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Liu, L.; Pu, Y.; Liu, Z.; Liu, J. Closed-Loop Supply Chains in Discrete Time. Encyclopedia. Available online: (accessed on 27 May 2024).
Liu L, Pu Y, Liu Z, Liu J. Closed-Loop Supply Chains in Discrete Time. Encyclopedia. Available at: Accessed May 27, 2024.
Liu, Lang, Yutao Pu, Zhenwei Liu, Junjie Liu. "Closed-Loop Supply Chains in Discrete Time" Encyclopedia, (accessed May 27, 2024).
Liu, L., Pu, Y., Liu, Z., & Liu, J. (2023, July 14). Closed-Loop Supply Chains in Discrete Time. In Encyclopedia.
Liu, Lang, et al. "Closed-Loop Supply Chains in Discrete Time." Encyclopedia. Web. 14 July, 2023.
Closed-Loop Supply Chains in Discrete Time

Durable products are mostly traded under discrete-time conditions, and consumers tend to have different purchase regret psychologies during the trading process of different types of durable products (innovative or remanufactured). In addition, different purchase regret psychologies can affect the dynamic decision-making behaviour of the nodal enterprises in the supply chain, thus affecting the dynamic decision-making optimization sequence of the supply chain and nodal enterprises. 

supply chain management post-purchase regret difference game Bass model closed-loop supply chain optimal decision-making

1. Introduction

The rapid development of science and technology has offered the market plenty of different functional characteristics of products meeting the diversified needs of people. However, the production process inevitably produces a large number of defective and waste products, resulting in environmental pollution and waste of resources [1]. According to the U.S. Environmental Protection Agency data, the resources obtained through the recycling of electronic scrap can reduce of ore energy by 97%, water consumption by 40%, air pollution by 86%, and water pollution by 76% compared to re-mining smelting. Recycling and remanufacturing used products can not only achieve the reuse of resources but also reduce production costs and help companies to achieve greater profits. Some companies such as Dell, Samsung, and Hewlett-Packard have established reasonable recycling systems, which not only develop a green, low-carbon, and environmentally friendly economic systems but also achieve economic benefits. A closed-loop supply chain can achieve a circular economy through the recycling of waste products [2]. Currently, academic research on the closed-loop supply chains has received much attention, and many scholars provide decision guidance for decision-makers in the supply chains by researching the closed-loop supply chain management. Mehran et al. [3] found that under stochastic demand and returns, manufacturing and remanufacturing costs are decisive for the optimal remanufacturing rate, and that an increase in the remanufacturing rate reduces the cost of installing and ordering products in the system and increases the volume of orders. Zhang et al. [4] designed a multi-product, sustainable, uncertain closed-loop supply chain network and found that an increase in customer demand can have strong economic and environmental impacts.

2. Optimal Decision-Making for Closed-Loop Supply Chains

The study of closed-loop supply chains can be divided into static and dynamic situations based on the changes in the decisions of the supply chain members over time. In addition, the decisions of the supply chain members are unchanged over time in a static environment. Xu et al. [5] studied closed-loop supply chains with abatement-dependent demand and found that when members make decisions to maximize their interests, a double profit effect occurs, which affects the operational efficiency of the closed-loop supply chain. Wang et al. [6] developed a two-period production decision model to study the impact of carbon taxes on optimal production decisions for new and remanufactured products. Zhang et al. [7] studied the choice of two third-party remanufacturing models, the outsourcing model, and the licensing model. Sun et al. [8] considered recycling product waste for remanufacturing using three-dimensional printing by building a competitive circular closed-loop supply chain and found that suppliers would avoid using recycled materials to print high-quality products. Kumar et al. [9] studied the problem of closed-loop supply chain management in cooperation with a hybrid production system in a stochastic market demand scenario, comparing the results of various incentive-based policies in both continuous and unspecified distribution. Allah et al. [10] constructed a multi-cycle closed-loop supply chain consisting of four participants and used the supplier’s operational inventory management strategy and consignment-based inventory management strategy to manage the products; they found that the retailer was always able to maximize the profit of a closed-loop supply chain.
Unlike the situation in a static environment, the decisions of the members of the supply chain change over time in a dynamic environment. Giovanni [11] used a goodwill model to study a closed-loop supply chain of single manufacturers and single retailers investing in green advertising and found that participants can limit the utility of green advertising by pursuing reverse revenue-sharing contracts. Later, Giovanni et al. [12] also examined a closed-loop supply chain consisting of a single manufacturer and a single retailer and found that optimal incentive strategies for product recall exist in the closed-loop supply chain when participants both assume that another participant implement the incentive strategy for the product take-back. Yang and Xu [13] established a closed-loop supply chain network consisting of multiple manufacturing and remanufacturing plants and multiple distribution centres in the context of a low-carbon economy and explored the impact of carbon emissions on the optimal decision-making strategies of supply chain participants. Xiang and Xu [14] studied a closed-loop supply chain consisting of a manufacturer, a retailer, and an internet service platform and constructed a dynamic goodwill model for two scenarios: retailer payment and manufacturer sharing. On this basis, Xiang and Xu [15] considered the impact of big data marketing, technological innovation, and overconfidence on the closed-loop remanufacturing supply chain and found that an appropriate cost-sharing ratio can be a “win-win” for both the manufacturers and third-party Internet recycling platforms, but excessive confidence levels can dampen the incentives for cost-sharing strategies and negatively affect the interests of the manufacturers. Singh et al. [16] investigated the impact of inflation on supply chain profits by constructing a three-level supply chain model and found a negative correlation between the supply chain profits and the rate of inflation.
A comparison of the advantages and disadvantages of static and dynamic closed-loop supply chains is shown in Table 1:
Table 1. Comparison of static and dynamic closed-loop supply chain research.

3. Closed-Loop Supply Chains in Discrete Time

Generally, decisions made in a closed-loop supply chain are of discrete time. Specifically, the strategy for each period will last for some time before it changes again, and finally the decision-maker combines the optimal decisions for each period to obtain an optimal sequence of decisions. For example, after a new Apple phone is launched, the seller will adjust the price according to the market feedback. If the market response is not good, the seller will adjust the price according to the channel price, and the store will reduce the price to promote. Between 29 July and 1 August 2022, the price of iPhone 13, iPhone 13 mini, iPhone Max, and iPhone 13 Pro was reduced by CNY600, while the price of iPhone 12 and iPhone 12 mini was reduced by CNY500. The dynamic situation with discrete decision time is more realistic than the dynamic situation with continuous time, so it is more practical to study the closed-loop supply chain under the dynamic situation with discrete time. Huang et al. [17] used the control theory dynamic analysis to develop a dynamic closed-loop supply chain model for a class of linear discrete-time systems and proposed a related strategy with a robust H1 control method to effectively suppress all uncertainties in this closed-loop supply chain system. Mahmoudzadeh et al. [18] proposed a robust decision optimization method to solve the production/pricing problem in a hybrid manufacturing/remanufacturing system by building a closed-loop supply chain in discrete time, which enables decision-makers to make rational decisions in each period of demand and return uncertainty. Zhang et al. [19] transformed the basic model of a closed-loop supply chain in which manufacturers and recyclers simultaneously recycle uncertain products into a nonlinear fuzzy switching model based on a discrete T-S fuzzy control system for their study and found that this approach not only suppresses the bullwhip effect but also allows the supply chain to maintain stability. Javid et al. [20] investigated the design problem of closed-loop supply chain networks in discrete time by developing a single-objective deterministic mixed-integer linear programming model. Gholizadeh et al. [21] investigated a multi-layered closed-loop supply chain for a disposable appliance recycling network in a discrete-time stochastic scenario to maximize the value of returned and manufactured products.

4. Product Heterogeneity

Remanufactured products and innovative products are not exactly the same. Innovative products mainly refer to new product development or old product upgrade [22], entering the market in the form of a brand new product. For example, the panoramic camera can realize a 360-degree photography without dead angle, which is a brand new product in the market, but its picture quality has a large gap with traditional cameras. If consumers have little need for panoramic recording but purchase the product, they may easily regret it. In contrast, remanufactured products are recycled waste products for remanufacturing treatment, and the product itself has not changed (such as the recycling of iPhones [23]). Therefore, innovative products and remanufactured products are heterogeneous, which will be focused on the sales process.

5. Bass Model

In 1969, Bass proposed a model for predicting sales of innovative consumer durables [24] and verified the feasibility of the model in relation to 11 common durable products. Subsequently, Robinson et al. [25] further considered the impact resulting from the price factor. Cesare et al. [26] determined the optimal product price and advertising strategy by building a Stackelberg differential game model. Fibich et al. [27] investigated the impact of boundary effects on the diffusion of new products by using a discrete Bass model.

6. Consumer’s Purchase Regret Psychology

In the past, scholars often use the “rational economic man hypothesis” in their research, which assumes that consumers’ attitudes toward products are completely rational [28]. In fact, after purchasing a product, consumers often regret the purchase because the product does not meet their psychological expectations, which is called purchase regret psychology, and the research on regret psychology can be divided into static and dynamic situations. Nasiry et al. [29] investigated the impact of two types of consumer regret decisions, early purchase and delayed purchase, on firm profits and policies in a presale environment with uncertain buyer valuation in the static case. Davvetas et al. [30] found that consumers’ brand identity can weaken the negative effects of regret psychology on satisfaction and behavioural intentions. Arslan et al. [31] used the SID strategy to study consumer repurchase behaviour and purchase regret psychology. Grigsby et al. [32] found that by recalling previous satisfying purchase experiences, consumers were able to reduce recent regrets of impulse purchases.


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