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Research Article

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

[version 1; peer review: 2 approved with reservations]
PUBLISHED 20 Mar 2025
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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, a critical staple food across many Asian countries. The government prioritizes price stability to prevent sharp increases that could lead to social unrest due to rice shortages. Approaches to price control are categorized as direct or indirect. Direct controls involve immediate interventions, such as increasing rice stocks through imports to rapidly influence market prices. Indirect controls comprises longer-term measures, like enhancing domestic production capacity to achieve gradual price stability. This study proposes optimization model to determine the optimal volume of rice imports required to minimize bimonthly changes in rice retail prices.

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 ten explanatory variables: rice production, the rupiah-dollar exchange rate, GDP per capita, agricultural land area, harvested dry rice price per kilogram, ground dry rice price per kilogram, domestic rice procurement, rice imports, rice stocks, and monthly rice distribution. 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 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%.

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.

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 optimizing supply chains and understanding price fluctuations, there is a gap in the literature regarding integrated models that combine distribution quantities with price control mechanisms. Studies such as those by Fitrawaty et al. (2023) provide valuable insights into factors affecting prices, but there remains a need for models that directly address how product flows and distribution strategies can stabilize retail market prices, particularly in the context of rice, a key staple in many developing economies.

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
PPt Rice production rate in month t (tonnes/month)
NTt The rupiah exchange rate against the dollar in the month of t (rupiah)
PDBt Gross Domestic Product (GDP) per capita in month t (rupiah)
LLt Agricultural land area in month t (ha)
GKPt Harvested Dry Rice price per kg in month t (rupiah per kg)
GKGt Ground Dry Rice price per kg in month t (rupiah per kg)
Xt Domestic rice procurement in month t (tonnes)
Yt Rice imports in month t (tonnes)
Ot Rice distribution in month t (tonnes)
It Rice stocks at the end of month t (tonnes)
Zt The rate of increase in rice prices between month t and the preceding month (percent)
Pt Rice price per kg in month t (rupiah per kg)
Parameters
XbT Domestic rice procurement in month b year T (tonnes)
PCTb2017 Percentage of domestic rice procurement to national rice production in month b of 2017
PBbT Domestic rice production in b year T (tonnes)
Prop Proportion of rice distribution to consumers relative to national rice consumption
DT¯ Average rice consumption per month in year T (tonnes)
smonth Standard deviation of rice consumption per month (tonnes)
syear2 Variation in rice consumption per year (tonnes)
Dt National rice consumption in month t (tonnes)
β0 Parameter intercept of compound linear regression model
βn 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.
dt Consumer demand for rice in month t (tonnes)
ss Lower limit of strategic inventory (tonnes)
h Rice storage capacity (tonnes)
pt Production capacity of domestic rice mills in month t (tonnes)
s The export capacity of rice from source countries to Indonesia (tonnes)
PBt20182022 Maximum rice production of domestic mills in month t 2018–2022 (tonnes)
Ft Intercept value for month t
Trt Slope factor value for month t
Bt Seasonal factor value in month t
FT Intercept value for year T
TrT Slope factor value for year T

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.

0bd5fb09-0de8-437e-8a7c-11da5391f319_figure1.gif

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 2,203,2506410.0003
February 4,419,2194,1940.0009
March 8,844,298167,8100.0190
April 6,664,739649,7800.0975
May 3,213,603572,3870.1781
June 3,328,442407,7240.1225
July 4,264,106162,2220.0380
August 5,141,666250,0000.0486
September 4,769,844200,0000.0419
October 2,769,836200,0000.0722
November 1,919,833200,0000.1042
December 2,113,599200,0000.0946
Total 9,652,435 3,014,758

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

Month2018201920202021 2022
January 1,595,0001,168,000934,0001,200,0001,420,000
February 3,289,0002,083,0001,328,0002,337,0002,350,000
March 5,547,0005,255,0003,632,0005,570,0005,490,000
April 4,358,0005,121,0005,626,0004,476,0004,450,000
May 2,812,0002,505,0003,586,0002,277,0002,380,000
June 2,574,0002,475,0002,059,0002,326,0002,510,000
July 3,117,0002,663,0002,578,0003,175,0002,710,000
August 3,083,0003,214,0003,345,0002,402,0002,350,000
September 2,972,0002,430,0003,161,0002,464,0002,500,000
October 1,907,0001,899,0002,455,0002,302,0002,380,000
November 1,606,0001,522,0001,858,0001,653,0001,880,000
December 1,084,000979,000935,0001,174,0001,110,000

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)
XbT=PCTb2017PBbT
(2)
Yt=It+OtXtIt1

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)
201825,792,716
201925,214,232
202025,348,135
202125,596,828
202225,941,627

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=Rice Distribution2018National Rice Consumption2018
(4)
DT¯=National rice consumption yearT12months
(5)
smonth=syear212month

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

YearAverage National Rice Consumption per Month (tonnes)
20182,149,393
20192,101,186
20202,112,345
20212,133,069
20222,161,802
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).

Month2018201920202021 2022
January 2,155,1882,152,2422,113,2392,143,0442,146,314
February 2,156,5872,153,2632,114,2972,142,9362,150,026
March 2,152,5562,114,1802,115,5442,141,9302,147,570
April 2,152,2622,113,0312,116,2662,140,0642,153,803
May 2,148,0602,100,7662,111,0012,139,3792,149,595
June 2,147,7662,108,9332,110,5592,137,9992,148,297
July 2,144,8452,110,4052,111,9212,136,9232,142,464
August 2,141,9682,107,5932,109,5952,135,6432,149,353
September 2,142,6942,108,7252,108,5022,134,4042,152,868
October 2,144,8372,109,7772,107,1292,132,2862,154,979
November 2,147,7172,110,3722,106,3142,131,5392,158,980
December 2,148,1552,112,5682,103,9212,134,2422,161,367

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)
Ot=PropDt
(7)
Ot=It1+XtIt

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)
Pt=10.437,470.000004PPt+0.0016NTt0,00006PDBt+0,0001LLt+0,1592GKPt+0,1742GKGt+0,0001Xt0,00004Yt0,00007Ot0,00009It

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.

Independent VariableCoefficient symbolCoefficient value t-statistic p-value
β0 10,437.3739.141<0.001
PPt β1 -0.000004-0.1110.912
NTt β2 0.00160.0930.926
PDBt β3 -0.00006-2.7670.008
LLt β4 0.00010.4570.650
GKPt β5 0.15922.0110.050
GKGt β6 0.17422.6490.011
Xt β7 0.00011.7590.085
Yt β8 -0.00004-0.6510.518
Ot β9 -0.00007-0.4130.682
It β10 -0.00009-5.281<0.001

By using a significance value α = 0.05 and the number of training data used as many as 60 data, a critical t-value = 2,000 was obtained. If the calculated t-statistic of each variable is compared to the critical t-value, it can be seen that the independent variables that significantly affect the price of rice are:

  • 1. Gross Domestic Product (GDP) per capita

  • 2. Harvested Dry Rice (GKP) price per kg.

  • 3. Ground Dry Rice (GKG) price per kg.

  • 4. Rice stocks at the end of month t.

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.

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)

(9)
MinZt=(PtPt1)/Pt1

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

(10)
Xtpt,tT
(11)
Yts,tT
(12)
Ot=Xt+Yt+It1ss,tT
(13)
It=It1+Xt+YtOt,tT
(14)
ssIth,tT
(15)
Ot=dt,tT
(16)
Xt0,tT
(17)
Yt0,tT
(18)
Ot0,tT
(19)
It0,tT

Constraint (10) 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 (11) 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 (12) 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 (13) 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 (14) 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 (15) 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 (16) to (19) 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 Ft, Trt, and Bt.

  • 2. Calculating the value of Ft, Trt, and Bt 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 7.

Table 7. 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 (20). The estimated rice production capacity of domestic mills for January–December 2023 is presented in Table 8.

(20)
pt=MaxPBt20182022

Table 8. Production Capacity of Domestic Rice Mills in January–December 2023.

MonthRice 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 9 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 9. Rice imports to Indonesia from seven major exporting countries in 2018–2022.

Year ChinaJapanMyanmar PakistanVietnam Thailand India
2018227.731.0026,220.00312,493.00387,542.37812,816.51350,818.03
201924.2790.00176,825.00174,894.0040,158.0079,447.41332.30
202023.764.0036,454.40134,100.0098,178.9689,406.2513,709.83
202142.63247.004,290.0037,036.0067,694.3375,369.00244,720.16
202212.0640.478,630.0099,202.00119,204.3091,713.80180,541.89
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, PDBt, is estimated using the double exponential smoothing method, based on annual GDP per capita data at current prices from 2014 to 2022. Table 10 presents the GDP per capita value for Indonesia at prevailing prices during the period 2014–2022.

Table 10. Indonesia's GDP per Capita at current prices.

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

The procedure is outlined as follows:

  • 1. Setting initial value of Ft and Trt.

  • 2. Calculating the value of Ft and Trt 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, Yt, is determined based on two conditions. If the rice stock at the end of the month It 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 It 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, Yt can be calculated using the Equation (21).

The rice stock at the end of month t, It, 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, It can be calculated with the Equation (22). The variable of rice distribution in month t, Ot, is set to be the same as consumer demand for rice in month t, dt. Mathematically, Ot can be calculated with the Equation (23)

(21)
Yt={0,ifIt1+XtOtssss(It1+XtOt),ifIt1+XtOt<ss
(22)
It=It1+Xt+YtOt
(23)
Ot=dt

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 2023 period

The results for the 2023 simulation period can be seen in Table 11, while the comparison graph of actual and predicted rice prices for 2023 is shown in Figure 2. The Mean Square Error (MSE) value resulting from the comparison between predicted and actual rice prices is IDR 3,363,769.44 (BPS-Statistics Indonesia, 2022h). This value is notably high due to the increase in the retail market price of rice in 2023, driven by factors such as rice scarcity, preparations for the 2024 election, and the lingering effects of the post-COVID-19 pandemic. Based on the predicted price values, Table 12 shows the actual and predicted rates of price increase between consecutive months in 2023.

Table 11. Simulation results for the period 2023.

Month Rice Import (tonnes)
Jan-23279,313.43
Feb-23234,887.87
Mar-23194,608.20
Apr-230.00
May-230.00
Jun-230.00
Jul-230.00
Aug-230.00
Sep-230.00
Oct-230.00
Nov-23140,088.17
Dec-23184,494.44
0bd5fb09-0de8-437e-8a7c-11da5391f319_figure2.gif

Figure 2. Comparison of actual and predicted rice prices for 2023.

Table 12. Actual and predicted price increase rates between 2 consecutive months for 2023.

MonthPredicted Increase Rate Actual Increase Rate
Jan-23
Feb-230,07%2,39%
Mar-23-0,81%0,28%
Apr-23-0,56%1,12%
May-23-0,36%1,54%
Jun-23-0,02%3,51%
Jul-23-0,20%0,00%
Aug-230,46%0,00%
Sep-230,30%1,85%
Oct-230,00%4,35%
Nov-230,37%1,74%
Dec-230,15%0,00%
Average -0,06% 1,52%
Standard Deviation 0,39% 1,47%

Based on Table 12, 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 0.46% and a standard deviation of 0.39%. These values are significantly lower than the expected price increase rate of 2–3%.

3.2. Results for the 2022 period

The results for the 2022 simulation period can be seen in Table 13, while the comparison graph of actual and predicted rice prices for 2022 is shown in Figure 3. The Mean Square Error (MSE) value resulting from the comparison between predicted and actual rice prices is IDR 31,577.62, indicating that the developed model represents the actual price in 2022 quite accurately. 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 the predicted price values, Table 14 shows the actual and predicted rates of price increase between consecutive months in 2022.

Table 13. Simulation results for the period 2022.

Month Rice Imports (tonnes)
Jan-220.00
Feb-220.00
Mar-22124,259.50
Apr-220.00
May-220.00
Jun-220.00
Jul-220.00
Aug-220.00
Sep-220.00
Oct-220.00
Nov-220.00
Dec-22130,645.58
0bd5fb09-0de8-437e-8a7c-11da5391f319_figure3.gif

Figure 3. Comparison of actual and predicted rice prices for 2022.

Table 14. Actual and predicted price increase rates between 2 consecutive months for 2022.

MonthPredicted Increase Rate Actual Increase Rate
Jan-22
Feb-220,53%0,25%
Mar-22-0,61%-0,03%
Apr-22-0,77%0,05%
May-22-0,47%-0,63%
Jun-22-0,07%-0,36%
Jul-22-0,12%-0,13%
Aug-220,43%0,09%
Sep-220,17%0,77%
Oct-22-0,24%1,34%
Nov-220,40%0,65%
Dec-220,04%2,22%
Average -0,06% 0,38%
Standard Deviation 0,43% 0,82%

Based on Table 14, the highest actual rice price increase rate observed in 2022 was 1.34%, 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 0.53% and a standard deviation of 0.43%. These values are notably lower than the expected increase rate of 2–3%.

3.3. Results for the 2021 period

The results for the 2021 simulation period are presented in Table 15, while the comparison graph of actual and predicted rice prices for 2021 is shown in Figure 4. The Mean Square Error (MSE) value resulting from the comparison between the predicted and the actual rice prices is IDR 9,604.53, indicating that the developed model represents the actual price in 2021 quite accurately. 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 obtained price predictions, Table 16 shows the actual and predicted price increase rates between consecutive months in 2021.

Table 15. Simulation results for period 2021.

Month Rice Imports (tonnes)
Jan-210.00
Feb-210.00
Mar-2144,473.95
Apr-210.00
May-210.00
Jun-210.00
Jul-210.00
Aug-210.00
Sep-210.00
Oct-210.00
Nov-21111,703.72
Dec-21176,133.02
0bd5fb09-0de8-437e-8a7c-11da5391f319_figure4.gif

Figure 4. Comparison of actual and predicted rice prices for 2021.

Table 16. Actual and predicted price increase rates between 2 consecutive months for period 2021.

MonthPredicted Increase Rate Actual Increase Rate
Jan-21
Feb-210,11%-0,05%
Mar-21-0,91%-0,07%
Apr-21-0,78%-0,29%
May-21-0,20%-0,26%
Jun-210,10%-0,07%
Jul-21-0,10%-0,23%
Aug-210,40%-0,20%
Sep-210,26%-0,09%
Oct-210,08%-0,04%
Nov-210,53%-0,08%
Dec-210,20%0,24%
Average -0,03% -0,10%
Standard Deviation 0,45% 0,15%

Based on Table 16, the highest actual rice price increase rate observed in 2021 was 0.24%, with a standard deviation of 0.15%. The developed model predicts a highest price increase rate of 0.53%. However, the price increase rate predicted by the model exhibits greater fluctuation, as evidenced by a standard deviation of 0.45%. 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 increase rate remains lower than the expected range of 2–3%.

3.4. Results for the 2020 period

The results for the 2020 simulation period are presented in Table 17, while the comparison graph of actual and predicted rice prices in 2020 is shown in Figure 5. The Mean Square Error (MSE) value resulting from the comparison between the predicted and the actual rice prices is IDR 62,490.62, indicating that the developed model represents the actual price in 2020 quite accurately. In 2020, the COVID-19 pandemic began to hit Indonesia, which caused rice demand to decrease and the rice prices per kilogram decreased from April and carried over until 2021. Based on the obtained price predictions, Table 18 shows the actual and predicted price increase rates between consecutive months in 2020.

Table 17. Simulation results for period 2020.

Month Rice Imports (tonnes)
Jan-200,00
Feb-200,00
Mar-200,00
Apr-200,00
May-200,00
Jun-200,00
Jul-200,00
Aug-200,00
Sep-200,00
Oct-200,00
Nov-200,00
Dec-200,00
0bd5fb09-0de8-437e-8a7c-11da5391f319_figure5.gif

Figure 5. Comparison of actual and predicted rice prices for 2020.

Table 18. Actual and predicted price increase rates between 2 consecutive months for 2020.

MonthPredicted Increase Rate Actual Increase Rate
Jan-20
Feb-200,36%0,13%
Mar-20-0,84%0,15%
Apr-20-0,99%0,54%
May-20-0,43%-0,26%
Jun-200,09%-0,34%
Jul-20-0,16%0,02%
Aug-200,33%-0,04%
Sep-200,24%-0,22%
Oct-20-0,04%-0,07%
Nov-200,42%-0,17%
Dec-200,26%-0,11%
Average -0,07% -0,03%
Standard Deviation 0,49% 0,24%

Based on Table 18, the highest actual rice price increase rate observed in 2020 was 0.54%, with a standard deviation of 0.24%. The developed model predicts a highest price increase rate of 0.42%. However, the price increase rate predicted by the model exhibits greater fluctuation, as evidenced by a standard deviation of 0.49%. 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%.

3.5. Sensitivity analysis

Sensitivity analysis was conducted by varying the lower limit of the strategic inventory 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, 500,000 tonnes, 1,000,000 tonnes, and 1,500,000 tonnes. The results of sensitivity analyses are summarized in Table 19.

Table 19. The summary of sensitivity analysis results.

YearStatisticsLower limit of strategic inventory ss (tonnes)
Actual300,000500,0001,000,0001,500,000
2023Standard Deviation1.47%0.39%0.40%0.41%0.43%
Maximum4.35%0.46%0.46%0.46%0.48%
2022Standard Deviation0.82%0.43%0.40%0.42%0.47%
Maximum2.22%0.53%0.43%0.51%0.81%
2021Standard Deviation0.15%0.53%0.48%0.49%0.50%
Maximum0.24%0.53%0.53%0.54%0.54%
2020Standard Deviation0.24%0.49%0.49%0.49%0.50%
Maximum0.54%0.42%0.42%0.42%0.42%

From 2020 to 2023, changes in the lower limit of the strategic inventory showed minimal impact on the rice price increase rate between consecutive months, with the maximum price increase rate ranging from 0.42% to 0.81% and the standard deviation of the price increase rate ranging from 0.39% to 0.53%. These values remain significantly lower than the expected price increase 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 increases between consecutive months.

However, in 2020 and 2021, the price increase rates generated by the model solutions fluctuated more than the actual price increase rates. This is reflected in the larger standard deviation of the price increase 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. Conclusions

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, considering 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 ten independent variables. The training data consists of 60 observations, covering the period from January 2018 to December 2022. The model's F-statistic is 17.66, which is greater than the critical F-value of 1.99 for 60 observations and ten independent variables, indicating that the independent variables collectively have a significant impact on rice prices. The model achieves a determination coefficient (R2) of 0.783.

The values of each independent variable are estimated using methods appropriate for their historical data patterns. The rice production rate, rupiah exchange rate against the dollar, agricultural land area, GKP price per kg, GKG price per kg, and the amount of rice procured from domestic mills are estimated using the triple exponential smoothing approach. GDP per capita is estimated using the double exponential smoothing approach. Rice consumer demand is predicted using triple exponential smoothing, and the amount of rice distributed to consumers per month is determined to meet these needs. End-of-month rice stocks are calculated as the sum of beginning-of-month stocks, domestic procurement, and imports, minus the rice distributed to consumers. Imports are initiated if end-of-month stocks fall below the strategic inventory lower limit, ensuring that stocks meet at least this lower limit.

The model is simulated for four periods: 2020, 2021, 2022, and 2023. 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 IDR 3,363,769.44. The model effectively controls the rate of increase in rice prices between consecutive months, achieving a maximum price increase rate of 0.42% to 0.53% and a standard deviation of 0.39% to 0.53%, which are lower than the expected rate of 2-3%. This demonstrates the model's effectiveness in determining the necessary quantity of rice imports to control price increases in Indonesia.

Future research can expand the rice supply chain network to include upstream levels, such as farmers and middlemen. However, this requires accurate historical data on rice production distributed from farmers to mills. Additionally, if data on domestic rice procurement, rice imports, and rice distribution are available, the accuracy of the rice price prediction model can be further improved.

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

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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 1; peer review: 2 approved with reservations]. F1000Research 2025, 14:311 (https://doi.org/10.12688/f1000research.161723.1)
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Reviewer Report 21 Apr 2025
Amelia Santoso, Universitas Surabaya, Surabaya, Indonesia 
Approved with Reservations
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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 ... Continue reading
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Santoso A. Reviewer Report For: Mitigating retail rice price volatility for sustainable supply chains: an optimization and regression-based approach [version 1; peer review: 2 approved with reservations]. F1000Research 2025, 14:311 (https://doi.org/10.5256/f1000research.177795.r374130)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.
  • 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
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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
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Reviewer Report 03 Apr 2025
Katsuhiko Takahashi, Hiroshima University, Higashi-Hiroshima, Japan 
Approved with Reservations
VIEWS 36
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 ... Continue reading
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Takahashi K. Reviewer Report For: Mitigating retail rice price volatility for sustainable supply chains: an optimization and regression-based approach [version 1; peer review: 2 approved with reservations]. F1000Research 2025, 14:311 (https://doi.org/10.5256/f1000research.177795.r374127)
NOTE: it is important to ensure the information in square brackets after the title is included in all citations of this article.
  • 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
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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

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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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