Setting the value of initials F_t, Tr_t, and B_t.
2. Calculating the value of F_t, Tr_t, and B_t for each actual data.
3. Estimating variable value using actual data.
4. Calculating the value of variable in the future.

The value of consumer rice demand parameters in January–December 2023 can be seen in Table 8.

Table 8. Estimated value of consumer rice demand parameters in January–December 2023.

Month	Consumer rice demand (tonnes)
January	306,353.53
February	238,003.89
March	299,846.76
April	245,702.75
May	246,251.26
June	241,651.63
July	238,251.03
August	242,128.17
September	242,638.50
October	243,853.31
November	378,680.64
December	287,062.10

The lower limit parameter of the strategic inventory of government enterprise is estimated based on the minimum monthly rice stock value at the end of each month during the period January 2018 - December 2022, which is 326,763 tonnes. This value is rounded to 300,000 tonnes. Similarly, the rice storage capacity parameter is estimated using the maximum monthly rice stock value (Satudata Indonesia, 2022) at the end of each month during the same period, which is 2,418,511 tonnes, rounded to 2,400,000 tonnes.

The rice production capacity of domestic rice mills for each month (t) in the period January–December 2023 is estimated using the maximum domestic rice production for each corresponding month (t) during the period 2018–2022, calculated using Equation (21). The estimated rice production capacity of domestic mills for January–December 2023 is presented in Table 9.

(21)

p_{t} = Max {PB}_{t 2018 - 2022}

Table 9. Production Capacity of Domestic Rice Mills in January–December 2023.

Month	Rice production capacity of domestic rice mills (tonnes)
January	1,595,000
February	3,289,000
March	5,570,000
April	5,626,000
May	3,586,000
June	2,574,000
July	3,175,000
August	3,345,000
September	3,161,000
October	2,455,000
November	1,880,000
December	1,174,000

The parameter for the rice export capacity of the source country of import to Indonesia is estimated using historical rice export data from Indonesia's seven largest rice import source countries. Table 10 shows rice export data from these seven countries to Indonesian during the period 2018 – 2022, measured in units of tonnes, as obtained from the National Statistics Buerau (BPS-Statistics Indonesia, 2022b; UN Comtrade, 2024).

Table 10. Rice imports to Indonesia from seven major exporting countries in 2018–2022.

Year	China	Japan	Myanmar	Pakistan	Vietnam	Thailand	India
2018	227.73	1.00	26,220.00	312,493.00	387,542.37	812,816.51	350,818.03
2019	24.27	90.00	176,825.00	174,894.00	40,158.00	79,447.41	332.30
2020	23.76	4.00	36,454.40	134,100.00	98,178.96	89,406.25	13,709.83
2021	42.63	247.00	4,290.00	37,036.00	67,694.33	75,369.00	244,720.16
2022	12.06	40.47	8,630.00	99,202.00	119,204.30	91,713.80	180,541.89
Total	330.45	382.47	252,419.40	757,725.00	712,777.96	1,148,752.97	790,122.21
Average	66.09	76.49	50,483.88	151,545.00	142,555.59	229,750.59	158,024.44

The total rice exports from all source countries during this period amounted to 109,238,309.19 tonnes. The average annual rice import between 2018 and 2022 are calculated to be 21,847,661.94 tonnes. To estimate the monthly rice export capacity of the seven source countries to Indonesia, the average annual rice import volume during the 2018–2022 period is divided by 12 months and rounded to the nearest value, resulting in a monthly export capacity of 1,820,638.49 tonnes, rounded to 1,820,000 tonnes.

2.9 Determination of independent variable values

For the rice production variables, including the rupiah exchange rate against the dollar, the area of agricultural land (BPS Statistics Indonesia, 2022f), the price of GKP per kg, the price of GKG per kg (BPS Statistics Indonesia, 2022g), and domestic rice procurement, the values are estimated using the triple exponential smoothing method, based on actual data from January 2018 to December 2022. For the rupiah exchange rate against the dollar, the value is determined using actual data from January 2019 to December 2022. The methodology for estimating these values follows a similar approach to that used for estimating consumer demand parameters.

The value of the GDP per capita variable in month t, PDB_t, is estimated using the double exponential smoothing method, based on annual GDP per capita data at current prices from 2014 to 2022. Table 11 presents the GDP per capita value for Indonesia at prevailing prices during the period 2014–2022.

Table 11. Indonesia's GDP per Capita at current prices.

Year	GDP per capita
2014	IDR 41,920,000.00
2015	IDR 45,140,000.00
2016	IDR 47,960,000.00
2017	IDR 51,890,000.00
2018	IDR 56,000,000.00
2019	IDR 59,100,000.00
2020	IDR 57,300,000.00
2021	IDR 62,300,000.00
2022	IDR 71,000,000.00
2023	IDR 75,000,000.00

The procedure is outlined as follows:

1. Setting initial value of F_t and Tr_t.
2. Calculating the value of F_t and Tr_t for each actual data.
3. Estimating variable value using actual data.
4. Calculating the value of variable in the future.
5. The GDP per capita per month variable is obtained by dividing the estimated GDP per capita by 12 months.

After taking steps 1–5, the estimated monthly GDP per capita for the period January–December 2023 is IDR 6,399,433.59. The rice import variable for month t, Y_t, is determined based on two conditions. If the rice stock at the end of the month I_t is less than the lower limit of the strategic inventory ss, imports are required to bring the rice stock to the strategic inventory threshold. However, if the rice stock at the end of the month I_t is greater than or equal to the lower limit of the strategic inventory ss, no imports are necessary. The change in the value of rice stocks at the end of the month, prior to any imports, is due to an increase in stocks from domestic rice procurement and a reduction in stocks for distribution to consumers. Mathematically, Y_t can be calculated using the Equation (22).

The rice stock at the end of month t, I_t, is determined based on the inflow of rice into and outflow of rice from rice stock in month t-1 or one month before. Rice stocks at the end of month t are rice stocks in month t-1 or one month before plus rice inflows that come from domestic rice procurement and rice imports, then minus rice distribution to meet consumer demand. Mathematically, I_t can be calculated with the Equation (23). The variable of rice distribution in month t, O_t, is set to be the same as consumer demand for rice in month t, d_t. Mathematically, O_t can be calculated with the Equation (24)

(22)

Y_{t} = {\begin{cases} 0, if I_{t - 1} + X_{t} - O_{t} \geq ss \\ ss - (I_{t - 1} + X_{t} - O_{t}), if I_{t - 1} + X_{t} - O_{t} < ss \end{cases}

(23)

I_{t} = I_{t - 1} + X_{t} + Y_{t} - O_{t}

(24)

O_{t} = d_{t}

2.10 Model behaviour evaluation

Evaluation of model behavior is conducted to assess the extent to which the model accurately replicates the actual behavior of the system. A standard approach involves analyzing simulation outputs, comparing them against historical data over time, and calculating the average deviation between simulated and observed values. The primary performance metric employed in this evaluation is the Mean Squared Error (MSE), along with the proportion of MSE attributed to bias (U^M), variance in equality (U^S), and covariance inequality (U^C). MSE, U^M, U^S, and U^C can be calculated using the equation (25)–(28) successively.

(25)

MSE = \frac{1}{n} \sum_{i = 1}^{n} {(X {(a)}_{i} - X {(m)}_{i})}^{2}

where,

X(a) = actual data

X(m) = model output

n = number of data

The smaller the value of MSE, the better the model is at representing the real system.

MSE can be decomposed into three separate components which are called ad Theil inaquality statistics (Morecroft, 2015). Theil statistics measure the portions of MSE explained by the three components, namely:

1. Bias U^M represents the difference between mean of actual data and mean of model outputs. It is calculated using equation (26).
2. Variance inequality (U^S), measures the difference between standar deviation of actual data and that of model outputs. Equation (27) is used to calculate U^S.
3. Covariance inequality (U^C), represents unexplained variation between actual data and model outputs.

Each of the following three equations is used to calculate U^M, U^S, and U^C respectively. Sum of the three components is 1

(26)

U^{M} = \frac{{(\bar{X} (a) - \bar{X} (m))}^{2}}{MSE}

where,

$\bar{X} (a)$ = mean of actual dat

$\bar{X} (m)$ = mean of model ouputs

(27)

U^{S} = \frac{{(S (a) - S (m))}^{2}}{MSE}

where,

$S (a)$ = standard deviation of actual data

$S (m)$ = standard deviation of model ouputs

(28)

U^{C} = \frac{(S (a) ∙ S (m)) ∙ 2 (1 - r)}{MSE}

where r is correlation coefficient between actual data and model output, and calculated using the following equation

(29)

r = \frac{\sum_{i} (X {(a)}_{i} - \bar{X} (a)) (X {(m)}_{i} - \bar{X} (m))}{\sqrt{\sum_{i} {(X {(a)}_{i} - \bar{X} (a))}^{2} \sum_{i} {(X (m) i - \bar{X} (m))}^{2}}}

where,

$X {(a)}_{i}$ = actual data i

$X {(m)}_{i}$ = model ouput i

3. Results and Discussion

In this section, the results related to the problem of determining the quantity of rice imports each month are presented. The simulation period spans 12 months over 4 years: January–December 2023, 2022, 2021, and 2020.

3.1 Results for the 2020 period

The model recommends no rice import in 2020, the GE interventions were in forms of domestic rice absorption, rice distribution, and stock storage. With this scheme, the developed price prediction model during the 2020 period resulted in rice a relatively fluctuating rate of rice price. The standard deviation of the predicted price change was 0.40%, which was higher than the standard deviation of the actual price variation of 0.24%. In 2020, rice prices tended to decline due to the impact of the COVID-19 pandemic that emerged after March 2020, with its effects carrying over into 2021. Figure 2 illustrates the behavior of the model compared to actual monthly rice price data and the monthly price increase over two consecutive months.

Figure 2. Comparison of actual and predicted rice prices and their respective increases over two consecutive months in the year 2020.

Based on table in Figure 2, the highest actual rice price change rate observed in 2020 was 0.54%, with a standard deviation of 0.24%. The developed model predicts a highest price variation rate of 0.57%, close to the actual one. However, the price change rate predicted by the model exhibits greater fluctuation, as evidenced by a standard deviation of 0.40%. This fluctuation can be attributed to the effects of the COVID-19 pandemic, which began impacting Indonesia after March 2020, with lingering effects into 2021. These effects led to a decrease in rice demand and a subsequent reduction in rice prices. Despite this, the predicted rice price increase rate remains lower than the expected range of 2–3%.

The behavior of monthly rice prices can be further analyzed using the U^M, U ^S, and U^C components of the Mean Squared Error (MSE). As shown in Table 12, the differences between actual and predicted monthly rice prices in 2020 are primarily attributed to discrepancies in the mean values of the predicted and actual prices, rather than differences in standard deviations.

Table 12. Variation Paramaters of actual and predicted monthly rice price for the period of 2020.

Parameter	Value
MSE	Rp 48,821.12
$U^{M}$	0.81
$U^{S}$	0.04
$U^{C}$	0.15
$U = U^{M} + U^{S} + U^{C}$	1.00

3.2 Results for the 2021 period

The model recommends a total rice import volume of 332,311 tons for 2021, whereas actual imports from the seven main rice-exporting countries amounted to 406,981.3 tons. The actual import volume includes special varieties of rice not produced domestically, which are permitted to be imported by private companies. The model suggests imports of 44,473.95 tons in March, 111,703.72 tons in November, and 176,133.02 tons in December, respectively. Incorporating rice imports along with other forms of government intervention, the model forecasts monthly rice prices for 2021. Figure 3 presents the actual and predicted monthly rice prices, as well as the rate of price change over two consecutive months.

Figure 3. Comparison of actual and predicted rice prices and their respective increases over two consecutive months in the year 2021.

In 2021, the COVID-19 pandemic continued to impact Indonesia, leading to a decrease in rice demand and a reduction in rice prices per kilogram. Based on the table in Figure 3, the highest actual rice price change rate observed in 2021 was 0.29%, with a standard deviation of 0.15%. The developed model predicts a highest price change rate of 0.80%, and the price change rate predicted by the model exhibits greater fluctuation, as evidenced by a standard deviation of 0.41%. This phenomenon occurred due to the effects of the COVID-19 pandemic which resulted in a decrease in rice demand and a decrease in rice prices. Despite this, the predicted rice price change rate remains lower than the expected range of 2–3%. The variation Paramaters of actual and predicted monthly rice price for the period of 2021 is presented in Table 13. Similar to the results for 2020 period, the differences between actual and predicted monthly rice prices in 2021 are primarily attributed to discrepancies in the mean values of the predicted and actual prices, rather than differences in standard deviations.

Table 13. Variation Paramaters of actual and predicted monthly rice price for the period of 2021.

Parameter	Value
MSE	Rp 206,539.70
$U^{M}$	0.97
$U^{S}$	<0.01
$U^{C}$	0.03
$U = U^{M} + U^{S} + U^{C}$	1.00

3.3 Results for the 2022 period

Application of the model for the year 2022 yielded a total recommended rice import volume of 254,905.08 tons, allocated across two shipments in March: 124,259.5 tons and 130,645.58 tons, respectively. This volume is substantially lower than the actual rice imports recorded in 2022, which totaled 428,843.2 tons. Nevertheless, despite the lower import recommendation, the model’s predicted monthly rice prices closely matched the actual observed prices throughout 2022. A detailed comparison of the predicted and actual monthly rice prices, along with their respective rates of change, is illustrated in Figure 4.

Figure 4. Comparison of actual and predicted rice prices and their respective increases over two consecutive months in the year 2022.

Compared to the outputs of model for 2020 and 2021, the MSE value resulting from the comparison between predicted and actual rice prices is much lower IDR 20,509.04, indicating that the developed model represents the actual price in 2022 quite accurately. This MSE is mostly due to difference in standard deviation between the predicted and actual prices, while their mean values are relative the same. The paramaters of variation between predicted and actual monthly rice price for 2022 period is presented in Table 14.

Table 14. Variation Paramaters of actual and predicted monthly rice price for the period of 2022.

Parameter	Value
MSE	Rp 20,509.04
$U^{M}$	<0.01
$U^{S}$	0.55
$U^{C}$	0.45
$U = U^{M} + U^{S} + U^{C}$	1.00

In 2022, the COVID-19 pandemic began to subside in August, which caused rice demand to increase and rice prices per kg to increase. Based on table in Figure 4, the highest actual rice price increase rate observed in 2022 was 2.22%, with a standard deviation of 0.82%. In comparison, the developed model results in a more controlled rice price increase, with the highest rate reaching 1.13% and a standard deviation of 0.49%. These values are notably lower than the expected increase rate of 2–3%.

3.4 Results for the 2023 period

The estimated rice import requirement for 2023 increased sharply, reaching a total of 1,033,392.11 tonnes. The imports were distributed across several months, including 279,313.43 tonnes in January, 234,887.87 tonnes in February, 194,608.20 tonnes in March, 140,088.17 tonnes in November, and 184,494.44 tonnes in December. Dibandingkan dengan volume import beras aktual pada 2023, which amounted to 3,049,924.4 tonnes (BPS-Statistics Indonesia, 2024), volume impor yang direkomendasikan oleh model jauh lebih rendah, tetapi jumlah yang direkomendasikan oleh model telah memenuhi konstrain including local production capacity, import limits, rice flow balance, and demand fulfillment.

According to the National Food Agency of Indonesia (BPN-National Food Agency, 2024), the sharp increase in rice imports in 2023 was an unavoidable measure necessitated by a decline in national rice production, primarily due to climate change and the effects of El Niño. This reduction in domestic rice production has raised concerns about a potential monthly rice balance deficit in early 2024. Consequently, the Government of Indonesia, through the National Food Agency (NFA), commissioned GA to import 2 million tons of rice, with an additional 1.5 million tons in 2023.

Beyond the impact of El Niño, other factors contributing to the increased demand for rice and the surge in retail rice prices include: (1) large-scale social assistance distributed to 10 million households in the context of the general election, and (2) inefficiencies in the Food Information System, which hindered accurate forecasting and disrupted supply chains (Department of Agricultural Socio-Economics, UGM, 2024). The diminishing impact of COVID-19 also contributed to rising rice demand in 2023, further driving price increases.

Compared to the predicted monthly rice prices generated by the model, despite the government's policy to drastically increase rice imports, the actual monthly rice prices in 2023 are significantly higher from the predicted values. Figure 5 illustrates the behavior of actual and predicted monthly rice prices in 2023, while Table 15 presents the variability parameters.

Figure 5. Comparison of actual and predicted rice prices and their respective increases over two consecutive months in the year 2023.

Table 15. Variation Paramaters of actual and predicted monthly rice price for the period of 2023.

Parameter	Value
MSE	Rp 3,248,225.36
$U^{M}$	0.83
$U^{S}$	0.14
$U^{C}$	0.03
$U = U^{M} + U^{S} + U^{C}$	1.00

Based on table in Figure 5, the highest actual rice price increase rate observed in 2023 was 4.35%, with a standard deviation of 1.47%. In contrast, the model developed yields a more controlled rice price increase, with the highest increase rate reaching 1.14% and a standard deviation of 0.45%. These values are yet lower than the expected price increase rate of 2–3%. Further empirical investigation may necessary to determine why the substantial rice imports—more than three times the recommended volume—failed to mitigate price fluctuations as predicted by the model.

3.5 Sensitivity analysis

Sensitivity analysis was conducted by varying the lower limit of the strategic inventory (ss) to examine the influence of changes in model parameters on the model's solution. The lower limit values of the strategic inventory considered were 300,000 tonnes (set for the base model), 500,000 tonnes, 1,000,000 tonnes, and 1,500,000 tonnes. The results of sensitivity analyses are summarized in Table 16.

Table 16. The summary of sensitivity analysis results.

Year	Change rate of monthly rice price	Lower limit of strategic inventory ss (tonnes)
Year	Change rate of monthly rice price	Actual	300,000	500,000	1,000,000	1,500,000
2020	Standard Deviation	0.24%	0.40%	0.49%	0.49%	0.50%
	Maximum	0.54%	0.75%	0.42%	0.42%	0.42%
2021	Standard Deviation	0.15%	0.41%	0.48%	0.49%	0.50%
	Maximum	0.29%	0.80%	0.53%	0.54%	0.54%
2022	Standard Deviation	0.82%	0.49%	0.40%	0.42%	0.47%
	Maximum	2.22%	1.13%	0.43%	0.51%	0.81%
2023	Standard Deviation	1.47%	0.45%	0.40%	0.41%	0.43%
	Maximum	4.35%	1.14%	0.46%	0.46%	0.48%

From 2020 to 2023, changes in the lower limit of the strategic inventory (ss) have minimal impact on the change rate of monthly rice price between two consecutive months, with the maximum price change rate ranging from 0.42% to 1.14% and the standard deviation of the price change rate ranging from 0.40% to 0.50%. These values remain significantly lower than the expected price change rate of 2–3%.

In 2022 and 2023, the price increase rates generated by the model solutions were more stable than the actual price increase rates. This stability is demonstrated by the smaller standard deviation of the price increase rates produced by the model compared to the actual rates, indicating that the developed model effectively controls the rate of rice price change between consecutive months.

However, in 2020 and 2021, the price change rates generated by the model solutions fluctuated more than the actual price change rates. This is reflected in the larger standard deviation of the price change rates produced by the model compared to the actual rates. This phenomenon can be attributed to the COVID-19 pandemic, which caused a decrease in rice demand and a subsequent decline in rice prices.

4. Concluding remarks

This study develops a model to determine the optimal quantity of rice imports required to minimize the rate of increase in rice prices between consecutive months. The model is formulated as a linear programming optimization problem, incorporating flow constraints within the rice supply chain network. These constraints include the capacity of domestic mills, the export capacity of rice from source countries, components of rice distribution, balance of rice flow, storage capacity, fulfillment of consumer demand, and non-negativity of variables.

The retail market price of rice is predicted monthly using a compound linear regression model with seven independent variables: the rupiah exchange rate against the US dollar, GDP per capita, the price of ground dry rice (GKG) per kilogram, domestic rice procurement, rice imports, rice distribution, and government-managed rice stock aimed at ensuring domestic availability and price stability. The model is trained using a dataset of 60 observations, covering the period from January 2018 to December 2022. The F-statistic of the model is 22.07, exceeding the critical F-value of 2.17 for 60 observations and seven independent variables, indicating that the independent variables collectively have a significant impact on rice prices. The model achieves an R-squared value of 0.748, demonstrating a strong level of explanatory power.

The values of each independent variable are estimated based on historical data patterns using appropriate forecasting methods. The rice production rate, rupiah exchange rate against the US dollar, agricultural land area, GKG price per kilogram, and domestic rice procurement from mills are estimated using the triple exponential smoothing approach. GDP per capita is estimated using the double exponential smoothing method, while rice consumer demand is projected using triple exponential smoothing. The quantity of rice distributed to consumers each month is determined to meet demand. End-of-month rice stocks are calculated as the sum of beginning-of-month stocks, domestic procurement, and imports, minus the distributed rice. Imports are triggered when end-of-month stocks fall below the strategic inventory lower limit, ensuring that stocks meet the minimum required threshold.

The model is applied to determine rice imports aimed at mitigating monthly price fluctuations for the years 2020, 2021, 2022, and 2023. The results indicate that the recommended import volumes closely replicate actual price behaviors for the years 2020, 2021, and 2022, with Mean Square Error (MSE) values of IDR 48,821.12, IDR 206,539.7, and IDR 20,509.04, respectively. In 2023, respecting the model’s constraints, the total volume of rice imports increased fourfold compared to 2022. The recommended import volume was able to maintain a maximum monthly price change rate of 0.41% and a standard deviation of 0.45%.

However, the recommended rice import volume for 2023 was significantly lower than the actual import volume, which amounted to 3,049,924.4 tonnes. Despite the higher actual import volume, the retail price of rice in 2023 was paradoxically higher than the predicted price for the same period, resulting in a large MSE value of IDR 3,363,769.44 between actual and predicted monthly rice prices. Several specific factors are identified as contributors to the unique conditions of 2023, distinguishing it from previous years (2020–2022). These factors include: (1) extreme El Niño weather conditions, (2) large-scale social assistance targeting 10 million households in the context of the 2024 general election, and (3) inefficiencies in the Food Information System, which impaired accurate forecasting and disrupted supply chains (BPN-National Food Agency of Indonesia, 2024; Department of Agricultural Socio-Economics, Universitas Gadjah Mada, 2024). Future models can be developed to incorporate these factors for improved predictive accuracy.

In conclusion, the model effectively controls the rate of change in rice prices between consecutive months through planned rice imports, achieving a maximum price increase rate of 0.42% to 1.14% and a standard deviation of 0.40% to 0.50%, which are lower than the expected rate of 2–3%. These findings demonstrate the model's effectiveness in determining the necessary rice import volumes required to stabilize prices in Indonesia.

Future research could expand the rice supply chain network to include upstream stakeholders, such as farmers and intermediaries. However, this would require accurate historical data on rice production and distribution from farmers to mills. Additionally, if reliable data on domestic rice procurement, rice imports, and rice distribution become available, the accuracy of the rice price prediction model can be further enhanced. Furthermore, social, environmental, and political factors could be incorporated to refine projections of independent variables influencing rice prices.

Ethics and consent

Ethical approval and consent were not required.

Third party ethics

The data used in this research are publicly available and were obtained from BPS-Statistics Indonesia: https://www.bps.go.id/en

Data availability

The data used to estimate the parameters of the rice price prediction model is published under a CC0 Public Domain Dedication, which does not retain any rights to the data.

DATA TYPE	DATA AVAILABILITY STATEMENT	DATA CITATION
Data dedicated into public domain	Indonesia population: Proyeksi Penduduk Indonesia 2015-2045 Hasil SUPAS 2015. https://www.bps.go.id/en/publication/2018/10/19/78d24d9020026ad95c6b5965/proyeksi-penduduk-indonesia-2015-2045-hasil-supas-2015.html	BPS-Statistics Indonesia: 2018. Proyeksi Proyeksi Penduduk Indonesia 2015-2045 Hasil SUPAS 2015. [2018-10-19]. https://www.bps.go.id/en/publication/2018/10/19/78d24d9020026ad95c6b5965/proyeksi-penduduk-indonesia-2015-2045-hasil-supas-2015.html
Data dedicated into public domain	GDP growth: Indonesia GDP Growth Rate 5.31 Percent, 2022. https://www.bps.go.id/id/pressrelease/2023/02/06/1997/ekonomi-indonesia-tahun-2022-tumbuh-5-31-persen.html	BPS-Statistics Indonesia: 2022a. Indonesia GDP Growth Rate 5.31 Percent. [2023-02-06]. https://www.bps.go.id/id/pressrelease/2023/02/06/1997/ekonomi-indonesia-tahun-2022-tumbuh-5-31-persen.html
Data dedicated into public domain	Domestic rice procurement: Produksi Padi dan Beras Menurut Provinsi, 2018-2022. https://www.bps.go.id/id/statistics-table/3/ZDNaak0yODBUVTlGYW5sa2REUkVUVVY1YVZkbmR6MDkjMw==/produksi-padisup1-sup-dan-beras-menurut-provinsi--2022.html?year=2022	BPS-Statistics Indonesia: 2022b. Produksi Padi dan Beras Menurut Provinsi 2018-2020. [2024-02-01]. https://www.bps.go.id/id/statistics-table/3/ZDNaak0yODBUVTlGYW5sa2REUkVUVVY1YVZkbmR6MDkjMw==/produksi-padisup1-sup-dan-beras-menurut-provinsi--2022.html?year=2022
Data dedicated into public domain	Rice imports: Imports of Rice by Major Countries of Origin, 2000-2022. https://www.bps.go.id/id/statistics-table/1/MTA0MyMx/impor-beras-menurut-negara-asal-utama-2017-2023.html	BPS-Statistics Indonesia: 2022c. Imports of Rice by Major Countries of Origin, 2000-2022. [2024-03-241].
Data dedicated into public domain	Rice distribution: Distribution Flow of Rice in Indonesia 2022. https://www.bps.go.id/id/publication/2022/10/24/2a4fb384020c45bbaeb535a6/distribusi-perdagangan-komoditas-beras-di-indonesia-2022.html	BPS-Statistics Indonesia: 2022d, Distribution Flow of Rice in Indonesia 2022. [2022-10-24]. https://www.bps.go.id/id/publication/2022/10/24/2a4fb384020c45bbaeb535a6/distribusi-perdagangan-komoditas-beras-di-indonesia-2022.html
Data dedicated into public domain	Rice consumption: Weekly Average Consumption of Several Food Items Commodity per Capita, 2007-2024. https://www.bps.go.id/en/statistics-table/1/OTUwIzE=/weekly-average-consumption-of-several-food-items-commodity-per-capita--2007-2023.html	BPS-Statistics Indonesia: 2022e, Weekly Average Consumption of Several Food Items Commodity per Capita, 2007-2024. [2024-02-26]. https://www.bps.go.id/en/statistics-table/1/OTUwIzE=/weekly-average-consumption-of-several-food-items-commodity-per-capita--2007-2023.html
Data dedicated into public domain	Rice stocks: Analisis Ketahapan Pangan Tahun 2022. https://satudata.pertanian.go.id/assets/docs/publikasi/Analisis_Ketahanan_Pangan_Tahun_2022.pdf	Satudata Indonesia: 2022. Analisis Ketahapan Pangan Tahun. [2022-11]. https://satudata.pertanian.go.id/assets/docs/publikasi/Analisis_Ketahanan_Pangan_Tahun_2022.pdf
Data dedicated into public domain	Agricultural land area; Rice production: Luas Panen, Produksi, dan Produktivitas Padi Menurut Provinsi 2020-2022. https://www.bps.go.id/id/statistics-table/3/WmpaNk1YbGFjR0pOUjBKYWFIQlBSU3Mw%20VHpOVWR6MDkjMw==/luas-panen--produktivitas--dan-produksi-padi-menurut-provinsi--2022.html?year=2022	BPS-Statistics Indonesia: 2022f. Luas Panen, Produksi, dan Produktivitas Padi Menurut Provinsi 2020-2022. [2024-02-01]. https://www.bps.go.id/id/statistics-table/3/WmpaNk1YbGFjR0pOUjBKYWFIQlBSU3Mw VHpOVWR6MDkjMw==/luas-panen--produktivitas--dan-produksi-padi-menurut-provinsi--2022.html?year=2022
Data dedicated into public domain	GKP price; GKG price: Average of Monthly Unhusked Rice Price by Quality, Component and GPP at Mills, 2020-2022. https://www.bps.go.id/id/statistics-table/2/MTA0NyMy/rata-rata-harga-gabah-bulanan-menurut-kualitas--komponen-mutu-dan-hpp-di-tingkat-penggilingan.html	BPS-Statistics Indonesia: 2022g. Average of Monthly Unhusked Rice Price by Quality, Component and GPP at Mills 2020-2022. [2025-01-02]. https://www.bps.go.id/id/statistics-table/2/MTA0NyMy/rata-rata-harga-gabah-bulanan-menurut-kualitas--komponen-mutu-dan-hpp-di-tingkat-penggilingan.html
Data dedicated into public domain	National rice price: Milling Rice Price by Quality (Rupiahs/Kg), 2020-2022. https://www.bps.go.id/id/statistics-table/2/NTAwIzI=/rata-rata-harga-beras-bulanan-di-tingkat-penggilingan-menurut-kualitas.html	BPS-Statistics Indonesia: 2022h. Milling Rice Price by Quality (Rupiahs/Kg), 2020-2022. [2024-10-16]. https://www.bps.go.id/id/statistics-table/2/NTAwIzI=/rata-rata-harga-beras-bulanan-di-tingkat-penggilingan-menurut-kualitas.html

Acknowledgements

The authors would like to acknowledge Mrs. Endah Ayu Ningsih and Mrs. Nurhayati from the Indonesian Ministry of Trade, who contributed to the data tabulation required for conducting this research.

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Lucia Diawati
Roles: Conceptualization, Formal Analysis, Investigation, Project Administration, Resources, Supervision, Validation, Writing – Review & Editing

Arif Shafwan Rasyid
Roles: Data Curation, Methodology, Software, Visualization, Writing – Original Draft Preparation

Competing interests

No competing interests were disclosed.

Grant information

The author(s) declared that no grants were involved in supporting this work.

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Diawati L and Rasyid AS. Mitigating retail rice price volatility for sustainable supply chains: an optimization and regression-based approach [version 2; peer review: 2 approved]. F1000Research 2025, 14:311 (https://doi.org/10.12688/f1000research.161723.2)

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Reviewer Report 14 Jun 2025

Katsuhiko Takahashi, Hiroshima University, Higashi-Hiroshima, Japan

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https://doi.org/10.5256/f1000research.183214.r389970

As a reviewer, I have reviewed the revised version. I have addressed the comments noted earlier, and the comments have been incorporated into the revised version of the manuscript, and I found the improvements to be sufficient. Therefore, there are no ... Continue reading

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Reviewer Report 13 Jun 2025

Amelia Santoso, Universitas Surabaya, Surabaya, Indonesia

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Reviewer Report 21 Apr 2025

Amelia Santoso, Universitas Surabaya, Surabaya, Indonesia

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https://doi.org/10.5256/f1000research.177795.r374130

Rice is a staple food with a high consumption rate in Indonesia. The increasing population of Indonesia and current trends indicate a decline in rice production. Indonesia must ensure a stable rice supply with consistent availability and affordable prices. This paper discusses the challenge of stabilizing rice retail prices in Indonesia by developing an optimization model to determine the optimal volume of rice imports required to minimize bimonthly changes in rice retail prices. This optimization model uses four constraints: local production capacity, import limits, rice flow balance, and demand fulfillment. The monthly retail price is modeled using a compound linear regression approach with ten explanatory variables. The model is tested using data from 2020 to 2023, and the results indicate that bimonthly rice price increases can be effectively controlled, with maximum inflation rates maintained between 0.42% and 0.53% and a standard deviation ranging from 0.39% to 0.53%. These values are significantly lower than the anticipated inflation rate of 2–3%. Although the paper has been written clearly and systematically, there are several questions or weaknesses, as follows:
In 1. Introduction:

The relationship of this research to previous research has been explained clearly and systematically. However, in the last paragraph, it is necessary to explain in more detail why it is essential to integrate distribution quantity with price control mechanisms.
Although the research objective is declared in the fifth paragraph, it is still necessary to restate it in the last paragraph to address the gap mentioned in the last paragraph.

In 2. Method:

In subsection 2.1, defining “Domestic rice procurement” in more detail is necessary. The definition is needed to explain equation (1), why “percentage of domestic rice procurement to national rice production” and “domestic rice production” are used to calculate “domestic rice procurement”.
Defining domestic rice procurement is also helpful in analyzing Table 1, which shows that domestic rice procurement data have a much smaller value than domestic rice production data. Does the difference indicate an oversupply of rice? If Indonesia can meet public demand from domestic rice production, does it still need to import?
The rice price prediction model (equation 8) is only influenced by Gross Domestic Product, Harvested Dry Paddy, Milled Dry Paddy, and Rice Stock significantly individually and together, with an R-squared value of 0.783. There are only four of the ten independent variables significant. There is probably a correlation or multi-collinearity between the independent variables of equation (8). It is because of using the dependent and independent variables of equations (2) and (7) as the independent variables of equation 8. It is necessary to explain the reason for determining the independent variables of equation 8. It is better to check the assumptions of multiple linear regression
The objective function (sub-session 2.6) is to minimize the rate of increase in rice prices between consecutive months. According to the explanation in the introduction, it is essential to stabilize the rice price. Is there no funding limit to stabilize prices?

In 3. Result and Discussion
According to the results in 2023, there is a high difference in rice price between the prediction and actual, and the analysis states, “This value is not ably high due to the increase in the retail market price of rice in 2023, driven by factors such as rice scarcity,…”, it is better to check independent variables chosen in prediction rice price model and relate to review 2c. In general, the rice price is driven by unbalancing end customer demand and supply (production, import and stock)

Is the work clearly and accurately presented and does it cite the current literature?

Yes
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Yes

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Production & Inventory Systems, Supply Chain Engineering, Humanitarian Supply Chain

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.

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Author Response 09 Aug 2025

Lucia Diawati, Industrial Engineering and Management, Bandung Institute of Technology, Bandung, 40132, Indonesia

09 Aug 2025

Author Response
The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Comment I (Introduction)
1. The proposed model is designed to regulate
... Continue reading
The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Comment I (Introduction)

The proposed model is designed to regulate monthly rice prices through government intervention, primarily by adjusting supply via import procurement. This strategic intervention aims to enable a swift response to mitigate potential shortages in rice availability, which, if left unaddressed, could evolve into a multifaceted crisis encompassing economic, social, and political dimensions.

The following paragraph will be added in Section 1 to clarify the gap with previous studies.

“While existing studies have made significant contributions to supply chain optimization and the analysis of price fluctuations, there remains a notable shortcoming in research that integrates rice distribution quantities with price control mechanisms capable of generating immediate effects. To address this shortcoming, the present study aims to develop a quantitative model for determining the optimal monthly volume of rice imports necessary to balance supply and demand, thereby minimizing increases in retail rice market prices. By optimizing import volumes, the authorized government enterprise can ensure a stable rice supply while preserving the affordability of rice, particularly as it serves as a key staple food in many developing economies.”

Response to Comment 2 (Method)

“Domestic rice procurement” refers to the volume of rice production acquired by a government-designated enterprise responsible for maintaining rice price stability and distributing the supply through market channels. Equation (1) outlines the methodology employed to estimate domestic rice procurement for the period 2021–2023, formulated as a function of the ratio of domestic rice procurement to national rice production, multiplied by monthly domestic rice production. This estimation approach was necessitated by the absence of actual procurement data for 2021–2023, with the only complete dataset available corresponding to 2017. Using this dataset, the monthly percentage of domestic procurement relative to national production was derived and subsequently utilized to estimate monthly domestic rice procurement for 2021–2023.

"Domestic rice procurement" refers to the amount of domestically produced rice absorbed by government enterprises for subsequent distribution to consumers through market mechanisms. As illustrated in Figure 1, rice is also absorbed by private rice distributors, resulting in total rice production being consistently greater than domestic rice procurement, as shown in Table 1. Further, theoretically, rice imports would be unnecessary if domestic supply fully met consumer demand in a perfectly functioning market system. However, the developed model does not capture the entire supply and demand dynamics of the rice market. Instead, it focuses specifically on the role of government enterprises in price regulation through market interventions. These interventions involve increasing market supply using rice under Bulog’s control, including stock reserves, rice security reserves, and domestically produced rice absorbed by government enterprises. The estimated volume of rice imports required in period t is determined by three factors: the projected rice stock at the end of period t-1, the estimated absorption of domestic rice production by the government enterprises in period t, and the forecasted distribution of rice by the government enterprises to the public in period t. The independent variables used to estimate the import volume in period t are based on predictive models for each independent variable, with model parameters estimated using historical data.

This observation is valid; however, the regression model for rice price prediction was constructed with consideration of previously developed models by prior researchers. Therefore, this study places greater emphasis on the overall validity of the model, rather than on the marginal contributions of individual independent variables. Further refinement of the prediction model is anticipated in future work.

When considering only financial costs, the expenditures related to price stabilization mainly consist of logistical components such as ordering costs, commodity value, transportation, customs duties, storage, and market operation expenses. The allocated budget for these efforts is substantial, reflecting the need to account for potential non-financial costs arising from significant rice price fluctuations. These non-financial costs—including social and political consequences—can often far exceed the direct financial expenditures.

Response to Comment 3 (Result and Discussion)
The rice price prediction model incorporates variables such as domestic rice production, imports, and rice stock levels. However, conditions in 2023 differed significantly from those in other years due to unique factors that impacted rice prices during that period. The factors include (1) the extreme El Niño event, (2) large-scale social assistance to 10 million households in the context of the general election, and (3) inefficiencies in the Food Information System, which hindered accurate forecasting and disrupted supply chains (Department of Agricultural Socio-Economics, Universitas Gadjah Mada, 2024).
The prediction model is extrapolative, incorporating supply-demand variables, technical production indicators (e.g., agricultural land area), and economic variables (e.g., IDR–USD exchange rate). Like all extrapolative models, it assumes continuity with historical trends. The exceptional conditions of 2023 reduced its accuracy, but its applicability is expected to improve in 2024 and beyond, subject to model revalidation using updated data.
Note:
Additional Reference:
*Department of Agricultural Socio-Economics, Faculty of Agriculture, UGM (March 2024). Rice Price Inflation: A Comprehensive Analysis and Policy-Oriented Solutions (in Bahasa Indonesia). https://sosek.faperta.ugm.ac.id/2024/03/29/kenaikan-harga-beras-analisis-dan-solusi-menyeluruh/#:~:text=Faktor%20Lingkungan%3A%20Salah%20satu%20penyebab,mempengaruhi%20ketersediaan%20beras%20di%20pasaran
The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Comment I (Introduction)

The proposed model is designed to regulate monthly rice prices through government intervention, primarily by adjusting supply via import procurement. This strategic intervention aims to enable a swift response to mitigate potential shortages in rice availability, which, if left unaddressed, could evolve into a multifaceted crisis encompassing economic, social, and political dimensions.

The following paragraph will be added in Section 1 to clarify the gap with previous studies.

“While existing studies have made significant contributions to supply chain optimization and the analysis of price fluctuations, there remains a notable shortcoming in research that integrates rice distribution quantities with price control mechanisms capable of generating immediate effects. To address this shortcoming, the present study aims to develop a quantitative model for determining the optimal monthly volume of rice imports necessary to balance supply and demand, thereby minimizing increases in retail rice market prices. By optimizing import volumes, the authorized government enterprise can ensure a stable rice supply while preserving the affordability of rice, particularly as it serves as a key staple food in many developing economies.”

Response to Comment 2 (Method)

“Domestic rice procurement” refers to the volume of rice production acquired by a government-designated enterprise responsible for maintaining rice price stability and distributing the supply through market channels. Equation (1) outlines the methodology employed to estimate domestic rice procurement for the period 2021–2023, formulated as a function of the ratio of domestic rice procurement to national rice production, multiplied by monthly domestic rice production. This estimation approach was necessitated by the absence of actual procurement data for 2021–2023, with the only complete dataset available corresponding to 2017. Using this dataset, the monthly percentage of domestic procurement relative to national production was derived and subsequently utilized to estimate monthly domestic rice procurement for 2021–2023.

"Domestic rice procurement" refers to the amount of domestically produced rice absorbed by government enterprises for subsequent distribution to consumers through market mechanisms. As illustrated in Figure 1, rice is also absorbed by private rice distributors, resulting in total rice production being consistently greater than domestic rice procurement, as shown in Table 1. Further, theoretically, rice imports would be unnecessary if domestic supply fully met consumer demand in a perfectly functioning market system. However, the developed model does not capture the entire supply and demand dynamics of the rice market. Instead, it focuses specifically on the role of government enterprises in price regulation through market interventions. These interventions involve increasing market supply using rice under Bulog’s control, including stock reserves, rice security reserves, and domestically produced rice absorbed by government enterprises. The estimated volume of rice imports required in period t is determined by three factors: the projected rice stock at the end of period t-1, the estimated absorption of domestic rice production by the government enterprises in period t, and the forecasted distribution of rice by the government enterprises to the public in period t. The independent variables used to estimate the import volume in period t are based on predictive models for each independent variable, with model parameters estimated using historical data.

This observation is valid; however, the regression model for rice price prediction was constructed with consideration of previously developed models by prior researchers. Therefore, this study places greater emphasis on the overall validity of the model, rather than on the marginal contributions of individual independent variables. Further refinement of the prediction model is anticipated in future work.

When considering only financial costs, the expenditures related to price stabilization mainly consist of logistical components such as ordering costs, commodity value, transportation, customs duties, storage, and market operation expenses. The allocated budget for these efforts is substantial, reflecting the need to account for potential non-financial costs arising from significant rice price fluctuations. These non-financial costs—including social and political consequences—can often far exceed the direct financial expenditures.

Response to Comment 3 (Result and Discussion)
The rice price prediction model incorporates variables such as domestic rice production, imports, and rice stock levels. However, conditions in 2023 differed significantly from those in other years due to unique factors that impacted rice prices during that period. The factors include (1) the extreme El Niño event, (2) large-scale social assistance to 10 million households in the context of the general election, and (3) inefficiencies in the Food Information System, which hindered accurate forecasting and disrupted supply chains (Department of Agricultural Socio-Economics, Universitas Gadjah Mada, 2024).
The prediction model is extrapolative, incorporating supply-demand variables, technical production indicators (e.g., agricultural land area), and economic variables (e.g., IDR–USD exchange rate). Like all extrapolative models, it assumes continuity with historical trends. The exceptional conditions of 2023 reduced its accuracy, but its applicability is expected to improve in 2024 and beyond, subject to model revalidation using updated data.
Note:
Additional Reference:
*Department of Agricultural Socio-Economics, Faculty of Agriculture, UGM (March 2024). Rice Price Inflation: A Comprehensive Analysis and Policy-Oriented Solutions (in Bahasa Indonesia). https://sosek.faperta.ugm.ac.id/2024/03/29/kenaikan-harga-beras-analisis-dan-solusi-menyeluruh/#:~:text=Faktor%20Lingkungan%3A%20Salah%20satu%20penyebab,mempengaruhi%20ketersediaan%20beras%20di%20pasaran
Competing Interests: No competing interests were disclosed. Close
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COMMENTS ON THIS REPORT

Author Response 09 Aug 2025

Lucia Diawati, Industrial Engineering and Management, Bandung Institute of Technology, Bandung, 40132, Indonesia

09 Aug 2025

Author Response
The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Comment I (Introduction)
1. The proposed model is designed to regulate
... Continue reading
The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Comment I (Introduction)

The proposed model is designed to regulate monthly rice prices through government intervention, primarily by adjusting supply via import procurement. This strategic intervention aims to enable a swift response to mitigate potential shortages in rice availability, which, if left unaddressed, could evolve into a multifaceted crisis encompassing economic, social, and political dimensions.

The following paragraph will be added in Section 1 to clarify the gap with previous studies.

“While existing studies have made significant contributions to supply chain optimization and the analysis of price fluctuations, there remains a notable shortcoming in research that integrates rice distribution quantities with price control mechanisms capable of generating immediate effects. To address this shortcoming, the present study aims to develop a quantitative model for determining the optimal monthly volume of rice imports necessary to balance supply and demand, thereby minimizing increases in retail rice market prices. By optimizing import volumes, the authorized government enterprise can ensure a stable rice supply while preserving the affordability of rice, particularly as it serves as a key staple food in many developing economies.”

Response to Comment 2 (Method)

“Domestic rice procurement” refers to the volume of rice production acquired by a government-designated enterprise responsible for maintaining rice price stability and distributing the supply through market channels. Equation (1) outlines the methodology employed to estimate domestic rice procurement for the period 2021–2023, formulated as a function of the ratio of domestic rice procurement to national rice production, multiplied by monthly domestic rice production. This estimation approach was necessitated by the absence of actual procurement data for 2021–2023, with the only complete dataset available corresponding to 2017. Using this dataset, the monthly percentage of domestic procurement relative to national production was derived and subsequently utilized to estimate monthly domestic rice procurement for 2021–2023.

"Domestic rice procurement" refers to the amount of domestically produced rice absorbed by government enterprises for subsequent distribution to consumers through market mechanisms. As illustrated in Figure 1, rice is also absorbed by private rice distributors, resulting in total rice production being consistently greater than domestic rice procurement, as shown in Table 1. Further, theoretically, rice imports would be unnecessary if domestic supply fully met consumer demand in a perfectly functioning market system. However, the developed model does not capture the entire supply and demand dynamics of the rice market. Instead, it focuses specifically on the role of government enterprises in price regulation through market interventions. These interventions involve increasing market supply using rice under Bulog’s control, including stock reserves, rice security reserves, and domestically produced rice absorbed by government enterprises. The estimated volume of rice imports required in period t is determined by three factors: the projected rice stock at the end of period t-1, the estimated absorption of domestic rice production by the government enterprises in period t, and the forecasted distribution of rice by the government enterprises to the public in period t. The independent variables used to estimate the import volume in period t are based on predictive models for each independent variable, with model parameters estimated using historical data.

This observation is valid; however, the regression model for rice price prediction was constructed with consideration of previously developed models by prior researchers. Therefore, this study places greater emphasis on the overall validity of the model, rather than on the marginal contributions of individual independent variables. Further refinement of the prediction model is anticipated in future work.

When considering only financial costs, the expenditures related to price stabilization mainly consist of logistical components such as ordering costs, commodity value, transportation, customs duties, storage, and market operation expenses. The allocated budget for these efforts is substantial, reflecting the need to account for potential non-financial costs arising from significant rice price fluctuations. These non-financial costs—including social and political consequences—can often far exceed the direct financial expenditures.

Response to Comment 3 (Result and Discussion)
The rice price prediction model incorporates variables such as domestic rice production, imports, and rice stock levels. However, conditions in 2023 differed significantly from those in other years due to unique factors that impacted rice prices during that period. The factors include (1) the extreme El Niño event, (2) large-scale social assistance to 10 million households in the context of the general election, and (3) inefficiencies in the Food Information System, which hindered accurate forecasting and disrupted supply chains (Department of Agricultural Socio-Economics, Universitas Gadjah Mada, 2024).
The prediction model is extrapolative, incorporating supply-demand variables, technical production indicators (e.g., agricultural land area), and economic variables (e.g., IDR–USD exchange rate). Like all extrapolative models, it assumes continuity with historical trends. The exceptional conditions of 2023 reduced its accuracy, but its applicability is expected to improve in 2024 and beyond, subject to model revalidation using updated data.
Note:
Additional Reference:
*Department of Agricultural Socio-Economics, Faculty of Agriculture, UGM (March 2024). Rice Price Inflation: A Comprehensive Analysis and Policy-Oriented Solutions (in Bahasa Indonesia). https://sosek.faperta.ugm.ac.id/2024/03/29/kenaikan-harga-beras-analisis-dan-solusi-menyeluruh/#:~:text=Faktor%20Lingkungan%3A%20Salah%20satu%20penyebab,mempengaruhi%20ketersediaan%20beras%20di%20pasaran
The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Comment I (Introduction)

The proposed model is designed to regulate monthly rice prices through government intervention, primarily by adjusting supply via import procurement. This strategic intervention aims to enable a swift response to mitigate potential shortages in rice availability, which, if left unaddressed, could evolve into a multifaceted crisis encompassing economic, social, and political dimensions.

The following paragraph will be added in Section 1 to clarify the gap with previous studies.

“While existing studies have made significant contributions to supply chain optimization and the analysis of price fluctuations, there remains a notable shortcoming in research that integrates rice distribution quantities with price control mechanisms capable of generating immediate effects. To address this shortcoming, the present study aims to develop a quantitative model for determining the optimal monthly volume of rice imports necessary to balance supply and demand, thereby minimizing increases in retail rice market prices. By optimizing import volumes, the authorized government enterprise can ensure a stable rice supply while preserving the affordability of rice, particularly as it serves as a key staple food in many developing economies.”

Response to Comment 2 (Method)

“Domestic rice procurement” refers to the volume of rice production acquired by a government-designated enterprise responsible for maintaining rice price stability and distributing the supply through market channels. Equation (1) outlines the methodology employed to estimate domestic rice procurement for the period 2021–2023, formulated as a function of the ratio of domestic rice procurement to national rice production, multiplied by monthly domestic rice production. This estimation approach was necessitated by the absence of actual procurement data for 2021–2023, with the only complete dataset available corresponding to 2017. Using this dataset, the monthly percentage of domestic procurement relative to national production was derived and subsequently utilized to estimate monthly domestic rice procurement for 2021–2023.

"Domestic rice procurement" refers to the amount of domestically produced rice absorbed by government enterprises for subsequent distribution to consumers through market mechanisms. As illustrated in Figure 1, rice is also absorbed by private rice distributors, resulting in total rice production being consistently greater than domestic rice procurement, as shown in Table 1. Further, theoretically, rice imports would be unnecessary if domestic supply fully met consumer demand in a perfectly functioning market system. However, the developed model does not capture the entire supply and demand dynamics of the rice market. Instead, it focuses specifically on the role of government enterprises in price regulation through market interventions. These interventions involve increasing market supply using rice under Bulog’s control, including stock reserves, rice security reserves, and domestically produced rice absorbed by government enterprises. The estimated volume of rice imports required in period t is determined by three factors: the projected rice stock at the end of period t-1, the estimated absorption of domestic rice production by the government enterprises in period t, and the forecasted distribution of rice by the government enterprises to the public in period t. The independent variables used to estimate the import volume in period t are based on predictive models for each independent variable, with model parameters estimated using historical data.

This observation is valid; however, the regression model for rice price prediction was constructed with consideration of previously developed models by prior researchers. Therefore, this study places greater emphasis on the overall validity of the model, rather than on the marginal contributions of individual independent variables. Further refinement of the prediction model is anticipated in future work.

When considering only financial costs, the expenditures related to price stabilization mainly consist of logistical components such as ordering costs, commodity value, transportation, customs duties, storage, and market operation expenses. The allocated budget for these efforts is substantial, reflecting the need to account for potential non-financial costs arising from significant rice price fluctuations. These non-financial costs—including social and political consequences—can often far exceed the direct financial expenditures.

Response to Comment 3 (Result and Discussion)
The rice price prediction model incorporates variables such as domestic rice production, imports, and rice stock levels. However, conditions in 2023 differed significantly from those in other years due to unique factors that impacted rice prices during that period. The factors include (1) the extreme El Niño event, (2) large-scale social assistance to 10 million households in the context of the general election, and (3) inefficiencies in the Food Information System, which hindered accurate forecasting and disrupted supply chains (Department of Agricultural Socio-Economics, Universitas Gadjah Mada, 2024).
The prediction model is extrapolative, incorporating supply-demand variables, technical production indicators (e.g., agricultural land area), and economic variables (e.g., IDR–USD exchange rate). Like all extrapolative models, it assumes continuity with historical trends. The exceptional conditions of 2023 reduced its accuracy, but its applicability is expected to improve in 2024 and beyond, subject to model revalidation using updated data.
Note:
Additional Reference:
*Department of Agricultural Socio-Economics, Faculty of Agriculture, UGM (March 2024). Rice Price Inflation: A Comprehensive Analysis and Policy-Oriented Solutions (in Bahasa Indonesia). https://sosek.faperta.ugm.ac.id/2024/03/29/kenaikan-harga-beras-analisis-dan-solusi-menyeluruh/#:~:text=Faktor%20Lingkungan%3A%20Salah%20satu%20penyebab,mempengaruhi%20ketersediaan%20beras%20di%20pasaran
Competing Interests: No competing interests were disclosed. Close
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Reviewer Report 03 Apr 2025

Katsuhiko Takahashi, Hiroshima University, Higashi-Hiroshima, Japan

Approved with Reservations

https://doi.org/10.5256/f1000research.177795.r374127

This paper considered the challenge of stabilizing rice retail prices in Indonesia, a critical staple food across many Asian countries. For the challenge, this study proposed an optimization model to determine the optimal volume of rice imports required to minimize bimonthly changes in rice retail prices. The model was tested using data from 2020 to 2023. The results indicated that bimonthly rice prices increase can be effectively controlled, with maximum inflation rates maintained between 0.42% and 0.53% and a standard deviation ranging from 0.39% to 0.53%. These values are significantly lower than the anticipated inflation rate of 2–3%. The challenge considered in this paper is interesting and effective not only in Indonesia, but also in Japan, where rice price inflation has become a problem. However, there are several questions or weaknesses in this paper that could be resolved or strengthened. Therefore, as a reviewer, I recommend that such question and weaknesses be resolved and strengthened. Specific questions and weaknesses include the followings:

In 1. Introduction, the subject matter of this study and previous research on it are described. Then, in the last paragraph, this paper states that there are gaps in the models considered in the previous studies and that there is still a need for model development. It is unclear what is meant by “gap” and what is meant by “need” here. It is necessary to clearly state what exactly is the gap between the conventional models and what is required, and what kind of models are needed to be developed based on the gap.
Also in 1. Introduction, it is not stated what the purpose of this study is. Although it is related to the above, it is necessary to clearly state what the purpose of this study is based on the gaps and needs.
In 2.1. Model development, it is stated that “the primary model to be developed is an optimization model aimed at minimizing monthly changes in rice retail prices over two consecutive months,” however, it is not clear whether the primary model is new or not and where is different from the previous model. It should be clearly stated whether it is a new model or not and what is different from the previous model.
In 2.5. Rice price prediction model, the compound linear regression model was built using 60 training data, namely time series data in the period January 2018- December 2022. In the model, the rice price for month t, Pt, is predicted from the current values of ten variables, PPt, NTt, PDBt, LLt, GKPt, GKGt, Xt, Yt, Ot, and It. The model is developed to be affected by the current values of all the ten variables, but isn’t it necessary to address the time lag in which past or future values are affected? If so, it is necessary to construct a model that takes this into account, and if not, it is necessary to explain the reasons why this is not necessary.
In 2.6. the objective function for rice import quantity model, the objective function aims to minimize the rate of increase in rice prices between consecutive months, specifically between the current month (t) and the previous month (t-1). However, the reason for this is not stated. The implication of the rate of price increase may be different when prices are low and when they are high, but if it is not affected, it is better to explain the reason that the rate of increase be the same regardless of the previous month's value.
In 2.7. Rice flow constraints in the rice supply chain network, the set of constraints that define the flow of rice in the rice supply chain network of government enterprise were described. Constraint (11) guarantees the quantity of rice imported from all import source countries in month (t) does not exceed the total rice export capacity of all import source countries to Indonesia. The constraint that when imports are required, the rice will be imported if the quantity meets the resources, but does the price of imported rice have no effect? If so, the effect should be incorporated otherwise, it is necessary to explain why.
In 2.8. Parameter estimation, the value of consumer rice demand parameters is estimated using the triple exponential smoothing method, based on monthly rice distribution data for the period January 2018- December 2022. In the parameters, the rice production capacity of domestic rice mills for each month (t) in the period January–December 2023 is estimated using the maximum domestic rice production for each corresponding month (t) during the period 2018–2022. Generally, the production capacity is likely to be affected by the results for the month in question, but it may also be related to the results of the previous and following months. It is better to explain the reason why this estimation is utilized and suitable for estimating the rice production capacity.
In 3. Results and Discussion, the results related to the problem of determining the quantity of rice imports each month are presented, and the results for the simulation period can be seen in Table11, the comparison graph of actual and predicted rice prices is shown in figures, and the Mean Square Error (MSE) value resulting from the comparison between predicted and actual rice prices is evaluated. This paper considered whether there is a difference or not compared to its actual price, but if the price increase can be reduced than its actual price, wouldn't it be better as an import decision for reducing the inflation of rice price? It is necessary to explain why you say it is better if there is no difference. Or, it would be necessary to evaluate whether it could be smaller or not and discuss the reason.
In 4. Conclusions, there is a description of the proposal of this paper, its content, and its results. the challenges are described, but in terms of further development, it is not clear that the current situation is sufficient. This paper said “The simulation results show that the predicted retail rice market prices are quite valid compared to actual prices for the periods 2020, 2021, and 2022, with Mean Square Error (MSE) values of IDR 62,490.62; IDR 9,604.53; and IDR 31,577.16, respectively. In 2023, the predicted prices are less valid due to factors not accounted for by the ten independent variables, such as rice scarcity and increased consumption in preparation for the 2024 elections, resulting in a large MSE value of IDR3,363,769.44.” As mentioned above, there is also the question of whether a comparison with ACTUAL is meaningful. Also, if it is less than the actual, it can be said to be good even if there is a difference between the actual and the comparison. Furthermore, the authors said that the ten variables were insufficient for the external factors of the election, but it would be better to indicate what variables should have been included, and moreover, it would be better to made a proposal that included those variables and evaluate the proposed model in this paper. If that kind of the revised model is proposed and evaluated, it can be expected that the value, limitations, and challenges of this research in the final conclusion will be improved.

Is the work clearly and accurately presented and does it cite the current literature?

Yes
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: production systems engineering, supply chain management, industrial engineering

CITE

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Author Response 21 Apr 2025

Lucia Diawati, Industrial Engineering and Management, Bandung Institute of Technology, Bandung, 40132, Indonesia

21 Apr 2025

Author Response

The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Question 1 and 2:

The term "gap" here may lead to ... Continue reading The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Question 1 and 2:

The term "gap" here may lead to misunderstanding. What is actually meant is the deficiency in the studies conducted with the required models for short-term rice price control over two consecutive months. The term "need" refers to the necessity for a model that can facilitate decision-making, allowing for a prompt determination of the quantity of rice to be imported. To avoid misinterpretation of the terms "gap" and "need," the last paragraph in Section 1 will be revised as follows:

“While existing studies have made significant contributions to supply chain optimization and the analysis of price fluctuations, there remains a notable shortcoming in research that integrates rice distribution quantities with price control mechanisms capable of generating immediate effects. To address this shortcoming, the present study aims to develop a quantitative model for determining the optimal monthly volume of rice imports necessary to balance supply and demand, thereby minimizing increases in retail rice market prices. By optimizing import volumes, the authorized government enterprise can ensure a stable rice supply while simultaneously preserving the affordability of rice as a staple food particularly in the context of rice, a key staple in many developing economies.”

Response to Question 3:

The primary model aims to minimize monthly rice price fluctuations over two consecutive months by adjusting import quantities. This strategy is intended to balance rice supply with market demand, thereby stabilizing prices and preventing significant shocks that could incite social and political unrest.
Most existing models focus on the design of the rice supply chain, including distribution locations and inventory levels. While effective for long-term impacts, these models necessitate structural adjustments that take time to implement (Melo et al., 2006; Min et al., 2007; Li & Bing, 2007; Wu & Zhang, 2014; Teng et al., 2007; Xu and Zhu, 2007; Dellaert et al., 2021; Athanasiou et al., 2008; Paksoy et al., 2012; Gouel, 2013; Dawe & Timmer, 2012).

Rice price prediction models have been developed by Serra & Gil (2012), Dorosh & Rashid (2013), Possamai et al. (2015), Mogale et al. (2017), Gholamian and Taghanzadeh (2017), and Cheraghalipour et al. (2019). Fitrawaty et al. (2023) identified several factors affecting rice prices and fluctuations.
The model in this study integrates the current rice supply chain and leverages imports as an intervention mechanism to mitigate major price fluctuations. The Indonesian government employs rice imports as a short-term price control policy to prevent public unrest from sharp price increases, delegating import authority to BULOG, a government enterprise.

Response to Question 4:

Your comment is well-taken, and we have indeed considered that aspect in our analysis. However, the decision adopted prioritizes achieving a rapid impact, based on the current conditions. One variable identified as having a potential lagged effect is the size of agricultural land. Upon closer examination, however, we found that the data for this variable are not based on direct measurements but are instead derived from estimates—specifically, by dividing estimated agricultural production by estimated paddy field productivity. Despite this limitation, statistical testing confirms the overall significance of the model.

Response to Question 5:

The formulation of this model is grounded in the dual role of the country as both a major rice consumer—where rice constitutes a staple food—and a significant rice producer, wherein substantial price fluctuations, either upward or downward, can have broad societal impacts. Elevated rice prices adversely affect consumers, while sharp price declines negatively impact farmers’ livelihoods. The model is operationalized from a defined starting point, using the prevailing market price at that time as a baseline. From this point forward, rice prices are assumed to be subject to control interventions.

Response to Question 6:

Although rice prices influence Indonesia's choice of import sources, this model aggregates imports from seven major countries—Thailand, India, Pakistan, Vietnam, Myanmar, Japan, and China—into a single source. Between 2018 and 2022, their respective shares were 31.3%, 21.57%, 20.69%, 19.46%, 6.89%, 0.01%, and 0.01%.

This aggregation is justified by the high variability in individual import volumes, with fluctuations from 2019 to 2022 ranging from 3.4% (Thailand) to 161.3% (Myanmar). In contrast, the combined import fluctuation from these countries was only 7.6% over the same period.
Price differences and other domestic and international factors contribute to these fluctuations. The model implicitly accounts for these influences, as reflected in the observed variation in import volumes from individual source countries.

Within the system boundary, the constraint on rice import volume is estimated in aggregate based on historical data from these seven countries.

Response to Question 7:

The use of the maximum monthly domestic rice production observed during the 2018–2022 period to estimate the production capacity parameter for each month in January–December 2023 is based on the premise that this value represents the achievable potential under previously realized conditions. This approach implicitly reflects a policy preference toward fostering the conditions necessary to attain maximum domestic rice production capacity, rather than depending on imports to fulfill national rice demand.

Response to Question 8:

In a country like Indonesia, rice prices exert a dual impact—affecting both consumers and producers (i.e., rice farmers). From the consumer perspective, price stability and affordability are essential, while from the producer’s standpoint, higher rice prices are desirable to compensate for increasing production costs. Accordingly, this study develops a model designed to minimize fluctuations in rice prices. The model is adaptable and can be calibrated to prioritize the interests of either consumers or producers, depending on the specific policy objective.

Response to Question 9:

The model developed in this study comprises two key components: (1) an optimization model that minimizes monthly rice price fluctuations by determining appropriate import quantities, and (2) an empirical model that predicts monthly rice prices using ten explanatory variables.

Building on previous studies (e.g., Serra & Gil, 2012; Dorosh & Rashid, 2013; Possamai et al., 2015; Mogale et al., 2017; Gholamian & Taghanzadeh, 2017; Cheraghalipour et al., 2019; Fitrawaty et al., 2023), this study identifies additional significant predictors of rice prices. The resulting model, with ten explanatory variables, yielded an F-statistic of 17.66 (well above the critical value of 1.99), and effectively controlled price increases.

A comparative analysis of the model output reveals that the actual monthly rice prices for the years 2020, 2021, and 2022 closely aligned with the model's optimal price projections. However, in 2023, a significant deviation was observed between the actual monthly rice prices and the optimal prices. This discrepancy is hypothesized to be attributable to specific factors that uniquely impacted rice prices during 2023. The factors include (1) the extreme El Niño event, (2) large-scale social assistance to 10 million households in the context of the general election, and (3) inefficiencies in the Food Information System, which hindered accurate forecasting and disrupted supply chains (Department of Agricultural Socio-Economics, Universitas Gadjah Mada, 2024).

The prediction model is extrapolative, incorporating supply-demand variables, technical production indicators (e.g., agricultural land area), and economic variables (e.g., IDR–USD exchange rate). Like all extrapolative models, it assumes continuity with historical trends. The exceptional conditions of 2023 reduced its accuracy, but its applicability is expected to improve in 2024 and beyond, subject to model revalidation using updated data.

Note:
Additional Reference:
*Department of Agricultural Socio-Economics, Faculty of Agriculture, UGM (March 2024). Rice Price Inflation: A Comprehensive Analysis and Policy-Oriented Solutions (in Bahasa Indonesia). https://sosek.faperta.ugm.ac.id/2024/03/29/kenaikan-harga-beras-analisis-dan-solusi-menyeluruh/#:~:text=Faktor%20Lingkungan%3A%20Salah%20satu%20penyebab,mempengaruhi%20ketersediaan%20beras%20di%20pasaran.
The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Question 1 and 2:

The term "gap" here may lead to misunderstanding. What is actually meant is the deficiency in the studies conducted with the required models for short-term rice price control over two consecutive months. The term "need" refers to the necessity for a model that can facilitate decision-making, allowing for a prompt determination of the quantity of rice to be imported. To avoid misinterpretation of the terms "gap" and "need," the last paragraph in Section 1 will be revised as follows:

“While existing studies have made significant contributions to supply chain optimization and the analysis of price fluctuations, there remains a notable shortcoming in research that integrates rice distribution quantities with price control mechanisms capable of generating immediate effects. To address this shortcoming, the present study aims to develop a quantitative model for determining the optimal monthly volume of rice imports necessary to balance supply and demand, thereby minimizing increases in retail rice market prices. By optimizing import volumes, the authorized government enterprise can ensure a stable rice supply while simultaneously preserving the affordability of rice as a staple food particularly in the context of rice, a key staple in many developing economies.”

Response to Question 3:

The primary model aims to minimize monthly rice price fluctuations over two consecutive months by adjusting import quantities. This strategy is intended to balance rice supply with market demand, thereby stabilizing prices and preventing significant shocks that could incite social and political unrest.
Most existing models focus on the design of the rice supply chain, including distribution locations and inventory levels. While effective for long-term impacts, these models necessitate structural adjustments that take time to implement (Melo et al., 2006; Min et al., 2007; Li & Bing, 2007; Wu & Zhang, 2014; Teng et al., 2007; Xu and Zhu, 2007; Dellaert et al., 2021; Athanasiou et al., 2008; Paksoy et al., 2012; Gouel, 2013; Dawe & Timmer, 2012).

Rice price prediction models have been developed by Serra & Gil (2012), Dorosh & Rashid (2013), Possamai et al. (2015), Mogale et al. (2017), Gholamian and Taghanzadeh (2017), and Cheraghalipour et al. (2019). Fitrawaty et al. (2023) identified several factors affecting rice prices and fluctuations.
The model in this study integrates the current rice supply chain and leverages imports as an intervention mechanism to mitigate major price fluctuations. The Indonesian government employs rice imports as a short-term price control policy to prevent public unrest from sharp price increases, delegating import authority to BULOG, a government enterprise.

Response to Question 4:

Your comment is well-taken, and we have indeed considered that aspect in our analysis. However, the decision adopted prioritizes achieving a rapid impact, based on the current conditions. One variable identified as having a potential lagged effect is the size of agricultural land. Upon closer examination, however, we found that the data for this variable are not based on direct measurements but are instead derived from estimates—specifically, by dividing estimated agricultural production by estimated paddy field productivity. Despite this limitation, statistical testing confirms the overall significance of the model.

Response to Question 5:

The formulation of this model is grounded in the dual role of the country as both a major rice consumer—where rice constitutes a staple food—and a significant rice producer, wherein substantial price fluctuations, either upward or downward, can have broad societal impacts. Elevated rice prices adversely affect consumers, while sharp price declines negatively impact farmers’ livelihoods. The model is operationalized from a defined starting point, using the prevailing market price at that time as a baseline. From this point forward, rice prices are assumed to be subject to control interventions.

Response to Question 6:

Although rice prices influence Indonesia's choice of import sources, this model aggregates imports from seven major countries—Thailand, India, Pakistan, Vietnam, Myanmar, Japan, and China—into a single source. Between 2018 and 2022, their respective shares were 31.3%, 21.57%, 20.69%, 19.46%, 6.89%, 0.01%, and 0.01%.

This aggregation is justified by the high variability in individual import volumes, with fluctuations from 2019 to 2022 ranging from 3.4% (Thailand) to 161.3% (Myanmar). In contrast, the combined import fluctuation from these countries was only 7.6% over the same period.
Price differences and other domestic and international factors contribute to these fluctuations. The model implicitly accounts for these influences, as reflected in the observed variation in import volumes from individual source countries.

Within the system boundary, the constraint on rice import volume is estimated in aggregate based on historical data from these seven countries.

Response to Question 7:

The use of the maximum monthly domestic rice production observed during the 2018–2022 period to estimate the production capacity parameter for each month in January–December 2023 is based on the premise that this value represents the achievable potential under previously realized conditions. This approach implicitly reflects a policy preference toward fostering the conditions necessary to attain maximum domestic rice production capacity, rather than depending on imports to fulfill national rice demand.

Response to Question 8:

In a country like Indonesia, rice prices exert a dual impact—affecting both consumers and producers (i.e., rice farmers). From the consumer perspective, price stability and affordability are essential, while from the producer’s standpoint, higher rice prices are desirable to compensate for increasing production costs. Accordingly, this study develops a model designed to minimize fluctuations in rice prices. The model is adaptable and can be calibrated to prioritize the interests of either consumers or producers, depending on the specific policy objective.

Response to Question 9:

The model developed in this study comprises two key components: (1) an optimization model that minimizes monthly rice price fluctuations by determining appropriate import quantities, and (2) an empirical model that predicts monthly rice prices using ten explanatory variables.

Building on previous studies (e.g., Serra & Gil, 2012; Dorosh & Rashid, 2013; Possamai et al., 2015; Mogale et al., 2017; Gholamian & Taghanzadeh, 2017; Cheraghalipour et al., 2019; Fitrawaty et al., 2023), this study identifies additional significant predictors of rice prices. The resulting model, with ten explanatory variables, yielded an F-statistic of 17.66 (well above the critical value of 1.99), and effectively controlled price increases.

A comparative analysis of the model output reveals that the actual monthly rice prices for the years 2020, 2021, and 2022 closely aligned with the model's optimal price projections. However, in 2023, a significant deviation was observed between the actual monthly rice prices and the optimal prices. This discrepancy is hypothesized to be attributable to specific factors that uniquely impacted rice prices during 2023. The factors include (1) the extreme El Niño event, (2) large-scale social assistance to 10 million households in the context of the general election, and (3) inefficiencies in the Food Information System, which hindered accurate forecasting and disrupted supply chains (Department of Agricultural Socio-Economics, Universitas Gadjah Mada, 2024).

The prediction model is extrapolative, incorporating supply-demand variables, technical production indicators (e.g., agricultural land area), and economic variables (e.g., IDR–USD exchange rate). Like all extrapolative models, it assumes continuity with historical trends. The exceptional conditions of 2023 reduced its accuracy, but its applicability is expected to improve in 2024 and beyond, subject to model revalidation using updated data.

Note:
Additional Reference:
*Department of Agricultural Socio-Economics, Faculty of Agriculture, UGM (March 2024). Rice Price Inflation: A Comprehensive Analysis and Policy-Oriented Solutions (in Bahasa Indonesia). https://sosek.faperta.ugm.ac.id/2024/03/29/kenaikan-harga-beras-analisis-dan-solusi-menyeluruh/#:~:text=Faktor%20Lingkungan%3A%20Salah%20satu%20penyebab,mempengaruhi%20ketersediaan%20beras%20di%20pasaran.
Competing Interests: There are no conflicts of interest associated with the preparation of this response. Close
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Author Response 21 Apr 2025

Lucia Diawati, Industrial Engineering and Management, Bandung Institute of Technology, Bandung, 40132, Indonesia

21 Apr 2025

Author Response

The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Question 1 and 2:

The term "gap" here may lead to ... Continue reading The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Question 1 and 2:

The term "gap" here may lead to misunderstanding. What is actually meant is the deficiency in the studies conducted with the required models for short-term rice price control over two consecutive months. The term "need" refers to the necessity for a model that can facilitate decision-making, allowing for a prompt determination of the quantity of rice to be imported. To avoid misinterpretation of the terms "gap" and "need," the last paragraph in Section 1 will be revised as follows:

“While existing studies have made significant contributions to supply chain optimization and the analysis of price fluctuations, there remains a notable shortcoming in research that integrates rice distribution quantities with price control mechanisms capable of generating immediate effects. To address this shortcoming, the present study aims to develop a quantitative model for determining the optimal monthly volume of rice imports necessary to balance supply and demand, thereby minimizing increases in retail rice market prices. By optimizing import volumes, the authorized government enterprise can ensure a stable rice supply while simultaneously preserving the affordability of rice as a staple food particularly in the context of rice, a key staple in many developing economies.”

Response to Question 3:

The primary model aims to minimize monthly rice price fluctuations over two consecutive months by adjusting import quantities. This strategy is intended to balance rice supply with market demand, thereby stabilizing prices and preventing significant shocks that could incite social and political unrest.
Most existing models focus on the design of the rice supply chain, including distribution locations and inventory levels. While effective for long-term impacts, these models necessitate structural adjustments that take time to implement (Melo et al., 2006; Min et al., 2007; Li & Bing, 2007; Wu & Zhang, 2014; Teng et al., 2007; Xu and Zhu, 2007; Dellaert et al., 2021; Athanasiou et al., 2008; Paksoy et al., 2012; Gouel, 2013; Dawe & Timmer, 2012).

Rice price prediction models have been developed by Serra & Gil (2012), Dorosh & Rashid (2013), Possamai et al. (2015), Mogale et al. (2017), Gholamian and Taghanzadeh (2017), and Cheraghalipour et al. (2019). Fitrawaty et al. (2023) identified several factors affecting rice prices and fluctuations.
The model in this study integrates the current rice supply chain and leverages imports as an intervention mechanism to mitigate major price fluctuations. The Indonesian government employs rice imports as a short-term price control policy to prevent public unrest from sharp price increases, delegating import authority to BULOG, a government enterprise.

Response to Question 4:

Your comment is well-taken, and we have indeed considered that aspect in our analysis. However, the decision adopted prioritizes achieving a rapid impact, based on the current conditions. One variable identified as having a potential lagged effect is the size of agricultural land. Upon closer examination, however, we found that the data for this variable are not based on direct measurements but are instead derived from estimates—specifically, by dividing estimated agricultural production by estimated paddy field productivity. Despite this limitation, statistical testing confirms the overall significance of the model.

Response to Question 5:

The formulation of this model is grounded in the dual role of the country as both a major rice consumer—where rice constitutes a staple food—and a significant rice producer, wherein substantial price fluctuations, either upward or downward, can have broad societal impacts. Elevated rice prices adversely affect consumers, while sharp price declines negatively impact farmers’ livelihoods. The model is operationalized from a defined starting point, using the prevailing market price at that time as a baseline. From this point forward, rice prices are assumed to be subject to control interventions.

Response to Question 6:

Although rice prices influence Indonesia's choice of import sources, this model aggregates imports from seven major countries—Thailand, India, Pakistan, Vietnam, Myanmar, Japan, and China—into a single source. Between 2018 and 2022, their respective shares were 31.3%, 21.57%, 20.69%, 19.46%, 6.89%, 0.01%, and 0.01%.

This aggregation is justified by the high variability in individual import volumes, with fluctuations from 2019 to 2022 ranging from 3.4% (Thailand) to 161.3% (Myanmar). In contrast, the combined import fluctuation from these countries was only 7.6% over the same period.
Price differences and other domestic and international factors contribute to these fluctuations. The model implicitly accounts for these influences, as reflected in the observed variation in import volumes from individual source countries.

Within the system boundary, the constraint on rice import volume is estimated in aggregate based on historical data from these seven countries.

Response to Question 7:

The use of the maximum monthly domestic rice production observed during the 2018–2022 period to estimate the production capacity parameter for each month in January–December 2023 is based on the premise that this value represents the achievable potential under previously realized conditions. This approach implicitly reflects a policy preference toward fostering the conditions necessary to attain maximum domestic rice production capacity, rather than depending on imports to fulfill national rice demand.

Response to Question 8:

In a country like Indonesia, rice prices exert a dual impact—affecting both consumers and producers (i.e., rice farmers). From the consumer perspective, price stability and affordability are essential, while from the producer’s standpoint, higher rice prices are desirable to compensate for increasing production costs. Accordingly, this study develops a model designed to minimize fluctuations in rice prices. The model is adaptable and can be calibrated to prioritize the interests of either consumers or producers, depending on the specific policy objective.

Response to Question 9:

The model developed in this study comprises two key components: (1) an optimization model that minimizes monthly rice price fluctuations by determining appropriate import quantities, and (2) an empirical model that predicts monthly rice prices using ten explanatory variables.

Building on previous studies (e.g., Serra & Gil, 2012; Dorosh & Rashid, 2013; Possamai et al., 2015; Mogale et al., 2017; Gholamian & Taghanzadeh, 2017; Cheraghalipour et al., 2019; Fitrawaty et al., 2023), this study identifies additional significant predictors of rice prices. The resulting model, with ten explanatory variables, yielded an F-statistic of 17.66 (well above the critical value of 1.99), and effectively controlled price increases.

A comparative analysis of the model output reveals that the actual monthly rice prices for the years 2020, 2021, and 2022 closely aligned with the model's optimal price projections. However, in 2023, a significant deviation was observed between the actual monthly rice prices and the optimal prices. This discrepancy is hypothesized to be attributable to specific factors that uniquely impacted rice prices during 2023. The factors include (1) the extreme El Niño event, (2) large-scale social assistance to 10 million households in the context of the general election, and (3) inefficiencies in the Food Information System, which hindered accurate forecasting and disrupted supply chains (Department of Agricultural Socio-Economics, Universitas Gadjah Mada, 2024).

The prediction model is extrapolative, incorporating supply-demand variables, technical production indicators (e.g., agricultural land area), and economic variables (e.g., IDR–USD exchange rate). Like all extrapolative models, it assumes continuity with historical trends. The exceptional conditions of 2023 reduced its accuracy, but its applicability is expected to improve in 2024 and beyond, subject to model revalidation using updated data.

Note:
Additional Reference:
*Department of Agricultural Socio-Economics, Faculty of Agriculture, UGM (March 2024). Rice Price Inflation: A Comprehensive Analysis and Policy-Oriented Solutions (in Bahasa Indonesia). https://sosek.faperta.ugm.ac.id/2024/03/29/kenaikan-harga-beras-analisis-dan-solusi-menyeluruh/#:~:text=Faktor%20Lingkungan%3A%20Salah%20satu%20penyebab,mempengaruhi%20ketersediaan%20beras%20di%20pasaran.
The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Question 1 and 2:

The term "gap" here may lead to misunderstanding. What is actually meant is the deficiency in the studies conducted with the required models for short-term rice price control over two consecutive months. The term "need" refers to the necessity for a model that can facilitate decision-making, allowing for a prompt determination of the quantity of rice to be imported. To avoid misinterpretation of the terms "gap" and "need," the last paragraph in Section 1 will be revised as follows:

“While existing studies have made significant contributions to supply chain optimization and the analysis of price fluctuations, there remains a notable shortcoming in research that integrates rice distribution quantities with price control mechanisms capable of generating immediate effects. To address this shortcoming, the present study aims to develop a quantitative model for determining the optimal monthly volume of rice imports necessary to balance supply and demand, thereby minimizing increases in retail rice market prices. By optimizing import volumes, the authorized government enterprise can ensure a stable rice supply while simultaneously preserving the affordability of rice as a staple food particularly in the context of rice, a key staple in many developing economies.”

Response to Question 3:

The primary model aims to minimize monthly rice price fluctuations over two consecutive months by adjusting import quantities. This strategy is intended to balance rice supply with market demand, thereby stabilizing prices and preventing significant shocks that could incite social and political unrest.
Most existing models focus on the design of the rice supply chain, including distribution locations and inventory levels. While effective for long-term impacts, these models necessitate structural adjustments that take time to implement (Melo et al., 2006; Min et al., 2007; Li & Bing, 2007; Wu & Zhang, 2014; Teng et al., 2007; Xu and Zhu, 2007; Dellaert et al., 2021; Athanasiou et al., 2008; Paksoy et al., 2012; Gouel, 2013; Dawe & Timmer, 2012).

Rice price prediction models have been developed by Serra & Gil (2012), Dorosh & Rashid (2013), Possamai et al. (2015), Mogale et al. (2017), Gholamian and Taghanzadeh (2017), and Cheraghalipour et al. (2019). Fitrawaty et al. (2023) identified several factors affecting rice prices and fluctuations.
The model in this study integrates the current rice supply chain and leverages imports as an intervention mechanism to mitigate major price fluctuations. The Indonesian government employs rice imports as a short-term price control policy to prevent public unrest from sharp price increases, delegating import authority to BULOG, a government enterprise.

Response to Question 4:

Your comment is well-taken, and we have indeed considered that aspect in our analysis. However, the decision adopted prioritizes achieving a rapid impact, based on the current conditions. One variable identified as having a potential lagged effect is the size of agricultural land. Upon closer examination, however, we found that the data for this variable are not based on direct measurements but are instead derived from estimates—specifically, by dividing estimated agricultural production by estimated paddy field productivity. Despite this limitation, statistical testing confirms the overall significance of the model.

Response to Question 5:

The formulation of this model is grounded in the dual role of the country as both a major rice consumer—where rice constitutes a staple food—and a significant rice producer, wherein substantial price fluctuations, either upward or downward, can have broad societal impacts. Elevated rice prices adversely affect consumers, while sharp price declines negatively impact farmers’ livelihoods. The model is operationalized from a defined starting point, using the prevailing market price at that time as a baseline. From this point forward, rice prices are assumed to be subject to control interventions.

Response to Question 6:

Although rice prices influence Indonesia's choice of import sources, this model aggregates imports from seven major countries—Thailand, India, Pakistan, Vietnam, Myanmar, Japan, and China—into a single source. Between 2018 and 2022, their respective shares were 31.3%, 21.57%, 20.69%, 19.46%, 6.89%, 0.01%, and 0.01%.

This aggregation is justified by the high variability in individual import volumes, with fluctuations from 2019 to 2022 ranging from 3.4% (Thailand) to 161.3% (Myanmar). In contrast, the combined import fluctuation from these countries was only 7.6% over the same period.
Price differences and other domestic and international factors contribute to these fluctuations. The model implicitly accounts for these influences, as reflected in the observed variation in import volumes from individual source countries.

Within the system boundary, the constraint on rice import volume is estimated in aggregate based on historical data from these seven countries.

Response to Question 7:

The use of the maximum monthly domestic rice production observed during the 2018–2022 period to estimate the production capacity parameter for each month in January–December 2023 is based on the premise that this value represents the achievable potential under previously realized conditions. This approach implicitly reflects a policy preference toward fostering the conditions necessary to attain maximum domestic rice production capacity, rather than depending on imports to fulfill national rice demand.

Response to Question 8:

In a country like Indonesia, rice prices exert a dual impact—affecting both consumers and producers (i.e., rice farmers). From the consumer perspective, price stability and affordability are essential, while from the producer’s standpoint, higher rice prices are desirable to compensate for increasing production costs. Accordingly, this study develops a model designed to minimize fluctuations in rice prices. The model is adaptable and can be calibrated to prioritize the interests of either consumers or producers, depending on the specific policy objective.

Response to Question 9:

The model developed in this study comprises two key components: (1) an optimization model that minimizes monthly rice price fluctuations by determining appropriate import quantities, and (2) an empirical model that predicts monthly rice prices using ten explanatory variables.

Building on previous studies (e.g., Serra & Gil, 2012; Dorosh & Rashid, 2013; Possamai et al., 2015; Mogale et al., 2017; Gholamian & Taghanzadeh, 2017; Cheraghalipour et al., 2019; Fitrawaty et al., 2023), this study identifies additional significant predictors of rice prices. The resulting model, with ten explanatory variables, yielded an F-statistic of 17.66 (well above the critical value of 1.99), and effectively controlled price increases.

A comparative analysis of the model output reveals that the actual monthly rice prices for the years 2020, 2021, and 2022 closely aligned with the model's optimal price projections. However, in 2023, a significant deviation was observed between the actual monthly rice prices and the optimal prices. This discrepancy is hypothesized to be attributable to specific factors that uniquely impacted rice prices during 2023. The factors include (1) the extreme El Niño event, (2) large-scale social assistance to 10 million households in the context of the general election, and (3) inefficiencies in the Food Information System, which hindered accurate forecasting and disrupted supply chains (Department of Agricultural Socio-Economics, Universitas Gadjah Mada, 2024).

The prediction model is extrapolative, incorporating supply-demand variables, technical production indicators (e.g., agricultural land area), and economic variables (e.g., IDR–USD exchange rate). Like all extrapolative models, it assumes continuity with historical trends. The exceptional conditions of 2023 reduced its accuracy, but its applicability is expected to improve in 2024 and beyond, subject to model revalidation using updated data.

Note:
Additional Reference:
*Department of Agricultural Socio-Economics, Faculty of Agriculture, UGM (March 2024). Rice Price Inflation: A Comprehensive Analysis and Policy-Oriented Solutions (in Bahasa Indonesia). https://sosek.faperta.ugm.ac.id/2024/03/29/kenaikan-harga-beras-analisis-dan-solusi-menyeluruh/#:~:text=Faktor%20Lingkungan%3A%20Salah%20satu%20penyebab,mempengaruhi%20ketersediaan%20beras%20di%20pasaran.
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Version 2

VERSION 2 PUBLISHED 20 Mar 2025

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Katsuhiko Takahashi, Hiroshima University, Higashi-Hiroshima, Japan
Amelia Santoso, Universitas Surabaya, Surabaya, Indonesia

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14 Jun 2025 | for Version 2

Katsuhiko Takahashi, Hiroshima University, Higashi-Hiroshima, Japan

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Approved

Competing Interests

No competing interests were disclosed.

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production systems engineering, supply chain management, industrial engineering

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard.

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13 Jun 2025 | for Version 2

Amelia Santoso, Universitas Surabaya, Surabaya, Indonesia

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Approved

This paper has been revised to accommodate all of my previous comments. No further comments.

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Production & Inventory Systems, Supply Chain Engineering, Humanitarian Supply Chain

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19 Views

21 Apr 2025 | for Version 1

Amelia Santoso, Universitas Surabaya, Surabaya, Indonesia

19 Views Cite this report Responses(1)

Approved With Reservations

The relationship of this research to previous research has been explained clearly and systematically. However, in the last paragraph, it is necessary to explain in more detail why it is essential to integrate distribution quantity with price control mechanisms.
Although the research objective is declared in the fifth paragraph, it is still necessary to restate it in the last paragraph to address the gap mentioned in the last paragraph.

In 2. Method:

In subsection 2.1, defining “Domestic rice procurement” in more detail is necessary. The definition is needed to explain equation (1), why “percentage of domestic rice procurement to national rice production” and “domestic rice production” are used to calculate “domestic rice procurement”.
Defining domestic rice procurement is also helpful in analyzing Table 1, which shows that domestic rice procurement data have a much smaller value than domestic rice production data. Does the difference indicate an oversupply of rice? If Indonesia can meet public demand from domestic rice production, does it still need to import?
The rice price prediction model (equation 8) is only influenced by Gross Domestic Product, Harvested Dry Paddy, Milled Dry Paddy, and Rice Stock significantly individually and together, with an R-squared value of 0.783. There are only four of the ten independent variables significant. There is probably a correlation or multi-collinearity between the independent variables of equation (8). It is because of using the dependent and independent variables of equations (2) and (7) as the independent variables of equation 8. It is necessary to explain the reason for determining the independent variables of equation 8. It is better to check the assumptions of multiple linear regression
The objective function (sub-session 2.6) is to minimize the rate of increase in rice prices between consecutive months. According to the explanation in the introduction, it is essential to stabilize the rice price. Is there no funding limit to stabilize prices?

Is the work clearly and accurately presented and does it cite the current literature?

Yes
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Yes

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Production & Inventory Systems, Supply Chain Engineering, Humanitarian Supply Chain

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Author Response

09 Aug 2025

Lucia Diawati, Industrial Engineering and Management, Bandung Institute of Technology, Bandung, 40132, Indonesia

The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Comment I (Introduction)

The proposed model is designed to regulate monthly rice prices through government intervention, primarily by adjusting supply via import procurement. This strategic intervention aims to enable a swift response to mitigate potential shortages in rice availability, which, if left unaddressed, could evolve into a multifaceted crisis encompassing economic, social, and political dimensions.
The following paragraph will be added in Section 1 to clarify the gap with previous studies.

“While existing studies have made significant contributions to supply chain optimization and the analysis of price fluctuations, there remains a notable shortcoming in research that integrates rice distribution quantities with price control mechanisms capable of generating immediate effects. To address this shortcoming, the present study aims to develop a quantitative model for determining the optimal monthly volume of rice imports necessary to balance supply and demand, thereby minimizing increases in retail rice market prices. By optimizing import volumes, the authorized government enterprise can ensure a stable rice supply while preserving the affordability of rice, particularly as it serves as a key staple food in many developing economies.”

Response to Comment 2 (Method)

“Domestic rice procurement” refers to the volume of rice production acquired by a government-designated enterprise responsible for maintaining rice price stability and distributing the supply through market channels. Equation (1) outlines the methodology employed to estimate domestic rice procurement for the period 2021–2023, formulated as a function of the ratio of domestic rice procurement to national rice production, multiplied by monthly domestic rice production. This estimation approach was necessitated by the absence of actual procurement data for 2021–2023, with the only complete dataset available corresponding to 2017. Using this dataset, the monthly percentage of domestic procurement relative to national production was derived and subsequently utilized to estimate monthly domestic rice procurement for 2021–2023.
"Domestic rice procurement" refers to the amount of domestically produced rice absorbed by government enterprises for subsequent distribution to consumers through market mechanisms. As illustrated in Figure 1, rice is also absorbed by private rice distributors, resulting in total rice production being consistently greater than domestic rice procurement, as shown in Table 1. Further, theoretically, rice imports would be unnecessary if domestic supply fully met consumer demand in a perfectly functioning market system. However, the developed model does not capture the entire supply and demand dynamics of the rice market. Instead, it focuses specifically on the role of government enterprises in price regulation through market interventions. These interventions involve increasing market supply using rice under Bulog’s control, including stock reserves, rice security reserves, and domestically produced rice absorbed by government enterprises. The estimated volume of rice imports required in period t is determined by three factors: the projected rice stock at the end of period t-1, the estimated absorption of domestic rice production by the government enterprises in period t, and the forecasted distribution of rice by the government enterprises to the public in period t. The independent variables used to estimate the import volume in period t are based on predictive models for each independent variable, with model parameters estimated using historical data.
This observation is valid; however, the regression model for rice price prediction was constructed with consideration of previously developed models by prior researchers. Therefore, this study places greater emphasis on the overall validity of the model, rather than on the marginal contributions of individual independent variables. Further refinement of the prediction model is anticipated in future work.
When considering only financial costs, the expenditures related to price stabilization mainly consist of logistical components such as ordering costs, commodity value, transportation, customs duties, storage, and market operation expenses. The allocated budget for these efforts is substantial, reflecting the need to account for potential non-financial costs arising from significant rice price fluctuations. These non-financial costs—including social and political consequences—can often far exceed the direct financial expenditures.

Response to Comment 3 (Result and Discussion)
The rice price prediction model incorporates variables such as domestic rice production, imports, and rice stock levels. However, conditions in 2023 differed significantly from those in other years due to unique factors that impacted rice prices during that period. The factors include (1) the extreme El Niño event, (2) large-scale social assistance to 10 million households in the context of the general election, and (3) inefficiencies in the Food Information System, which hindered accurate forecasting and disrupted supply chains (Department of Agricultural Socio-Economics, Universitas Gadjah Mada, 2024).
The prediction model is extrapolative, incorporating supply-demand variables, technical production indicators (e.g., agricultural land area), and economic variables (e.g., IDR–USD exchange rate). Like all extrapolative models, it assumes continuity with historical trends. The exceptional conditions of 2023 reduced its accuracy, but its applicability is expected to improve in 2024 and beyond, subject to model revalidation using updated data.
Note:
Additional Reference:
*Department of Agricultural Socio-Economics, Faculty of Agriculture, UGM (March 2024). Rice Price Inflation: A Comprehensive Analysis and Policy-Oriented Solutions (in Bahasa Indonesia). https://sosek.faperta.ugm.ac.id/2024/03/29/kenaikan-harga-beras-analisis-dan-solusi-menyeluruh/#:~:text=Faktor%20Lingkungan%3A%20Salah%20satu%20penyebab,mempengaruhi%20ketersediaan%20beras%20di%20pasaran

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03 Apr 2025 | for Version 1

Katsuhiko Takahashi, Hiroshima University, Higashi-Hiroshima, Japan

36 Views Cite this report Responses(1)

Approved With Reservations

In 1. Introduction, the subject matter of this study and previous research on it are described. Then, in the last paragraph, this paper states that there are gaps in the models considered in the previous studies and that there is still a need for model development. It is unclear what is meant by “gap” and what is meant by “need” here. It is necessary to clearly state what exactly is the gap between the conventional models and what is required, and what kind of models are needed to be developed based on the gap.
Also in 1. Introduction, it is not stated what the purpose of this study is. Although it is related to the above, it is necessary to clearly state what the purpose of this study is based on the gaps and needs.
In 2.1. Model development, it is stated that “the primary model to be developed is an optimization model aimed at minimizing monthly changes in rice retail prices over two consecutive months,” however, it is not clear whether the primary model is new or not and where is different from the previous model. It should be clearly stated whether it is a new model or not and what is different from the previous model.
In 2.5. Rice price prediction model, the compound linear regression model was built using 60 training data, namely time series data in the period January 2018- December 2022. In the model, the rice price for month t, Pt, is predicted from the current values of ten variables, PPt, NTt, PDBt, LLt, GKPt, GKGt, Xt, Yt, Ot, and It. The model is developed to be affected by the current values of all the ten variables, but isn’t it necessary to address the time lag in which past or future values are affected? If so, it is necessary to construct a model that takes this into account, and if not, it is necessary to explain the reasons why this is not necessary.
In 2.6. the objective function for rice import quantity model, the objective function aims to minimize the rate of increase in rice prices between consecutive months, specifically between the current month (t) and the previous month (t-1). However, the reason for this is not stated. The implication of the rate of price increase may be different when prices are low and when they are high, but if it is not affected, it is better to explain the reason that the rate of increase be the same regardless of the previous month's value.
In 2.7. Rice flow constraints in the rice supply chain network, the set of constraints that define the flow of rice in the rice supply chain network of government enterprise were described. Constraint (11) guarantees the quantity of rice imported from all import source countries in month (t) does not exceed the total rice export capacity of all import source countries to Indonesia. The constraint that when imports are required, the rice will be imported if the quantity meets the resources, but does the price of imported rice have no effect? If so, the effect should be incorporated otherwise, it is necessary to explain why.
In 2.8. Parameter estimation, the value of consumer rice demand parameters is estimated using the triple exponential smoothing method, based on monthly rice distribution data for the period January 2018- December 2022. In the parameters, the rice production capacity of domestic rice mills for each month (t) in the period January–December 2023 is estimated using the maximum domestic rice production for each corresponding month (t) during the period 2018–2022. Generally, the production capacity is likely to be affected by the results for the month in question, but it may also be related to the results of the previous and following months. It is better to explain the reason why this estimation is utilized and suitable for estimating the rice production capacity.
In 3. Results and Discussion, the results related to the problem of determining the quantity of rice imports each month are presented, and the results for the simulation period can be seen in Table11, the comparison graph of actual and predicted rice prices is shown in figures, and the Mean Square Error (MSE) value resulting from the comparison between predicted and actual rice prices is evaluated. This paper considered whether there is a difference or not compared to its actual price, but if the price increase can be reduced than its actual price, wouldn't it be better as an import decision for reducing the inflation of rice price? It is necessary to explain why you say it is better if there is no difference. Or, it would be necessary to evaluate whether it could be smaller or not and discuss the reason.
In 4. Conclusions, there is a description of the proposal of this paper, its content, and its results. the challenges are described, but in terms of further development, it is not clear that the current situation is sufficient. This paper said “The simulation results show that the predicted retail rice market prices are quite valid compared to actual prices for the periods 2020, 2021, and 2022, with Mean Square Error (MSE) values of IDR 62,490.62; IDR 9,604.53; and IDR 31,577.16, respectively. In 2023, the predicted prices are less valid due to factors not accounted for by the ten independent variables, such as rice scarcity and increased consumption in preparation for the 2024 elections, resulting in a large MSE value of IDR3,363,769.44.” As mentioned above, there is also the question of whether a comparison with ACTUAL is meaningful. Also, if it is less than the actual, it can be said to be good even if there is a difference between the actual and the comparison. Furthermore, the authors said that the ten variables were insufficient for the external factors of the election, but it would be better to indicate what variables should have been included, and moreover, it would be better to made a proposal that included those variables and evaluate the proposed model in this paper. If that kind of the revised model is proposed and evaluated, it can be expected that the value, limitations, and challenges of this research in the final conclusion will be improved.

Is the work clearly and accurately presented and does it cite the current literature?

Yes
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Partly
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

Partly

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

production systems engineering, supply chain management, industrial engineering

Respond to this report

Responses (1)

Author Response

21 Apr 2025

Lucia Diawati, Industrial Engineering and Management, Bandung Institute of Technology, Bandung, 40132, Indonesia

The reviewer report is highly appreciated. The following are the authors’ responses to the report.

Response to Question 1 and 2:

The term "gap" here may lead to misunderstanding. What is actually meant is the deficiency in the studies conducted with the required models for short-term rice price control over two consecutive months. The term "need" refers to the necessity for a model that can facilitate decision-making, allowing for a prompt determination of the quantity of rice to be imported. To avoid misinterpretation of the terms "gap" and "need," the last paragraph in Section 1 will be revised as follows:

“While existing studies have made significant contributions to supply chain optimization and the analysis of price fluctuations, there remains a notable shortcoming in research that integrates rice distribution quantities with price control mechanisms capable of generating immediate effects. To address this shortcoming, the present study aims to develop a quantitative model for determining the optimal monthly volume of rice imports necessary to balance supply and demand, thereby minimizing increases in retail rice market prices. By optimizing import volumes, the authorized government enterprise can ensure a stable rice supply while simultaneously preserving the affordability of rice as a staple food particularly in the context of rice, a key staple in many developing economies.”

Response to Question 3:

The primary model aims to minimize monthly rice price fluctuations over two consecutive months by adjusting import quantities. This strategy is intended to balance rice supply with market demand, thereby stabilizing prices and preventing significant shocks that could incite social and political unrest.
Most existing models focus on the design of the rice supply chain, including distribution locations and inventory levels. While effective for long-term impacts, these models necessitate structural adjustments that take time to implement (Melo et al., 2006; Min et al., 2007; Li & Bing, 2007; Wu & Zhang, 2014; Teng et al., 2007; Xu and Zhu, 2007; Dellaert et al., 2021; Athanasiou et al., 2008; Paksoy et al., 2012; Gouel, 2013; Dawe & Timmer, 2012).

Rice price prediction models have been developed by Serra & Gil (2012), Dorosh & Rashid (2013), Possamai et al. (2015), Mogale et al. (2017), Gholamian and Taghanzadeh (2017), and Cheraghalipour et al. (2019). Fitrawaty et al. (2023) identified several factors affecting rice prices and fluctuations.
The model in this study integrates the current rice supply chain and leverages imports as an intervention mechanism to mitigate major price fluctuations. The Indonesian government employs rice imports as a short-term price control policy to prevent public unrest from sharp price increases, delegating import authority to BULOG, a government enterprise.

Response to Question 4:

Your comment is well-taken, and we have indeed considered that aspect in our analysis. However, the decision adopted prioritizes achieving a rapid impact, based on the current conditions. One variable identified as having a potential lagged effect is the size of agricultural land. Upon closer examination, however, we found that the data for this variable are not based on direct measurements but are instead derived from estimates—specifically, by dividing estimated agricultural production by estimated paddy field productivity. Despite this limitation, statistical testing confirms the overall significance of the model.

Response to Question 5:

The formulation of this model is grounded in the dual role of the country as both a major rice consumer—where rice constitutes a staple food—and a significant rice producer, wherein substantial price fluctuations, either upward or downward, can have broad societal impacts. Elevated rice prices adversely affect consumers, while sharp price declines negatively impact farmers’ livelihoods. The model is operationalized from a defined starting point, using the prevailing market price at that time as a baseline. From this point forward, rice prices are assumed to be subject to control interventions.

Response to Question 6:

Although rice prices influence Indonesia's choice of import sources, this model aggregates imports from seven major countries—Thailand, India, Pakistan, Vietnam, Myanmar, Japan, and China—into a single source. Between 2018 and 2022, their respective shares were 31.3%, 21.57%, 20.69%, 19.46%, 6.89%, 0.01%, and 0.01%.

This aggregation is justified by the high variability in individual import volumes, with fluctuations from 2019 to 2022 ranging from 3.4% (Thailand) to 161.3% (Myanmar). In contrast, the combined import fluctuation from these countries was only 7.6% over the same period.
Price differences and other domestic and international factors contribute to these fluctuations. The model implicitly accounts for these influences, as reflected in the observed variation in import volumes from individual source countries.

Within the system boundary, the constraint on rice import volume is estimated in aggregate based on historical data from these seven countries.

Response to Question 7:

The use of the maximum monthly domestic rice production observed during the 2018–2022 period to estimate the production capacity parameter for each month in January–December 2023 is based on the premise that this value represents the achievable potential under previously realized conditions. This approach implicitly reflects a policy preference toward fostering the conditions necessary to attain maximum domestic rice production capacity, rather than depending on imports to fulfill national rice demand.

Response to Question 8:

In a country like Indonesia, rice prices exert a dual impact—affecting both consumers and producers (i.e., rice farmers). From the consumer perspective, price stability and affordability are essential, while from the producer’s standpoint, higher rice prices are desirable to compensate for increasing production costs. Accordingly, this study develops a model designed to minimize fluctuations in rice prices. The model is adaptable and can be calibrated to prioritize the interests of either consumers or producers, depending on the specific policy objective.

Response to Question 9:

The model developed in this study comprises two key components: (1) an optimization model that minimizes monthly rice price fluctuations by determining appropriate import quantities, and (2) an empirical model that predicts monthly rice prices using ten explanatory variables.

Building on previous studies (e.g., Serra & Gil, 2012; Dorosh & Rashid, 2013; Possamai et al., 2015; Mogale et al., 2017; Gholamian & Taghanzadeh, 2017; Cheraghalipour et al., 2019; Fitrawaty et al., 2023), this study identifies additional significant predictors of rice prices. The resulting model, with ten explanatory variables, yielded an F-statistic of 17.66 (well above the critical value of 1.99), and effectively controlled price increases.

A comparative analysis of the model output reveals that the actual monthly rice prices for the years 2020, 2021, and 2022 closely aligned with the model's optimal price projections. However, in 2023, a significant deviation was observed between the actual monthly rice prices and the optimal prices. This discrepancy is hypothesized to be attributable to specific factors that uniquely impacted rice prices during 2023. The factors include (1) the extreme El Niño event, (2) large-scale social assistance to 10 million households in the context of the general election, and (3) inefficiencies in the Food Information System, which hindered accurate forecasting and disrupted supply chains (Department of Agricultural Socio-Economics, Universitas Gadjah Mada, 2024).

The prediction model is extrapolative, incorporating supply-demand variables, technical production indicators (e.g., agricultural land area), and economic variables (e.g., IDR–USD exchange rate). Like all extrapolative models, it assumes continuity with historical trends. The exceptional conditions of 2023 reduced its accuracy, but its applicability is expected to improve in 2024 and beyond, subject to model revalidation using updated data.

Note:
Additional Reference:
*Department of Agricultural Socio-Economics, Faculty of Agriculture, UGM (March 2024). Rice Price Inflation: A Comprehensive Analysis and Policy-Oriented Solutions (in Bahasa Indonesia). https://sosek.faperta.ugm.ac.id/2024/03/29/kenaikan-harga-beras-analisis-dan-solusi-menyeluruh/#:~:text=Faktor%20Lingkungan%3A%20Salah%20satu%20penyebab,mempengaruhi%20ketersediaan%20beras%20di%20pasaran.

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Competing Interests

There are no conflicts of interest associated with the preparation of this response.

Alongside their report, reviewers assign a status to the article:

Approved - the paper is scientifically sound in its current form and only minor, if any, improvements are suggested

Approved with reservations - A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.

Not approved - fundamental flaws in the paper seriously undermine the findings and conclusions

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