Research Article  Open Access
Emergency Strategies of ClosedLoop Supply Chain with Single Retailer Recycling under Demand Disruptions
Abstract
The uncertainty caused by emergencies will influence the normal operation of the supply chain. Considering demand disruptions, a closedloop supply chain consisting of one manufacturer and two competing retailers based on decentralized decisionmaking is considered. In the supply chain, one retailer recovers endoflife products while the other does not. Analytic results show that, when the disturbance of demand occurs, the manufacturer and retailers adjust the wholesale price and retail prices of products according to the direction of the market demand disruptions. Under demand disruptions, the retailer who participates in recovering can gain more profits, especially in the case of the positive disruption. Theoretic and pragmatic references for the emergency decisionmaking of closedloop supply chain enterprises are provided.
1. Introduction
Enterprises are paying more attention than ever to the ClosedLoop Supply Chain (CLSC) in response to governmental regulation and public concerns on environmental pollution and resource consumption. CLSC management has been a popular item on agendas of various industries in the United States since 2005, including automobile, refrigerator compressor, electronic instruments, machinery manufacturing, office appliances, tires, cartridges, industrial valves, and so on. In the past decade, the task of developing CLSC in China has been accepted as a vital need for enterprises. The Chinese government has implemented the Circular Economy Promotion Law which underlines the CLSC management since 2009, and revised it in 2018.
Actually, enterprises participating in CLSC operation can not only win the market share and considerable profits but also have a good impact on the whole ecological environment [1–4]. For instance, Xerox Corporation provides prepaid mailboxes so that customers can easily return their used copy or print cartridges to Xerox without any costs [5]. According to the analysis report of the American Iron and Steel Association, remanufacturing of scrap steel products in the United States has achieved remarkable results: saving energy by 47%–74%, reducing air pollution by 86%, reducing water pollution by 76%, reducing solid waste by 97%, and saving water by 40% [6].
Academic research on CLSC has been quite rich, but most of the literature still focused on the operation of CLSC under stable demand. With the increasingly rapid economic globalization, once an unexpected event interferes with a node in the supply chain, it can easily affect the operation of other parties in the supply chain. For instance, in 2008, the global economic crisis led to a sharp reduction in orders in the industrial chain and a decline in demand from downstream producers, which directly led to a clifflike decline in supplier output. In 2011, the earthquake of 9.1 magnitude that took place 321 miles northeast of Tokyo at a depth of 15.2 miles, which is the largest earthquake even to hit Japan, caused a shortage of auto parts exports, which led to a substantial increase in the manufacturing costs of several major Japanese joint venture car enterprises located in China.
Supply chain emergencies refer to risks caused by exogenous events and disruption of normal activities of enterprises on the chain [7]. By studying the irregularity and seriousness of emergencies from two aspects, including possibility and impact of supply chain risk management, it can be concluded that emergencies have the characteristics of low probability of occurrence and high impact consequences [8, 9]. In this situation, enterprises are required to quickly formulate emergency decisionmaking plans when supply chains are disrupted.
This paper explores a closedloop supply chain with one manufacturer and two retailers. One of the retailers participates in waste product recovering. The manufacturer decides the wholesale price as well as the compensation price, while the retailer chooses the retail price, recovering rate, and order quantity. The objective of this paper is to investigate the impact of demand disturbance on supply chain members and to analyze how manufacturers and retailers with dynamic game relationships make optimal emergency decisions when some emergent events occur. A game theoretic model of a closedloop supply chain with one manufacturer and two retailers is established to solve the following problems.(i)What are the optimal decisions of supply chain members when demand disruption occurs?(ii)Is there a direct relationship between retailers’ participation in recycling and their market competitiveness under demand disruption?(iii)What are the influences of different market demand disruptions on the decisionmaking of CLSC members?
The contributions of this paper are summarized as follows. Firstly, the impact of demand disruption on optimal CLSC decisions and profits is examined, when the dynamic game between retailers is considered simultaneously. Secondly, the optimal decisions are analyzed from the perspectives of both the manufacturer and the two retailers. Thirdly, practical suggestions on how to maintain the market competitiveness of retailers under demand disruption are put forward. The remainder of this paper is organized as follows: Section 2 reviews the related literature in the field of supply chain management. Section 3 establishes the model and obtains the optimal results under stable condition. Section 4 discusses CLSC optimal decisions under demand disruption. Section 5 provides numerical examples to examine the propositions and shed practical implications. Finally, the conclusions and future research directions are summarized in Section 6.
2. Literature Review
In recent years, scholars have carried out research on different types of CLSC problems. Savaskan et al. [5] investigate how reverse channel choice affects the forward channel decisions and the usedproduct return rates by considering three different modes in the collection channels of manufacturers, retailers, and third party participation in recycling. Yang et al. [10] developed a model of a general CLSC network, which formulates and optimizes the equilibrium state of the network using variational inequalities. Shi et al. [11] studied the production planning problem for a multiproduct closedloop system, in which the manufacturer has two channels for supplying products: producing brandnew products and remanufacturing returns into new ones. They maximize the manufacturer’s expected profit by jointly determining the production quantities of brandnew products, the quantities of remanufactured products, and the acquisition prices of the used products, subject to a capacity constraint. Choi et al. [12] investigated a CLSC which consists of a retailer, a collector, and a manufacturer, and examined the performance of different CLSCs under different channel leaderships. Through a systematic comparison, they find that the retailerled model gives the most effective CLSC. Huan et al. [13] considered optimal strategies of a CLSC with a dual recycling channel, within which the manufacturer sells products via the retailer in the forward supply chain, while the retailer and the third party competitively collect used products in the reverse supply chain. Abbey et al. [14] studied empirically to investigate consumer perceptions of remanufactured consumer products in the CLSC. The results indicate that discounting had a consistently positive, linear effect on remanufactured product attractiveness. Moreover, consumers who consider remanufactured products green typically found remanufactured products significantly more attractive. De Giovanni et al. [15] considered a dynamic CLSC with one manufacturer and one retailer, both of which are investing in a product recovery program to increase the return rate of previously purchased products. Gaur et al. [16] developed an integrated optimization model for ClosedLoop Supply Chain Configuration (CLSCC) and presented a realworld case study of a battery manufacturer. They discussed the key observations and managerial implications drawn from the computational experiments. The significant outcomes of the study suggest that the performance of the firm’s base case integrated CLSCC model is significantly better than the current supply chain model. Reimann et al. [17] focused on the link between remanufacturing and the opportunity to lower the variable remanufacturing cost via process innovation. Their analysis also shows that compared with integrated supply chain, decentralized supply chain is more likely to take up manufacturing, especially when the cost of process innovation is sufficiently high.
From above, most literature assume that the internal and external environments of CLSC remain stable. In actual operations, however, any kinds of unexpected events (market or human factors, such as natural disasters, terrorist attacks, national conflicts, and economic turbulence) will make the optimal decisionmaking under stable conditions unfeasible. Therefore, the research on dealing with supply chain emergencies has attracted wide attention of scholars, and disturbance management emerged. Disruption management was first proposed by Clausen et al. [18] and was initially applied in the fields of aviation as well as supply chain management. Qi et al. [19] considered the impact of emergency management on supply chain based on the work of Clausen and opened up a new avenue for supply chain management. Kleindorfer and Saad [20] investigated risks arising from natural disasters, strikes, and economic chaos, as well as acts of purposeful agents, including terrorists. The implications for the design of management systems intended to cope with supply chain disruption risks discussed. Xiao et al. [21] studied the impact of two pricesensitive, partially replaceable retailers who bear the production deviation cost caused by accidents on production planning. Hou et al. [22] explore the contract coordination mechanism between the manufacturer and the two suppliers in the case of demand uncertainty and supply risk. Huang et al. [23] provided a twoperiod pricing and production decision model in a onemanufactureroneretailer dualchannel supply chain and examined how to adjust the prices and the production plan to meet the maximal profit under a disruption scenario. Huang et al. [24] showed how the members of a centralized and decentralized dualchannel supply chain adjust their production plans according to the disturbance of production costs. Giri and Sharma [25] considered a CLSC inventory system involving a singlemanufacturer and a singleretailer with stochastic market demand and random return of used item. They proposed the optimal quantity of finished products manufactured from raw materials to maximize the total profit of the integrated system. Huang and Wang [26] investigated cost disruptions of new and remanufactured products in a CLSC where a manufacturer and a thirdparty collector recycle used products through onlinerecycling and offlinerecycling channels, respectively. Huang and Wang [27] studied disruptions of market demand and supply quantity of used products in a CLSC where the manufacturer licenses the third party to undertake remanufacturing activities.
To the best of our knowledge, very few research results on emergency strategies of CLSC in a single retailer recycling under demand disruption have been achieved. We attempt to fill the research gap by including such concerns, which highlights the originality and contributions of this paper. We construct a CLSC model based on decentralized decisionmaking, which is composed of one manufacturer and two competing retailers. One retailer participates in the recovering of waste products, while the other does not. This paper discusses the emergency decisionmaking of supply chain members under demand disruptions. The research work could provide some references for the emergency decisionmaking of CLSC enterprises.
3. The Basic Model
3.1. Model and Symbolic Description
The supply chain consisting of a single manufacturer and two competing retailers is considered in this paper. The manufacturer dominates in the production of two products: new products and remanufactured products. The remanufactured products, having the same quality as the new ones, are processed from the waste products recovered by the retailer. Two competing retailers are in a follower position in the supply chain operation. They get new and remanufactured products at the same wholesale price from the manufacturer. Each retailer independently decides the price for two kinds of products; hence, different prices are set according to two retailers. We suppose that waste products are recovered by only one of the retailers (retailer 1). The basic model is shown in Figure 1 with all notations introduced in Table 1.

3.2. ClosedLoop Supply Chain Decisions under Stable Condition
The profit functions of the manufacturer and two retailers are obtained as follows:
In the decentralized decisions of the closedloop supply chain where the manufacturer acts as the Stackelberg leader, the solution of the following proposition (see Appendix A for proof) is obtained by using backward induction method (the superscript represents the optimal solution). For convenience, we define
Proposition 1. In the closedloop supply chain where a single retailer is responsible for recovering the used products, the optimal strategies of the manufacturer and retailers are given as follows:(a)The wholesale price ( ), compensation price (b), and profit () are obtained as(b)The retail price , recovering rate of waste products , and profit of retailer 1 are shown as(c)The retail price and profit of retailer 2 are displayed as(d)The total sales of the two retailers are presented as .
4. ClosedLoop Supply Chain Decision under Demand Disruption
When the disturbance of demand occurs, the market size is turned into , while the market demand of the retailer is changed to (i, j = 1, 2, “–” represents the results of market disruption). When , the optimal strategy under stable condition cannot meet the demand due to the sudden expansion of the market; therefore, additional production costs will be generated. When , the supply chain will suffer additional processing costs due to abrupt decrease of market size. It is assumed that the additional production or processing costs are borne by the manufacturer.
Based on the basic model and abovementioned assumptions, profit functions of the manufacturer and retailers under demand disruptions are obtained as follows.
Lemma 1. Under demand disruption caused by emergencies, if , then , . On the contrary, if , then , . and are, respectively, the optimal order quantity and recovering rate of waste products.
The proof is given in Appendix B.
4.1. Scenario I
When , strategies of retailers in Lemma 1 can be summarized as the following optimization problems.
The optimal retail prices and and recovery rate of retailers, which are functions of wholesale price and compensation price , can be obtained. The solution process is introduced as follows.
Taking partial derivative of with respect to and and partial derivative of with respect to , let , , and , we can get
By substituting equations (9) and (11) into equation (4), the decisionmaking problem of the manufacturer can be transformed into the following optimization problem.
Equation (13) shows that when the market's demand suddenly occurs positive disruption, the expected order quantity under the stable condition cannot meet the actual order quantity. Equations (14) and (15) show that the recovery rate of retailer 1 under the demand disruption should not be lower than that under the stable condition. We use the backward induction method to solve (P1), (P2), and (P3) and derive the following proposition.
Proposition 2. When , the optimal compensation price of the manufacturer under decentralized decisionmaking is , the optimal wholesale price and the optimal profit of the manufacturer are, respectively, and , as shown in Table 2.
As is indicated in Proposition 2, when , under different disruptions, the optimal compensation price of the manufacturer remains constant as , with strong robustness. With the increase of market demand, the manufacturer will suffer additional production costs. So, the manufacturer would improve the wholesale price to compensate extra costs. With the increase of the wholesale price, the retailer must maintain its profits by raising the retail price, to control the excessive increase of market demand. Additionally, the manufacturer’s optimal profit increases as the market demand disruption increases.
 
, , . 
Proposition 3. When , the retailers make strategies to pursue profit maximization after observing the manufacturer's decision. The results are shown in Tables 3 and 4.
When , the optimal recovery rate of retailer 1 and the optimal total orders are as same as the optimal solution under stable condition. When , with the increase of the wholesale price of the manufacturer, retailer 1 can transfer additional production costs to consumers via increased retail price. It can not only compensate for the loss caused by the manufacturer’s increasing wholesale price, but also maintains their own profits. When , the recovery rate of retailer 1 reaches a maximum value of 1 (that is, all waste products in the market can be effectively recycled). The profit of retailer 1 increases when the demand disruption occurs.
To sum up, under the demand disruption, the retail price of retailer 2 is higher than that of retailer 1. Being in competition with retailer 2, retailer 1 can get extra profit via recovering the waste products and will increase its market sales by lowering the retail price. In terms of profit, retailer 1 can also get more profits than retailer 2.
 
, . 

4.2. Scenario II ()
When the demand disruption , the profit function of the manufacturer is as follows:
By using Karush–Kuhn–Tucker (KKT) conditions, the decisionmaking problem of two retailers can be transformed into the following optimization problems.
Similarly, the decisionmaking problems of the manufacturer can be transformed into the following optimization problems.
Equation (19) indicates that when the market’s demand size suddenly shows negative disruption, the expected order quantity under the stable condition exceeds the actual order quantity under demand disruption. Equations (20) and (21) are used to ensure that the constraints of retailer 1 can be effectively satisfied. We use the backward induction method to solve (P4), (P5), and (P6) and derive the propositions as follows.
Proposition 4. When , the optimal compensation price of the manufacturer under decentralized decisionmaking is , while the optimal wholesale price and the optimal profit of the manufacturer are, respectively, and , as shown in Table 5.
It can be seen from Proposition 4 that, when , under different disruptions, the optimal compensation price of the manufacturer still remains , with strong robustness. The wholesale price of the manufacturer is inversely proportional to the absolute value of market demand disruption. That is, the larger the decrease of demand is, the lower the wholesale price is. With the reduction of the wholesale price of the manufacturer, the retailer will decrease the retail price, in order to control the excessive reduction of market demand. By substituting the optimal solution of the manufacturer and into the profit function of retailers, the optimal solution under the demand disruption can be obtained.
 
. 
Proposition 5. When , with the goal of maximizing their own profits, the retailers develop their own optimal strategy based on the manufacturer's decision. The results are shown in Tables 6 and 7.
When , the optimal recovery rate of retailer 1 and the optimal total orders are the same as the optimal solution under stable condition, with strong robustness. The change of the retail price of retailer 1 and the wholesale price of the manufacturer shows consistent trends. Retailers must reduce prices to avoid unsalable products due to the reduction of demand. Therefore, profits of retailers are greatly reduced.
Comparing with Tables 6 and 7, we can see that the retail price of retailer 2 is higher than that of retailer 1. With the extra profit from the recovery of the waste products, retailer 1’s profit is higher than retailer 2’s even when the market demand reduces. Therefore, retailers who do not participate in recovering will have less ability to stabilize the market than retailers who participate in recovering waste products under demand disruption.
 
. 
