Model of multiperiod production-distribution for closed-loop supply chain considering carbon emission and traceability for agri-food products

Abstract

Purpose

This study aimed to develop the integration of the multiperiod production-distribution model in a closed-loop supply chain involving carbon emission and traceability. The developed model was for agricultural food (agri-food) products, considering the reverse flow of food waste from the disposal center (composting center) to producers.

Findings

The results indicate that integrating the production and distribution model considering food waste recycling provides low carbon emissions in lower total costs. The sensitivity analysis also found that there are trade-offs between production and distribution rate and food waste levels on carbon emission and traceability.

Research limitations/implications

This study focuses on the mathematical modeling of a multiperiod production-distribution formulation for a closed-loop supply chain.

Originality/value

The model of the agri-food closed-loop supply chain in this study that considers food recycling and carbon emissions would help stakeholders involved in the agri-food supply chain to reduce food waste and carbon emissions.

Citation

Yuniarti, R., Masudin, I., Rusdiansyah, A. and Handayani, D.I. (2023), "Model of multiperiod production-distribution for closed-loop supply chain considering carbon emission and traceability for agri-food products", International Journal of Industrial Engineering and Operations Management, Vol. 5 No. 3, pp. 240-263. https://doi.org/10.1108/IJIEOM-10-2022-0045

1. Introduction

As the human population increases, it has affected the availability of food supplies for consumption. The scarcity of food from agricultural sources that are increasingly limited has resulted in increasingly severe threats to humankind. Agricultural food (agri-food) products are one of the commodities that need more attention. This is because agri-food products have product characteristics prone to damage and quick decline in quality. With a short product life, the production and distribution process along the supply chain flow of agri-food products has the risk of damage that cannot be produced or repaired, which will become food waste. The largest source of agricultural product food waste along the supply chain network is in the production and distribution process (Göbel et al., 2015; Scherhaufer et al., 2018). A study by Annosi et al. (2021) indicates that 30% of the food waste is along with the production and distribution processes of the agri-food supply chain networks.

Research related to reducing food waste in perishable food products by paying attention to the integration of production and distribution has been widely discussed. For example, Amorim et al. (2013) stated that the discussion of the integration of production and distribution in the supply chain network is growing in importance in the area of perishable products. Moreover, the linking of manufacturing and distribution processes has been examined by Nair (2005) in the supply chain context who found that manufacturing and distribution strategies significantly impact performance measures. Solina and Mirabelli (2021) also developed integrative production and distribution models to reduce food waste in the supply chain environment. Every actor in the production-distribution chain must assure food safety and quality through the handling, manufacturing, packaging and transportation of products, making the traceability system essential (Kresna et al., 2017). Yeh et al. (2019) employed a traceability system to maintain the safety and freshness of fish products throughout the production-distribution process. Similarly, Mawengkang and Mathelinea (2018) who developed a production-integration model in the marine product processing industry by taking the traceability system into account, are the only study that has looked into this. Companies must combine production-distribution while taking traceability into account to be profitable, yet carbon emissions must be controlled. To be profitable, businesses must combine production and distribution while taking traceability into account, yet it is crucial to limit carbon emissions (Yadav et al., 2021). This is because some of the process' overall carbon emissions will be expensive. Carbon emissions are becoming more critical in this aspect, and businesses need to take note (Manupati et al., 2019).

In terms of the variables considered in the integrative production-distribution models, some studies include different variables in the models. For example, Handayani et al. (2021) developed a mathematical model for producing and distributing perishable products considering carbon emission and traceability to minimize total costs. Moreover, Farahani et al. (2012) investigated the effect of food quality on production and distribution planning integration by shortening the time travel between production and distribution. Various studies have been conducted in the field of perishable foods such as fruits and vegetables (Ahumada and Villalobos, 2009; Osvald and Stirn, 2008; Shukla and Jharkharia, 2013). One of the earliest studies conducted by Ahumada and Villalobos (2009) focused on a simulation model in Agrifood Supply Chain (ASC) of various perishable and nonperishable agri-foods and vegetables. Furthermore, Verdouw et al. (2010) developed a basic model for designing fresh and processed fruit supply chain (SC). Zhang and Wilhelm (2011) presented a mathematical model for the crop industry, including vegetables, fruits, ornamental plants, tree nuts, berries and dried fruits. Shukla and Jharkharia (2013) published a literature review from 1991 to 2011 on the production of fresh produce such as fruits, flowers and vegetables. In addition, several studies have been conducted on mathematical models in the field of ASC and food supply chain (FSC). A transport planning model for FSC, in which several storage centers provide fruit logistics centers on demand during low seasons, was developed by Nadal-Roig and Plà-Aragonés (2015). Although there has been much discussion regarding the integration of production and distribution in supply chains and the variables involved in the model, few researchers have paid much attention to recycling spoiled food products for processing into fertilizers. The integration of production and distribution of perishable food products in a closed-loop supply chain environment by considering carbon emissions and recycling use from disposal centers has never been carried out. Literature studies carried out in the context of this research have supported the mathematical modeling of agricultural supply design optimization. This paper proposes a multiperiod model, a multilevel network closed-loop supply chain (CLSC) that includes farmers as producers, distribution centers, customer locations and composting centers. In this study, the vermicompost facility is one method of recycling organic waste (vegetables), which is considered reverse flow. This process results in a significant amount of organic fertilizer, which can maintain human health and the environment. Thus, this study aims to develop a production and distribution integration model by considering traceability and carbon emissions for total costs in a closed supply chain. Total costs include production, processing and packaging, transportation, inventory, finished product inventory, production carbon emissions, shipping carbon emissions and traceability costs. The model of the integrative production and distribution model considering carbon emission and traceability in this study could provide the decision-makers to configure a sustainable agri-food closed-loop supply chain.

This article has a five-section structure. The first part (introduction) explains the background knowledge and findings between the previous research and the research statement. The second section discusses studies that are relevant to the production-distribution optimization model approach. The following is the proposed approach (third section), which describes the methods, and the fourth section discusses the results and discussion. In this section, a discussion of the results and sensitivity analysis were done by developing a recommendation to stakeholders. Finally, section five is the conclusions and further potential research.

2. Literature review

This study uses a literature review to identify optimization approaches that researchers and practitioners widely use to solve, which researchers in modeling production-distribution integration problems have widely used. In addition, it also reviews the production-distribution integration model in the closed-loop supply chain for perishable products. Finally, at the end of the literature review, we discuss the previous literature related to the variables involved in the integrated production-distribution model in the closed-loop supply chain for agri-food products.

2.1 Mixed integer programming and optimization

Mixed-integer programming is one of the most commonly used linear model developments in solving production and distribution optimization problems. The advantage of this mixed integer linear programming (MILP) compared to linear programming (LP) is that MILP can accommodate integer variables in the decision variables and constraints of the developed model (Moretti et al., 2021). In terms of the production-distribution model in agri-food products, the MILP approach is widely applied. de Keizer et al. (2015) Modeled the production-distribution problem into MILP models for food products. For example, the production and distribution integration model used MILP to determine detailed product quality service levels. Other studies by Liu and Papageorgiou (2013) that developed an integrative production-distribution model for perishable food products showed that MILPeffectively solved multiobjective problems. Moreover, Meisel et al. (2013) provided a production and inter-modal transportation planning model and found a 6% saving in the integrated models. Regarding the complexity of problem-solving, some studies show that MILP is superior in solving the complex model of binary variables of the production-distribution problem. For example, Safaei et al. (2010) developed a multisite production-distribution model to decrease the costs of set up, production, inventory, distribution and transportation. Moreover, Thanh et al. (2008) and Masudin (2015) show the effectiveness of the MILP approach in solving location problems in the design of complex supply chains.

Goal programming, mixed-integer linear and non-LP models, and the traceability case optimization approach are employed. The most frequently used model in the literature is called MILP. Rong and Grunow are two researchers who have employed an optimization strategy to address traceability issues (Rong and Grunow, 2010). Utilizing the MILP technique, they created production and distribution planning to manage food safety risks in food supply chains based on traceability. The MILP concept was also put up by Moniz et al. (2013) to schedule production while taking traceability into account. Gautam et al. (2017) used a multiobjective integer non-LP (MOINLP) method, taking into account two objective functions to reduce the cost of logistics overall, the cost of adopting radio frequency identification (RFID) for traceability and the cost of contamination in the kiwifruit supply chain. Mawengkang and Mathelinea (2018) carried out the same study. Utilizing the MILP technique, their study takes traceability into account when production and distribution are planned to satisfy consumer demand for high-quality products.

2.2 Production-distribution optimization in closed-loop supply chain

The integration of production and distribution in the traditional conventional supply chain management network is widely discussed. However, reverse logistics processes such as recycling, remanufacturing and redistribution for closed-loop supply chain systems should be further considered in an integrated production and distribution model. Afra and Behnamian (2021) developed a multiproduct production and routing problem considering remanufacturing process in the model. Their model includes product return for remanufacturing and restoration for redistribution with startup costs and environmental considerations. Moreover, Jing and Li (2018) modeled the integration of production and distribution in a closed-loop supply chain network. They consider remanufacturing and recycling processes in a decentralized closed-loop supply chain system. Other studies developed an integrative production and distribution in closed-loop supply chain networks considering reverse logistics such as reuse (Ech-Charrat et al., 2017), redistribution (Zahedi et al., 2021) and recycling (Masudin et al., 2019).

One of the environmental problems in SC is the amount of waste produced which is responded to by the recycling process, attracting the attention of experts and researchers (Piyathanavong et al., 2019). Restoring the value of a product involves reverse logistics activities such as recycling, product improvement and waste management (Domínguez-Caamaño et al., 2017). Therefore, reverse logistics includes activities that start with used products until they can be reused in the market (Fleischmann et al., 1997). The importance of reverse logistics produces economic benefits and has a positive social image for the company (Kannan et al., 2012). Therefore, better evaluation of product returns and effective back logistics can have an impact on competitive advantage. Several reverse logistics network design models have been developed as CLSC which is defined as a chain in which forward and reverse logistics are combined. In CLSC, material flow is circular, and manufactured products are not disposed of after use, but rather disassembled, reused, recovered, or recycled as raw materials and remarketed to consumers (Mangla et al., 2018). Pishvaee and Torabi (2010) presented a mixed integer LP model to minimize investment costs and transportation costs in a reverse logistics network using a multiechelon annealing simulation algorithm.

2.3 Production-distribution optimization, carbon emission and traceability

Several researchers have optimized the production-distribution integration model by considering environmental variables. The environmental variables included in the model, such as carbon emission, energy reduction and traceability, have been studied by several researchers. Manupati et al. (2019) included carbon emission in the production-distribution model for a sustainable supply chain system. Their integrated production and distribution model was developed for a multiechelon supply chain network considering three policies of carbon emission: carbon tax, strict carbon capping and carbon cap-and-trade. Other studies by Moon et al. (2016) proposed bi-objective optimization problems of production and distribution integration. They developed four stages production-distribution system under carbon emission constraints using mixed-integer programming. Moreover, Wang et al. (2021b) integrated production and transportation problems for the e-commerce supply chain by involving carbon emissions in the model. Their integration model focused on analyzing the transportation scheduling model to optimize carbon emissions and costs.

The traceability system in the supply chain network has been paid more attention. Some studies attempted to elaborate on the impacts of the traceability system on the performance of the supply chain. For example, in the context of traceability, some studies have discussed the integration of production and distribution models. Masudin et al. (2021) and Yüksel (2022) investigated the relationship between traceability and supply chain performance. They found that the traceability system impacts significantly on supply chain performance. Other studies by Costa et al. (2013) included traceability in their production-distribution model. They constructed reference processes of agri-food tracking for the foundation of food safety. Moreover, Handayani et al. (2021) developed a production and distribution integration model with the constraint of traceability to minimize total costs. The study indicated that the proposed production and distribution model integration could produce the minimum total production and distribution cost with high traceability and low carbon emissions.

Several previous studies researched the integration of production and distribution in supply chain networks that took into account the presence of carbon emissions as shown in Table 1. Gautam et al. (2017) took a case study of the kiwifruit supply chain and analyzed the impact of traceability using RFID tags. Using a (MOINLP) model is formulated by considering two objective functions which include (1) minimizing the total cost of combining logistics costs and the cost of implementing RFID tags and (2) the cost of liability for contamination. Meanwhile, Manupati et al. (2019) differs from production-distribution and inventory problems in a multiechelon supply chain with three carbon policies, strict carbon and cover, and carbon trading and time considerations by developing a nonlinear mixed integer programming model. In another study, Usman et al. (2018), developed a reliable initial model of an integrated traceability system for the halal food supply chain. The method is based on a unified modeling language (UML) such as use cases, sequences, and business process diagrams. The objective model is formulated by considering two objective functions which include (1) the risk of failure that may occur during outbound logistics activities and (2) maximizing the quality of information on halal products. Furthermore, Jabarzadeh et al. (2020) used a multiobjective mixed-integer LP method to solve the optimization model for perishable products in terms of total network costs and carbon emissions and maximize responsiveness to demand. Meanwhile, Zhang et al. (2017) proposed the MILP model for multiitem production scheduling by considering carbon emissions in production. The MILP method was also chosen by Moon et al. (2016) in formulating the trade-off problem between optimal advantages and disadvantages in production-distribution planning with carbon emission limits and inaccurate information about raw material resources. On the other hand, our literature review shows that MILP has been widely proposed for production-distribution problems related to traceability and carbon emissions. However, the MILP method for combining traceability and carbon emissions in production distribution issues is still limited. Therefore, this study proposes the MILP method by considering traceability and carbon emissions simultaneously.

3. Research methodology

The initial stage in this research is determining the supply chain actors involved in the model to be developed. The supply chain actors in this model are farmers as producers, distribution centers, customers and composting centers whose function is to recycle organic vegetables from distribution centers and customers. The next stage is to develop a mathematical model formulated using the MILP approach. The goal of this study is to create a mathematical model utilizing the MILP method. When it comes to identifying actual issues, such as food waste, carbon emissions and traceability cost, MILP is thought to be helpful. In order to evaluate and test the proposed model's accomplishment, a numerical analysis based on actual examples was conducted. The sensitivity analysis, meantime, looks at the effects of changes on the performance output. MILP is considered effective in capturing real problems, such as food waste, carbon emissions, long-distance shipping and traceability. This mathematical model is designed for a multiperiod and multiproduct in closed loop vegetable supply chain. The next stage is to determine the parameters and decision variables needed in the model. The decision variables determined are the location of the farmer and the number of vegetables that must be produced, the number of vegetables that must be sent to the distribution center, the level of inventory at the distribution center and distribution center, the level of carbon emissions resulting from processing vegetables at the distribution center, and the level of carbon emissions produced from the distribution center. The following decision variables are the number of vegetables sent from the farmer distribution center, the amount of vegetable waste sent from the distribution center to the composting center, the amount of vegetable waste sent from customers to the composting center and the amount of compost sent to the composting center.

The mathematical model developed aims to minimize costs, including production costs at producers and distribution centers, transportation costs, storage costs, carbon emission costs, traceability costs and the composting process.

Furthermore, numerical analysis was conducted to test and assess the proposed model. Meanwhile, sensitivity analysis was conducted to determine the impact of changes on output performance. The parameters in the sensitivity test were.

1. The level of production from farmers,

2. The level of consumer demand,

3. The cost of producing agri-food products for farmers, and

4. The percentage of food waste produced by consumers of agri-food products.

Based on the developed model and the sensitivity test results are then analyzed. The results of this study would be discussed from different perspectives and the recommendations for involved stakeholders are proposed at the end of the discussion section.

4. Model development

4.1 Integration of production-distribution models in the agricultural food closed-loop supply chain

In this study, a production and distribution integration model was developed to optimize the CLSC performance of organic agri-food products from the economical aspect by considering carbon emissions, product traceability and food waste processing of organic agri-food products. The logistics network is a multiperiod for multiproducts consisting of four echelon types, including producers (farmers), distribution centers, markets and composting centers, as shown in Figure 1. Mathematical model of integration of production-distribution network formulated into a mathematical model using a mixed-integer programming approach. This model allows decision-makers to optimize inventory levels and distribution on the CLSC concept of organic agri-food products. At the model testing stage, numerical analysis is based on real case examples in the agri-food supply chain industry. At the model testing stage, numerical analysis is done based on real case examples in the agri-food supply chain industry. This analysis was carried out to give a general picture of the effectiveness and evaluation of the suggested model. In this model, there are three product forms, including organic vegetables, food waste and compost, where the details of the movement of the three products are as follows:

1. Fresh and agri-food products are sent to producers (farmer) distribution centers. The observed period is two periods.

2. The agri-food waste products from the distribution center and consumers are sent to the compost processing center.

3. Compost products from organic agri-food waste processing are obtained from the amount of waste product conversion at the composting center, and then delivered to agri-food producers (farmers).

Figure 1 shows the organic agri-food production system with p = 1, 2, … P produced by the farmer as much as i = 1, 2, … I. After harvesting, the organic agri-food is sent to the distribution center as much as j = 1, 2, … J for packaging. This packaging process produces carbon emissions with a threshold that has been set according to government regulations. In addition, during the distribution process, carbon emissions can also arise. Agri-food can then be sold to the market (customer) with a demand pattern from the end customer. The rotten organic agri-food cannot be consumed, so it is sent to the composting center as much as l = 1, 2, … L for processing organic agri-food waste into compost. The finished compost is sent back to the producers (farmers) to be used as organic fertilizer.

The development of the production-distribution integration model in a closed-loop supply chain for organic agri-food products depicted in Figure 1 considers several assumptions, including (1) the farmer's location, distribution center, customer and composting center has been determined previously, (2) the quality of the agri-food industry. For example, food products that decreased at the distribution center and the customer could not be used anymore were transferred to the composting center and (3) the initial inventory at the farmer's location, the distribution center was zero.

4.1.1 Index

The index used in the developed model is as follows:

• Time period with index t, t = 1, 2, … T

• Agri-food organic products with index p, p = 1, 2, …P

• Farmer with index i, i = 1, 2, … I

• Distribution center with index j, j = 1, 2, … J

• Customer with index k, k = 1, 2, … K

• Organic food waste with index s, s = 1, 2, … S

• Composting center with index l, l = 1, 2, … L

• Compost with index v, v = 1, 2, … V

4.1.2 Parameter

The parameters used in the developed model are as follows:

• D_pjt: agri-food product demand (p) at distribution center (j) in period t (tons)

• CP_pit: cost of producing agri-food product (p) to farmer (i) in period t ($/ton)

• CG_pjt: cost of processing and packing agri-food product (p) at distribution center (j) ($/ton)

• Cs_pit: storage cost (p) to farmer (i) in period t ($/ton)

• Ch_pjt: storage cost (p) at distribution center (j) in period t ($/ton)

• Ce_pjt: carbon emission cost for processing and packing product (p) at distribution center (j) in period t ($/kg-CO₂/ton)

• Ct_ijt: carbon emission cost for delivery from farmer (i) to distribution center (j) in period t ($/kg-CO₂/ton)

• Ec_pjt: carbon emission level for processing and packaging food products (p) at

• distribution center (j) in period t (kg-CO₂/ton)

• Et_pjt: level of carbon emission produced in the process of shipping food product (p) in period t (kg-CO₂/ton)

• alpha_t: percentage of food waste (s) wasted in distribution center (j) in period (t) (%)

• beta_t: percentage of food waste (s) wasted on customers (k) in period (t) (%)

• w: conversion rate of fruit into composting center

• Ck_slt: the cost of making compost from food waste (s) in composting center (l) in period t ($/ton)

• VC_p: variable cost for delivery of food product (p) or waste (w) ($)

• d_ij: distance from farmer (i) to distribution center j (km)

• d_jk: distance from distribution center (j) to customer (k) (km)

• d_jl: distance from distribution center (j) to composting center (l) (km)

• d_kl: distance from customer (k) to composting center (l) (km)

• d_li: distance from composting center (l) to farmer (i) (km)

• Cc_pj: food product traceability cost (p) at distribution center (j) in period t ($/ton)

4.1.3 Decision variables

The decision variables used in the developed model are as follows:

• Y_pj: binary variable, value 1 if agri-food production (p) is done and value 0 otherwise

• P_pit: number of agri-food (p) produced by farmer (i) in period t (tons)

• X_pijt: number of agri-food (p) sent from farmer (i) to distribution center (j) in period t (tons)

• Is_pit: agri-food inventory level (p) on farmer (i) in period t (tons)

• Ih_pjt: agri-food inventory level (p) at the distribution center (j) in period t (tons)

• ECP_pjt: agri-food processing carbon emission level (p) at distribution center (j) in period t (kg-CO₂/ton)

• ECT_ijt: carbon emission level from agri-food delivery process (p) from a farmer (i) to distribution center (j) in period t (kg-CO₂/ton)

• Ws_jlt: the amount of agri-food waste (s) sent from distribution center (j) to composting center (l) in period t (tons)

• Ww_klt: the amount of agri-food waste (s) sent from the customer (k) to composting center (l) in period t (tons)

• Wc_lit: the amount of compost (v) that can be sent from composting center (l) to farmer (i) in period t (tons)

4.2 Mathematical model

The framework shown in Figure 1 can be formulated mathematically to minimize the total cost. The costs formulated are costs for production costs at producers and distribution centers, transportation costs, storage costs, carbon emission costs, traceability costs and the cost of the composting process. Therefore, the objective function equation to minimize total cost can be formulated as follows:

(1)Minimize TC=(∑p∈P∑i∈I∑t∈TCPpitPpit+∑p∈P∑j∈J∑t∈TCGpjtXpijt)+(∑p∈P∑i∈I∑j∈J∑t∈TXpjtdijVCp+∑p∈P∑j∈J∑k∈K∑t∈TDpjtdjkVCp+∑s∈S∑j∈J∑l∈L∑t∈TWsjltdjlVCp+∑s∈S∑k∈K∑l∈L∑t∈TWwkltdklVCp+∑v∈V∑l∈L∑i∈I∑t∈TWclitdliVCp)+(∑p∈P∑i∈I∑t∈TCspitIspit+∑p∈P∑j∈J∑t∈TChpjtIhpjt)+(∑p∈P∑j∈J∑t∈TCepjtECPpjt+∑i∈I∑j∈J∑t∈TCtijtECTijt)+(∑p∈P∑i∈I∑t∈TCcpjPpit)+(∑j∈J∑l∈L∑t∈TWsjltCkplt+∑k∈K∑l∈L∑t∈TWwkltCkplt)

To minimize the objective function in equation (1), there are several constraints which are formulated as follows:

(2)∑i∈IPpit≤∑i∈IXpijt

(3)Ppit≤YpjCPpit

(4)∑j∈JXpijt≤Ppit

(5)Ispit=Ispi(t−1)+Ppit−∑j∈JXpijt

(6)Ihpjt=Ihpj(t−1)+∑i∈IXpijt−Dpjt

(7)Ispit+Ppit≥∑j∈JXpijt

(8)Ihpjt+∑i∈IXpijt≥Dpjt

(9)Wsjlt=αtIhpjt

(10)Wwklt=βtDpjt

(11)Wclit=(∑j∈J∑l∈L∑k∈K∑t∈TWsjlt+Wwklt)w

(12)ECPpjt=XpijtEcpjt

(13)ECTijt=XpijtEtpjt

(14)Ypj,∈{0,1} ∀l∈L

(15)Ppit,Xpijt,Ispit,Ihpjt,ECPpjt,ECTijt,Wsjlt,Wwklt,Wclit≥0 ∀i∈I,j∈J,k∈K,l∈L,t∈T

Constraint (2) ensures that the amount of agri-food product (p) produced by the farmer (i) does not exceed the farmer's capacity (i), while constraint (3) ensures that the amount of agri-food product (p) can be produced if the farmer (i) opened. Furthermore, constraint (4) ensures that the amount of agri-food product (p) delivered to distribution (j) does not exceed the amount of production at the farmer (i). Constraint (5) indicates the level of agri-food product inventory (p) at farmer (i) in period t (tons). Constraint (6) shows the level of agri-food product inventory (p) at the distribution center (j) in period t (tons), and constraint (7) ensures that the amount of agri-food product (p) in the farmer exceeds the number of products delivered to the farmer and distribution center (j). Moreover, constraint (8) ensures that the number of agri-food products (p) in the distribution center (j) exceeds the number of customer demands (k). Constraint (9) indicates the amount of agri-food product (s) wasted from the distribution center (j) by the percentage of agri-food products that become food waste. Constraint (10) shows the amount of agri-food product (s) wasted by customers (k) equal to the percentage of agri-food product that becomes waste from demand (k). Furthermore, constraint (11) indicates the amount of compost (v) that can be delivered from the composting center (l) to the farmer (i) in period t (tons). Constraint (12) indicates the level of carbon emissions from processing agri-food products at the distribution center (j), and constraint (13) indicates the level of carbon emission in the process of sending agri-food products from the farmer (i) to the distribution center (j). Finally, constraint (14) shows the binary number on the farmer (i), and constraint (15) shows the non-negativity value limit on the determined decision variable.

4.3 Data on agri-food product supply chain

This study was conducted on Indonesia's supply chain network of organic agricultural products. The data used is historical data on customer requests to the distribution center. In this case study, two farmers, I1 and I2, produce two product types (P1 and P2) in two periods (t1 and t2). The production capacity produced by farmer 1 (I1) is 156 and 100 tons for products 1 and 2, respectively. Meanwhile, the production capacity produced by farmer 2 (I2) for products 1 and 2 is 120 and 166 tons, respectively. Moreover, there are two distribution centers (J1 and J2) that have different demands of product types (P1 and P2) in two periods (t1 and t2). For example, the demand at the distribution center is 223 and 244 tons for products 1 and 2, respectively. Farmers' production costs in producing each product are shown in Table 2. In the meantime, Table 3 displays the storage expenses for each product at the distribution facility.

This study considers the existence of carbon emissions generated in the distribution centers for the processing, packaging and delivery of agri-food. In the case study, the two operating distribution centers are J1 and J2, which distribute two types of agri-food products, namely P1 and P2. The carbon emission level for processing and packaging in the distribution center is 0.02 kg-CO₂/tons. The costs of carbon emissions for the processing, packaging and shipping processes of products are shown in Tables 4 and 5.

Based on the framework, the production and distribution network model require distance data between facilities. For example, the distance from farmers (I1 and I2) to distribution centers (J1 and J2) is 50 and 80 km, respectively. Moreover, the distance from distribution centers (J1 and J2) to customers (K1 and K2) is 20 and 50 km. Moreover, the distance between the distribution center (J1 and J2) to the composting center (L1 and L2) is 69 and 104 km. In addition, the distance from customers (K1 and K2) to composting centers (L1 and L2) is 10 km and 20 km respectively, while the distance from composting centers (L1 and L2) to farmers (I1 and I2) is 90 and 52 km, respectively.

In this case study, the storage cost of agri-food products to the farmer (i) is $5/ton. Meanwhile, the cost of processing and packaging agri-food products at the distribution center is $20/ton. The carbon emissions in shipping agri-food products are 0.05 (kg-CO₂/ton). The percentage of agri-food product waste at the distribution center at the time of observation was 13% and 12%, respectively. Furthermore, the percentage of agri-food product waste originating from customers during the observation period was 12% and 11%, respectively. The conversion rate of agri-food waste products into compost is 110%. The cost of composting from agri-food waste products is $7/ton. The variable cost for delivering agri-food products or waste is $0.073/ton. The cost of traceability of agri-food products at the distribution center is $25/ton.

4.4 Results

Based on the solver calculations, the total cost incurred by the closed-loop supply chain network of organic agri-food is $55.205. Table 6 shows all the components that make up the total costs in the closed-loop supply chain network of organic agri-food products. The table shows that the highest cost composition is the cost of the organic product agri-food cultivation process, contributing 52.81% of the total cost. The delivery of food products from farmers to the distribution center is equal to the consumer demand, so there is no food waste in the distribution center for the two types of products. This results in no food waste distribution from the distribution center to the composting center, so the transportation cost from the distribution center to the composting center is $0. Additionally, this results in zero costs for the distribution center's inventory and for composting vegetable waste generated there.

The optimal results from the calculation for the number of agri-food products produced and delivered by the farmer to the distribution center, the amount of waste sent from the customer to the composting center and the amount of compost sent from the composting center to the farmer can be seen in Tables 7–14.

Based on the results of data processing using the solver in the spreadsheet, the two farmers were open to meeting the demands of the agri-food product market. As a result, the number of agri-food products (p) produced can be seen in Figure 2, which shows that farmer 2 (i2) produces more products in both types of agri-food products because of the capacity of farmer 2 (i2) is greater than the capacity of farmer 1.

Table 11 shows that the total carbon emission level in the distributor packaging process is lower than the total carbon emission in the delivery process from farmers to distribution centers. This is because the packaging process carried out by distributors is simple, so carbon emissions from the process are low. In comparison, the delivery process uses gasoline-fueled vehicles, so the resulting carbon emissions are more significant than the packaging process. Figure 3 illustrates the level of carbon emissions from the processing of agri-food products at distribution centers which shows that the amount of carbon emissions released is influenced by the number of products processed and the level of carbon emissions in each process. The more products are processed at the distribution center, the more carbon emissions will increase.

The agri-food waste from the customer can be seen in Figure 4. The waste is sent to the composting center to be processed into compost and returned to the farmer to be used as fertilizer to plant agri-food products.

Based on Table 6, the results of the cost traceability calculation are 21.1485% of the total cost. Product traceability costs are affected by the amount of product processed and packaged. Traceability costs cover the movement of agro-food products through the production, packaging and distribution stages. In this case, traceability traces and detects agri-food products through (i) the stages of farmer production, the packaging process at the distribution center, (j) and the transportation process. With this traceability system, consumers can find out what, when, how and where products are processed, packaged and shipped.

4.5 Discussion

Food-related items produce emissions during manufacture and delivery. Prashar (2020) and Saga et al. (2019) indicated that the increasing number of products manufactured and distributed along the supply chain would result in carbon emissions increasing. The findings of this study have shown that food manufacturing and distribution activities contribute to carbon emissions. It also shows that total carbon emissions in the production process are smaller than the total distribution of carbon emissions. For example, the total carbon emission generated in distribution activities is 23.35 kg-CO₂ (71%). Meanwhile, the total carbon emission in the production process is 9.34 kg-CO₂ (29%). The amount of carbon emissions in the distribution process is caused by the use of vehicles that require fuel. The more products shipped, the more fuel is used, which would increase the number of carbon emissions. These findings are relevant to previous research which indicates that the largest producer of carbon emissions along the supply chain is in distribution activities (Bonilla et al., 2015; Gurtu et al., 2017; Li et al., 2022). Furthermore, Aktas and Temiz (2020) found that for agri-food products, production activities are not as much as distribution activities in producing carbon emissions. This is because there are not many machining activities that require fuel in the processing of agri-food products. Thus, the production of carbon emissions is not more than distribution activities.

From the perspective of product types, research results related to this agri-food product produce carbon emissions that are different from other types of manufactured products in the production process. For example, Wakeland et al. (2012) found that the carbon emissions in the car manufacturing process are greater than the carbon emissions resulting from the process of sending cars from producers to consumers. This is caused by the process of making products which is very long and requires complicated and lengthy machining processes and other tools, which would require a lot of energy. Wang et al. (2021a) also claimed that the carbon emissions generated during the production of machinery products are less than those during the distribution process. The findings of this study, which stated that indicated that distribution processes result in a higher number of carbon emissions have impacted the carbon emission and total costs. Table 6 shows the cost of carbon emissions in the production process of 0.0003% of the total cost, and the cost of carbon emissions for the shipping process is 0.73%. This means that the costs incurred for carbon emissions in the production process are significantly lower than the carbon emission costs in distribution processes. This result is relevant to the discussion by Ilyas et al. (2021) who believed that carbon emission costs contribute considerably to the total costs of distribution. Another study also found that the more frequently product delivered from facilities to other facilities, the more cost of carbon emission incurred (Glock and Kim, 2015; Sopha et al., 2016).

In addition to the cost of carbon emissions, traceability costs are also considered in this production-distribution integration model, which is much higher than the cost of carbon emissions. Costs associated with traceability are directly correlated with production volumes such as tracking and tracings. The movement of agri-food products through the production, supply and distribution stages, is known as traceability costs. Kelepouris et al. (2007) indicated that traceability costs are one of the costs involved in the product tracking process both from the point of origin to the point of consumption and the other way around. Traceability costs in the agri-food production process are very important because they are related to the short life of agri-food products. Delays and inaccuracies in tracking and tracing agri-food products would destroy these products and turn them into waste. As is well known, agri-food products cannot be recycled and redistributed for consumption, so product tracking and tracing to find out the speed of delivery and product expiration is an important issue that needs attention. Ramesh and Jarke (2001) revealed that an ideal traceability system consists of a plan that determines the time, place and how the traceability process is built. Traceability in their context refers to monitoring raw materials and food products as they move through the production, inventory and distribution stages.

4.6 Sensitivity analysis and managerial implications

Sensitivity analysis was used to evaluate the solution's effectiveness for the problem parameters and test the robustness of the proposed model results. This study conducted a sensitivity test on several parameters in the proposed model. The parameters carried out by the sensitivity test are the level of production from farmers, the level of consumer demand, the cost of producing agri-food products for farmers, and the percentage of food waste generated by consumers of agri-food products. The analysis is carried out by evaluating how much influence the parameter changes have on the total cost of the developed model. The four-parameter changes are −10%, −5%, +5%, and +10%. The results of the sensitivity analysis test are shown in Table 15 and Figure 5.

Based on Table 15 and Figure 5, it can be seen that changes in the demand level parameter have the most effect on the total cost. This shows that if there is a decrease in demand, the total cost would decrease significantly and vice versa. The second parameter that affects the total cost is the production cost of agri-food products. Parameters of production level and amount of agri-food product waste from consumers have almost the same pattern of changes in total costs.

The development of production and distribution integration in a closed-loop supply chain network by integrating traceability and carbon emissions to provide an overview of policy recommendations to stakeholders involved in multiechelon and multiperiod supply chains, namely producers, distributors, food waste centers, and of course, the government. Government policies related to carbon emission regulations that focus on environmental issues significantly impact the business world. The regulation of carbon emission taxes issued by the industrial sector encourages the industry to evaluate the production and distribution processes to minimize the carbon emissions produced and correlate with the production and distribution costs incurred by the industry. Touratier-Muller et al. (2019) and Renukappa et al. (2013) showed that government initiatives are the driving factors for business sectors to reduce carbon emissions in their production and distribution activities. Government participation to take part in efforts to reduce carbon emissions and increase traceability, one of which is by providing logistics infrastructure such as quality roads and Internet networks. A study by Guerrero-Ibanez et al. (2015) and Shammar and Zahary (2020) indicated that the logistics infrastructures such as quality roads and Internet networks would affect significantly carbon emission reduction and traceability.

In the context of production, the total cost is affected by the agricultural production process, from seed to harvest. It means that farmers (producers) should optimize the compost of leftover food to help plant growth and, at the same time, reduce unused food waste. Thus, coordination between the food waste collection center (composting center) and the farmers should be developed based on the planting seasons. Sayara et al. (2020) show that the right composting time and the correct type of compost would affect the yield of agri-food products. As a result, the findings of the agri-food production-distribution model would impact total reduction costs and decrease the amount of food waste.

This study shows that the highest carbon emission level is generated from shipping agri-food products. Thus, the distribution and transportation sectors should consider implementing an environmentally friendly and sustainable distribution approach. Several approaches can be used, such as the principle of green distribution which can reduce carbon significantly (Klimecka-Tatar et al., 2021). Moreover, the distribution and transportation sectors for agri-food businesses are encouraged to adopt reverse logistics in distribution activities. Semieniuk and Yakovenko (2020) believed that the implementation of the redistribution of recycled products could reduce carbon emissions and increase the company's environmental and financial performance.

5. Conclusion and future research

This study has successfully modeled the production-distribution integration model in a closed-loop supply chain of agri-food products by considering the costs of carbon emissions, waste treatment and traceability. The results of this study indicate that the most significant carbon emission comes from distribution activities. Meanwhile, traceability costs are strongly influenced by the number of agri-food products produced, packaged and delivered to consumers. The agri-food waste received by collectors in this model indicated that the wastes from the customer and distribution centers are sent to the composting center to be processed into compost and sent back to the farmer to be used as fertilizer for planting agri-food products. Further research can be developed from the limitations of this research, for example, involving investment costs for land clearing or investment costs in the distribution process. Carbon emissions are limited to carbon emissions in the delivery process from farmers to distribution centers. Further research can calculate the level of carbon emissions in each supply chain involved in the closed-loop supply chain network model. Moreover, this research is also limited to the economic aspect. Further research can integrate aspects of sustainability in the design of the supply chain network. In addition, besides considering the economic aspect, it could also consider environmental and social aspects.

Figures

Figure 1

Production-distribution network on closed-loop supply chain

Figure 2

The volume of agri-food products produced by farmers

Figure 3

Carbon emission levels of agri-food product processing in Distribution Center

Figure 4

Amount of agri-food waste coming from customers

Figure 5

Sensitivity test results for the percentage of savings on total costs

Table 1

Comparison of models related to the proposed research topic

Authors	Network supply chain	Concern		Approach
		Carbon emission	Traceability
Rong and Grunow (2010)	Forward	–	√	Mixed-integer linear programming
Kallel and Benaissa (2011)	Forward	–	√	Mixed-integer linear programming
Gautam et al. (2017)	Forward	–	√	Multi-objective integer nonlinear programming
Moon et al. (2016)	Forward	√	–	Mixed-integer linear programming
Mawengkang and Mathelinea (2018)	Forward	–	√	Mixed-integer linear programming
Manupati et al. (2019)	Forward	√	–	Mixed-integer programming
Zhang et al. (2017)	Forward	√	–	Mixed-integer linear programming
Usman et al. (2018)	Forward	–	√	Goal Programming
Jabarzadeh et al. (2020)	Closed Loop SC	–	√	Mixed-integer linear programming
Proposed Model	Closed Loop SC	√	√	Mixed-integer linear programming

Source(s): Authors work

Table 2

Cost of producing food product (p) on the farmer (i) in period t ($/ton)

Farmer (I)	Product (P)	Period (t)		Total
		1	2
I1	P1	65	65	130
	P2	60	60	120
I2	P1	65	65	130
	P2	60	60	120
Total		250	250	500

Source(s): Authors work

Table 3

Cost of product storage (p) at the distribution center (j) ($/ton)

Distribution center (J)	Product (P)
J1	P1	40
	P2	38
J2	P1	40
	P2	38

Source(s): Authors work

Table 4

Cost of carbon emissions for processing and packaging the product (p) at the distribution center (j) in period t ($/CO₂/ton)

Distribution center (J)	Product (P)	Period (t)		Total
		1	2
J1	P1	1.5	1.5	3
	P2	1.4	1.4	2.8
J2	P1	1.4	1.4	2.8
	P2	1.5	1.5	3
Total		5.8	5.8	11.6

Source(s): Authors work

Table 5

Cost of carbon emissions for delivery from the farmer (i) to distribution center (j) in period t ($/CO₂/ton)

Distribution center (J)	Product (P)	Period (t)		Total
		1	2
J1	P1	1.5	1.5	3
	P2	1.4	1.4	2.8
J2	P1	1.4	1.4	2.8
	P2	1.5	1.5	3
Total		5.8	5.8	11.6

Source(s): Authors work

Table 6

Cost calculation results

Cost component	Amount ($)	Percentage (%)
Cost of producing Agri-food at farmers	29.155	52.8123
Processing and packaging costs at the distribution center	9.340	16.9188
Transportation costs from Farmer to distribution center	2.595	4.7023
Transportation costs from distribution center to customer	984.77	1.7838
Transportation costs from the distribution center to composting center	0.00	0.0000
Transportation costs from the customer to the composting center	59.59	0.1079
Transportation costs from composting center to Farmer	302.14	0.5473
Farmer inventory costs	310	0.5615
Inventory costs at distribution center	0.00	0.0000
Cost of carbon emissions for packaging	0.19	0.0003
Cost of shipping process carbon emissions	407	0.7373
Cost of traceability product	11675.00	21.1485
Cost of composting food waste from distribution center to composting center the	0.00	0.0000
Cost of composting food waste from the customer to the composting center	375.41	0.6800
Total cost	55.205	100

Source(s): Authors work

Table 7

Binary variable agri-food product (p) produced by the farmer (i)

Farmer (I)	Product (P)	Period (T)		Total
		1	2
I1	P1	1	1	4
	P2	1	1	4
I2	P1	1	1	4
	P2	1	1	4
Total		4	4	8

Source(s): Authors work

Table 8

Agri-food products (p) quantity produced by the farmer (i) in period t (tons)

Farmer (I)	Product (P)	Period (T)		Total
		1	2
I1	P1	50	60	110
	P2	50	50	100
I2	P1	57	60	117
	P2	69	71	140
Total		226	241	467

Source(s): Authors work

Table 9

Agri-food products (p) quantity delivered from farmer (i) to distribution center (j) in period t (tons)

Farmer (I)	Distribution center (J)	Product (P)	Period (T)		Total
			1	2
I1	J1	P1	50	50	115
		P2	0	0	0
	J2	P1	0	0	5
		P2	50	50	100
I2	J1	P1	0	0	0
		P2	60	58	118
	J2	P1	57	60	117
		P2	9	13	22
	Total		226	241	467

Source(s): Authors work

Table 10

Inventory level of agri-food product (p) at Farmer (i) in period t (tons)

Farmer (I)	Product (P)	Period (T)		Total
		1	2
I1	P1	0	0	0
	P2	0	0	0
I2	P1	0	0	0
	P2	18	44	62
Total		18	44	62

Source(s): Authors work

Table 11

The carbon emission level of processing agri-food products (p) at the distribution center (j) in period t (kg-CO₂/ton)

Distribution center (J)	Product (P)	Period (T)		Total
		1	2
J1	P1	1.00	1.10	2.10
	P2	1.20	1.16	2.36
J2	P1	1.14	1.30	2.44
	P2	1.18	1.26	2.44
Total		4.52	4.82	9.34

Source(s): Authors work

Table 12

Level of carbon emission in the process of delivering agri-food products (p) from farmer (i) to distribution center (j) in period t (kg-CO₂/ton)

Farmer (I)	Distribution center (J)	Product (P)	Period (T)		Total
			1	2
I1	J1	P1	2.50	2.75	5.25
		P2	0	0	0
	J2	P1	0	0.25	0.25
		P2	2.50	2.50	5
I2	J1	P1	0	0	0
		P2	3	2.90	5.90
	J2	P1	2.85	3	5.85
		P2	0.45	0.65	1.10
	Total				23.35

Source(s): Authors work

Table 13

Amount of agri-food waste(s) sent from customer (k) to composting center (l) in period t (tons)

Customer (K)	Composting center (L)	Product (P)	Period (T)		Total
			1	2
K1	L1	S1	6	6.05	12.05
		S2	7.20	6.38	13.58
K2	L2	S1	6.84	7.15	13.99
		S2	7.08	6.93	14.01
	Total		27	27	53.63

Source(s): Authors work

Table 14

The amount of compost (v) that can be sent from the composting center (l) to the farmer (i) in period t (tons)

Composting center (L)	Farmer (I)	Product (P)	Period (T)		Total
			1	2
L1	I1	P1	6.60	6.66	13.26
		P2	7.92	7.02	14.94
L2	I2	P1	7.52	7.87	15.39
		P2	7.79	7.62	15.41
	Total		30	29	58.99

Source(s): Authors work

Table 15

Parameter sensitivity test on changes in the total cost

Parameter	Sensitivity	−10%	−5%	0%	+5%	+10%
Production rate (P)	Total cost ($)	55.34	55.28	55.21	55.13	55.06
	Change in total cost (%)	0.24	0.13	0.00	−0.13	−0.26
Demand rate (D)	Total cost ($)	49.54	52,373	55.21	58.04	60.31
	Change in total cost (%)	−10.26	−5.13	0.00	5.13	9.24
Production cost (Cp)	Total cost ($)	52.29	53,747	55.66	56.66	58.12
	Change in total cost (%)	−5.28	−2.64	0.00	2.64	5.28
Food waste (Wc)	Total cost ($)	55.13	55,168	55.24	55.24	55.28
	Change in total cost (%)	−0.13	−0.07	0.00	0.07	0.13

Source(s): Authors work

Funding: No funding was received to assist with the preparation of this manuscript.

Author contributions: Rahmi Yuniarti (RY) and Ilyas Masudin (IM) prepared the manuscript. RY and Dwi Iryaning Handayani (DH) modeled the formulations and interpreted the data. RY and Ahmad Rusdiansyah (AR) perform data collection, simulation and supervision. RY and IM were the major contributors to writing the manuscript. All authors read and approved the final manuscript.

Statement of informed consent: There are no human subjects in this article, and informed consent is not applicable.

Data availability: The datasets generated during and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Code availability: Not applicable.

Conflict of interest: The authors hereby declare that there are no potential conflicts of interest in terms of authorship, research and/or publication of this article.