Optimizing sustainable cocoa supply chains: A Closed-loop model considering a profit-sharing policy and value loss during storage

In various cocoa-producing nations, cocoa stands as a vital commodity, serving as the generates significant waste in the form of husks, which could potentially be repurposed into organic fertilizers. Unfortunately, most existing studies on cocoa supply chains overlook the management of cocoa waste through a closed-loop supply chain (CLSC) framework. This study addresses this gap by presenting a comprehensive model for a cocoa CLSC system that considers value loss within the supply chain. Moreover, a profit-sharing strategy is introduced to foster sustained collaboration among stakeholders. Through the optimization of decision variables e.g. the size of transfer batch, this model aims to maximize total profit within the cocoa supply chain. The result shows that the optimal size of transfer batch is 459 units which leads to 44,782,000 IDR total profit. Additionally, by reusing cocoa husks as organic fertilizers within a closed-loop supply chain, this model also contributes to reducing environmental impact and promoting sustainability within the cocoa industry.


Introduction
Cocoa beans serve as the raw material used for producing a range of chocolate-based products [1].According to [2] cocoa pods have a morphological structure with a percentage of cocoa bean only 24% of the fruit unit, while the epidermis waste is 2% and cocoa pod husk is 74%.It means that if one cocoa pod weighs 500 grams, it produces 120 grams of cocoa bean and 380 grams of waste.Thus, harvesting in large quantities will produce abundant waste.Most of the cocoa waste has not been utilized and is only discarded to rot [3].As a result of excessive decay of cocoa waste, it will adversely affect environmental pollution [4].In fact, cocoa pod husk has a C-Organic content of 26.61%, C/N Ratio < 20, pH 5.4, (N + P2O5 + K2O) of 4.84 which are important substances in organic fertilizer [5].Therefore, the abundant of cocoa waste needs to be managed well, e.g.reprocessed them into an organic fertilizer.
Until now, the cocoa waste is managed independently by players within the supply chain.Several studies conducted by [6][7][8] identified various supply chain network structures in different regions.None of the studies consider a reverse flow of materials where the cocoa waste is changed into an organic fertilizer which is used by cocoa farmers to fertilize their farms.In fact, if the waste could be organized in an effective and efficient way within supply chain system, the total operation cost would be minimized.Therefore, it is necessary to design a supply chain network that improve the flow of cocoas including its waste hence it would give positive impacts on economic, environment and society.This study proposes a utilization of a closed loop supply chain (CLSC) model for managing the cocoa flows.The cocoa waste flows back into the upstream of supply chain and becomes the input of the system.
Previous research on Closed Loop Supply Chain (CLSC) has been done as a solution to problems in supply chain network systems in various industrial fields, including food industries, such as in [9][10][11][12].A CLSC study done by [9] optimized the profit of palm oil supply chain where a Linear Programming (LP) mathematical model is utilized.The results showed that the reverse logistics flows had a positive impact on economic profits in the supply chain of the complex agro-industrial sector.On the other side, a research conducted by [10] discusses optimizing the shrimp supply chain network with the aim of minimizing total costs using CLSC perspective.Further, Xie et al [11] develop CLSC implemented on the food industry to manage mushroom within the supply chain network.They used a multi-objective CLSC model e.g.minimizing total supply chain costs and minimizing the total costs for dealing with environmental impacts.Meanwhile, research by Roghanian et al. [12] focuses on optimizing the orange or citrus industry supply chain with multi-objective mathematical modelling by considering three aspects of sustainability including maximizing demand responsiveness, minimizing total costs and carbon emissions.
Those studies assume that all players in the supply chain network have the same commitment to coordination.Meanwhile, in general, in the cocoa supply chain system in Indonesia, farmers have the choice to coordinate or not with other players in the supply chain [6][7][8].Therefore, a coordination mechanism is designed to be benefitted all players in the supply chain network (e.g. a win-win solution strategy).One mechanism that can be implemented is a profit-sharing strategy [13].In this mechanism, a fairness sharing will be distributed to all parties involved in the supply chain.Profits resulting from business or investment are shared fairly based on a percentage or ratio that has been previously agreed upon by all supply chain players involved [14].
Many studies have been conducted on profit sharing and revenue sharing.[15] proposed a three-stage supply chain coordination model in the manufacturing industry based on a revenue sharing mechanism.This model allows an efficient system to be achieved and can increase the profits of all players in the supply chain.Meanwhile, other research using a revenue sharing mechanism using a closed loop supply chain system was carried out by [16].The research examines the coordination of a closed, continuous supply chain involving one manufacturer and two retailers competing on price.Apart from that, this research also considered the characteristics of risk taking (risk aversion) possessed by producers and retailers.A study done by [17] implement a profit sharing mechanism for CLSC in agrifood industries.Producers offer a fairness profit through a discounted price mechanism (depends on the size of the cocoa pod transfer batch) for the reverse flows.However, this approach still ignores the value loss which may occur in agrifood products such as considered by [18][19][20].
The profit-sharing mechanism in [17] may cause farmers would store cocoa pods to obtain maximum profit due to minimizing the transportation costs as well as elevating the benefit of deliver a higher transfer batch to its downstream partner.In addition, after harvested the cocoa pods are stored for a certain time to reduce the pulp content that cover the wet cocoa beans to obtain the quality of cocoa beans [21].However, according to research by [22] the storage time of cocoa pods is at risk of quality deterioration or value loss of the cocoa beans produced.Storage of cocoa pods for 21 days caused cocoa beans to germinate with a percentage of 11% on the fourth day and 18% on the sixth day during the fermentation process, a value far above the acceptable level of 5% in good fermentation.In addition, another impact of storing cocoa pods for too long can cause cocoa beans have unwanted mold with a percentage of 3% on the fourth day and 5% on the sixth day during the fermentation process.This will degrade the quality of cocoa pods which means that during a certain time, a value loss may occur to the cocoa pods.
Based on these studies, no research has been found in the CLSC models that apply profit sharing mechanisms as well as value loss during storage for problems in the agri-food industries.Therefore, this research is aimed at filling this gap by proposing a CLSC model on cocoa supply chain applying a profitsharing strategy where the value loss is considered in the developed model.

Research methods
The methods consist of several stages included (i) system characterization, (ii) modelling dan finally establishing (iii) numerical tests to evaluate the model behavior.At the system characterization stage, observation is done at one of cocoa supply chains in central java, specifically a village called Giriwarno located at Wonogiri.Interview with farmers, and stakeholders has been done to identified players within the cocoa supply chain.Fig. 1 illustrates the general system.Based on Fig. 1, the variables and parameters involved in the system are identified and adjusted to suit the real system.The supply chain players are divided into two groups, farmers as the cocoa suppliers and the villageowned enterprise (badan usaha milik desa or BUMDes) as the cocoa producer.BUMDes appeals farmers to join the CLSC system by offering the profit-sharing policy.After taking cocoa beans from the cocoa pods and sell them to the market, BUMDes reprocesses the waste and produces the organic fertilizer.The organic fertilizer is sold to farmers at discounted price as an implementation of the profitsharing policy.In other words, farmers would get benefits from selling their cocoas to BUMDes through price reduction mechanism while buying the organic fertilizer from BUMDes.The higher the size of cocoas batch is delivered the more farmers will get benefits.The value loss is occurred to cocoa pods while farmers hold them in the storage.Once they reach the transfer batch size (Q), they will be delivered to BUMDes.[18].

Figure 2. Illustration of value loss cost and size of batch
The relation between the size of transfer batches and the value loss cost is referred to [18] as can be seen in Fig. 2. From this system characteristic, the variables and parameters involved are defined and the mathematical model is established.Further, to examine the model, MATLAB 2023 is used to conduct numerical tests.At the numerical tests, two scenarios are established.The first scenario is model evaluation without profit sharing policy meanwhile the second scenario, applying the profit-sharing policy.

Model development
The mathematical model is developed through two phases, the first is creating the profit sharing function and the second is establishing the value loss function developed by [18].As mentioned previously, the profit-sharing mechanism is established by BUMDes through a discount price for organic fertilizer when it is bought by farmers who sell their cocoa pods to BUMDes.The discount rate depends on the size of delivering/tansfer batch (Q) as illustrated in Fig. 3. Further, Eq. 1-3 represent the price of organic fertilizers at different Q which is ranged from minimum price (Cbmin) to maximum price (Cbmax).As seen in Fig. 3, there are three conditions of the fertilizer price function as following.If the selected Q is smaller than the minimum batch or the Qlow (to get discount) then the price will be maximum or farmer will pay at regular price which means that there is no discount as represented by Eq. 1.Farmers will get discount if the size of cocoa pods transfer batch higher than Qlow and it is continued until the maximum transfer batch or Q up (Eq.2).Further, the selected Q is subordinated of the minimum price once it is higher than the highest Q as presented by Eq.3 (means that there is no more discount after the highest Q).

𝐶𝑏 𝑚𝑎𝑥 → 𝑄 ≤ 𝑄 𝑙𝑜𝑤
(1) It is assumed in the model that the demand of cocoa bean comes from market to BUMDes at size D which drives demand of cocoa pods from farmer at size of 4D (the ratio between cocoa bean and cocoa pods is 1:4) and leads to 1.5D for organic fertilizer (the ratio between organic fertilizer and cocoa waste is 1:2, all waste from cocoa bean process goes to organic fertilizer factory).
Further, adopting [18] to represent the value loss then the total profit function for farmers, BUMDes and both can be seen in Eq. 4-6.
Where V1, V2 and V3 respectively represent the price of cocoa pods, cocoa bean and organic fertilizer,  =   ⁄ is the delivery frequencies, S1 and S2 are the setup cost of cocoa bean and organic fertilizer factory, Ct1 and Ct2 are the transportation cost of cocoa pods and cocoa bean, while p (the picking rate) and   =  − (the transfer time function) are notation developed by blackburn 2009.

Numerical test
A numerical test using Matlab software is conducted based on the given parameters in Table 1.As can be seen in Fig. 5, the optimal value of transfer batch is ±459.45units leading to 44,782,000 IDR total profit of the CLSC system.Further, Tabel 2 shows that the profit-sharing strategy potentially increases the profit of the integrated system.Without profit sharing strategy, farmers would prefer to send the cocoa pods in smaller batch to avoid the value loss.It would significantly increase the setup and transportation cost in BUMDes which leads to a lower total profit.Changing the size of transfer batch around from 459 to 200 units will reduce the total profit around 12%.In assessing the impact of transfer batch size on profit and operational costs within the BUMDes system, it is imperative to consider the broader environmental implications.While the focus primarily rests on financial outcomes, the environmental dimension remains pivotal, especially in the context of sustainable cocoa production.The decision to optimize batch sizes not only influences economic gains but also ecological sustainability.
Moreover, within the global cocoa trade, local practices hold significance.In regions where BUMDes systems operate, aligning profitability with sustainability is paramount.Balancing economic viability with environmental stewardship can ensure resilience in the face of climate change and resource constraints.Adapting batch transfer sizes to minimize financial losses must also consider their ecological footprint.Therefore, while optimizing for profit within the BUMDes system is crucial, integrating environmentally conscious practices is equally vital.Implementing strategies that align profit motives with sustainability goals not only benefit local ecosystems but also contribute positively to the global cocoa industry, promoting responsible and resilient practices across international supply chains.This can be a potential study in the forthcoming research.

Conclusion
The established CLSC model, incorporating profit-sharing policies and cocoa product value loss, demonstrates a better performance in total profit compared to conventional models.Moreover, the impact of cocoa value loss during storage affects overall revenue and results.Therefore, exploring the correlation between cocoa batch transfer size, farmer picking rates and transfer batch could be an intriguing avenue for future research.Additionally, investigating sustainable practices in cocoa batch transfers, considering environmental impacts and resource conservation, could significantly contribute to the holistic sustainability of the cocoa industry.

Figure 1 .
Figure 1.Illustration of the observed system.

Figure 3 .
Figure 3. Discounted price of organic fertilizer.

Fig 4 .
Meanwhile Fig 5, shows the total profit at different values of Q.As seen in Fig 4, the higher Q will lead to a more value loss.Therefore, without profit sharing strategy, farmers will focus in reducing their cost by selecting the smaller Q and it may increase the total cost in BUMDes system.

Table 1 .
Model parameters, variables and their values.

Table 1 ,
Matlab software is utilized and the result can be seen at Table2and illustrated by Fig.4 and 5. Total profit of the proposed model.