對環境愈漸重視的的現今，每個人都能舉手之勞地落實資源回收，成為生態永續循環中責無旁貸的一份子。許多企業運用二手品再生作為原料，延長了原本供應鏈的長度，使用過的商品重新被納入供應鏈中，再次產生價值，逆向供應鏈、再製造系統等運作因而蓬勃。此外，近年來物料成本的上漲，回收不僅是環保意識使然，更能帶來經濟上的效益。
由於回收品品質參差不齊，因應單一新品市場的情況，僅納用某程度品質之上的回收品，未達標準者只能報廢處理，可能造成浪費。許多產業，如二手車、機械設備、電子產品等，都有次等品市場的商機，透過收購無法恢復至新品狀態的廢舊品，用較低的價格售出、或是拆卸為零件做其他用途等，一樣能二度產生使用價值。
因此，本研究考量了具兩個品質分級市場的逆物流供應鏈，之中存在兩個零售商通路，可代表其兩個零售商所屬的群體。製造商可經由雙零售商通路獲取二手品、或是自行回收。在以製造商為先行決策並有策略優勢的情況下，使用進化穩定策略的方法，分別求得各方之策略，再透過導入數值到所建立的模式中，進行數值分析，了解可能造成穩定策略改變之影響因素及其影響程度。
透過數值分析的結果，可以發現，在不同的條件下、面臨不同的競爭強度時，皆有可能傾向不同的策略選擇。在模型建構部分所求得的結果，能幫助決策者快速地因應某數值條件，了解在這個情狀之下、應如何做決策。

SUMMARY

Sustainable development has become a popular issue these years. Governments have promoted recycling and reusing to public. One can easily implement environmental protection concepts by little effort. Companies benefit economically from using recycled products as raw materials to reduce costs. Usually, recycled products in good condition are adopted. Remaining products are rejected, which waste a lot. There are opportunities for the secondary market in some industries, like second-hand car, mechanical equipment and electronic product. Second-class recycled products can be remanufactured and sold in lower prices. Besides, they can also be disassembled as parts for other uses. This study considers a reverse supply chain which has two quality-grading markets. There are two competing retailers. The manufacturer obtains used products by either purchasing from the retailers or collecting itself. The manufacturer has an advantage as a first decision maker. Under this circumstance, we use Evolutionarily Stable Strategy (ESS) to find appropriate strategies for every point of view. After we lead consequences of the model, numerical examples and sensitivity analysis are carried out. By this study, we can understand whether the factors we discuss are impact or not in this system, and how to make decisions when the numerical condition changes in different competitive strength.

INTRODUCTION

Rise in environment awareness for decades, going green for a sustainable Earth is a common concept. In Europe, there are statutes and regulations to confine electronic and mechanical waste. In Japan, Suntory, a consumer product company, reuses recycled plastic bottles to 50% for the environmental care. Nevertheless, not only governments and large enterprises act eco-friendly, but many companies do. Several products use cannibalized design, only the depleted part should be replaced by new component, like toner cases and refills. According to the above, quality grading in recycling relaxes restrictions of qualified recycled products and helps every core be reused if there is remaining value. Mitra (2007) considered two cellphone markets in India due to distinguish quality of commodities. The process is distributed into remanufactured products and refurbished products, which are separately sold to the markets.

Commodity flow in multi-channel in a supply chain is common. In reverse logistic, there might be multiple recycling pathways and might have competitive relationships. Savaskan et al. (2004) investigated three alternative reverse channel formats: (1) directly collect from customers, (2) contract the collection to the retailers, (3) contract the collection to a third party. In this study, there are one manufacturer and two retailers. Different competitive strength in different market conditions might influence the profits for each retailer. Hence, the manufacturer and the retailers face the decision-making problems in this situation.

Xiao & Yu (2006) considered rival retailers with four ESS in dissimilar circumstances, and found out the influential factors of their strategy. Li et al. (2014) considered an ESS in a retailer Stackelberg closed-loop supply chain, and found out the main factor of the strategy. We analyze influence level of some factors of our problem.

PROBLEM DECRIPTION AND METHODS

First, introduce the background of the problem. There is a primary market selling new products, and a secondary market selling the other valuable non-new ones. We discuss one manufacturer and two retailers in the reverse supply chain. The manufacturer has a remanufactured system, producing remanufactured products, which are as new products; and refurbished products, which are in slightly worse quality. End products in two quality levels are sold separately in two markets. Qualities of end products are decided by qualities of recycled products as raw materials. Thence, recycled items are divided into two quality levels when they are collected from customers. There are two retailers in the system. The manufacturer has an advantage as a first decision maker, it can either purchase recycled products from retailers or collect them itself. If it wants to purchase from the retailers, two retailers will both have to decide whether it participate in collecting recycled products or not. When the retailer does not take recycle strategy, the profit of the retailer is zero.

Second, we establish a mathematical model to find out ESS of the manufacturer and the retailers. We firstly state the profit functions of the manufacturer and the two retailers when they select different strategies and then take the expected payoffs of them. According to Malthusian Equation, we develop the recycled quantity’s growth rates of each. Using the growth rate functions, we apply the duplicated dynamic equation to depict the evolutionary course of the manufacturer and the two retailers’ strategies respectively. Under the stability theorem of differential equation, the equilibrium point should be less than zero after differentiation if there is an ESS.

Last, basis on the differentiated forms above, we figure out a reference value of each. With the reference value, we can judge what decision should be made immediately from everyone’s point of view whenever the numerical condition changes. We can view the reference values as formulas for seeking out strategies of each member in this system.

RESULTS AND DISCUSSION

We analyzed the problem with different parameters in the reference values, trying to find out the impact degree under different numerical conditions.

Three factors, quality ratio , collection rate and cost of classification , are discussed apart. We observe whether the factor severely affects the selection of strategy if its quantity changes, and how it affects the decision under different competing coefficient.

We divide the problem into two situations:
(1) Recycling source of the retailers is the same. Qualities of recycled items a retailer collected are uneven. But the quality ratios of the manufacturer and the retailers are all in line with the proportion of the quality ratio in the market , i.e., .
(2) Recycling sources of the retailers are not the same. One retailer is able to collect more items in better quality than the other due to some external factors. Thus, the proportions of two qualities recycled items in two retailers are different.

Judging by the results of sensitivity analysis, we can draw some conclusions as below. To retailers and manufacturer, changes in quality ratio will not affect decision making if they are still profitable. But it is adverse to the profit when the ratio gets lower. Collection rate becoming higher is not certainly good to the retailers since it makes one more easily be negatively influenced by competing coefficient and its collection rate or . To manufacturer, changes in is also affected to its profit and strategy selection. Therefore, collection rate is definitely an impact factor to the members. Last one is cost of classification . We can intuitively understand that higher cost is disadvantageous to everyone. But through the analysis results, we learn more about that retailer in higher collection rate itself is more significantly influenced by changing .

CONCLUSION

This thesis focuses on a quality-grading product in a reverse supply chain, considering multi-channel in recycling. The manufacturer has an advantage as a first decision maker, who should determine either to purchase recycled products from retailers or to collect them itself. Then the retailers might have a chance to decide whether it participate in collecting recycled products or not.

We seek for Evolutionarily Stable Strategy (ESS) of the members in the supply chain. So we establish a model to find out the stable strategies for the manufacturer and the retailers. Using the reference values of the members obtained, we can easily judge which decisions should be made under different numerical environments.

At the end, numerical examples and sensitivity analysis are carried out to analyze three factors in two situations. We found out that quality ratio is not impact to the strategy selection; collection rate and cost of classification might alter one’s decision under some certain circumstances.

The thesis can provide a method to the companies in a similar reverse supply chain system to develop a decision process that helps make decisions fast when facing variety.

施勵行 (2004) 資源再生與永續性社會：俊傑出版社。
鄭本榮、楊超、楊珺 & 曹曉剛 (2016) 閉環供應鏈的銷售渠道選擇與協調策略研究 系統工程理論與實踐，36，180-1192。
韓小花 & 薛聲家 (2010) 競爭的閉環供應鏈回收渠道的演化博弈決策 計算機集成製造系統，16，1487-1493。
Andritsos, D. A., & Tang, C. S. (2010). Launching New Products Through Exclusive Sales Channels. European Journal of Operational Research, 204, 366-375.
Apaloo, J., Brown, J. S., & Vincent, T. L. (2009). Evolutionary Game Theory: ESS, Convergence Stability, and NIS. Evolutionary Ecology Research, 11, 489-515.
Cachon, G. r. P., & Fisher, M. (2000). Supply Chain Inventory Management and the Value of Shared Information. Management Science, 46, 1032-1048.
Cheng, A. (2008). US Retailers Hope Licensing Brands Will Help Traffic, Profits. Dow Jones Newswire.
Choi, S. C. (1991). Price Competition in a Channel Structure with a Common Retailer. Marketing Science, 10, 117-134.
Ferrer, G., & Swaminathan, J. M. (2006). Managing New and Remanufactured Products. Management Science, 52, 15-26.
Fisher, R. (1930). The Genetical Theory of Nature Selection: The Clarendon Press.
Fleischmann, M., Bloemhof-Ruwaard, J. M., Dekker, R., Laan, E. v. d., Nunen, J. A. E. E. v., & Wassenhove, L. N. V. (1997). Quantitative Models for Reverse Logistics: A Review European Journal of Operational Rcsearch, 103, 1-17.
Friedman, D. (1991). Evolutionary Games in Economics. Econometrica, 59, 637-666.
Han, X. H., & Dong, Z. N. (2010). Reverse Channel Decision Analysis for Bilateral Competing Closed-Loop Supply Chain. Industrial Engineering Journal, 13(4), 23-27.
Huang, M., Song, M., Lee, L. H., & Ching, W. K. (2013). Analysis for Strategy of Closed-Loop Supply Chain with Dual Recycling Channel. International Journal of Production Economics, 144, 510-520.
Huizhong, D., & Hongli, S. (2012). Research on Duplication Dynamics and Evolutionary Stable of Reverse Supply Chain. Paper presented at the 2012 International Conference on Applied Physics and Industrial Engineering.
Jacobsson, N. (2000). Emerging product strategies: selling services of remanufactured products. IIIEE, Lund University.
Jr., V. D. R. G., & Wassenhove, L. N. V. (2009). The Evolution of Closed-Loop Supply Chain Research. Operations Research, 57, 10-18.
Kaya, O. (2010). Incentive and Production Decisions for Remanufacturing Operations. European Journal of Operational Research, 201(2), 442-453.
Lewontin, R. C. (1976). Evolution and the Theory of Games. Boston Studies in the Philosophy of Science, 27, 286-311.
Li, J., Du, W., Yang, F., & Hua, G. (2014). Evolutionary Game Analysis of Remanufacturing Closed-Loop Supply Chain with Asymmetric Information. Sustainability, 6, 6312-6324.
Ma, W.-m., Zhao, Z., & Ke, H. (2013). Dual-Channel Closed-loop Supply Chain with Government Consumption-Subsidy. European Journal of Operational Research, 226, 221-227.
Ma, W., & Zheng, A. (2014). Dual Recycling Channel Strategy of Closed-loop Supply Chain Based on Stackelberg Theory. Paper presented at the International Conference on Mechatronics, Electronic, Industrial and Control Engineering.
Mitra, S. (2007). Revenue Management for Remanufactured Products. Omega, 35, 553-562.
Qi, X., Bardb, J. F., & Yu, G. (2004). Supply Chain Coordination with Demand Disruptions. Omega, 32, 301-312.
Savaskan, R. C., Bhattacharya, S., & Wassenhove, L. N. V. (2004). Closed-Loop Supply Chain Models with Product Remanufacturing. Management Science, 50, 239-252.
Savaskan, R. C., & Wassenhove, L. N. V. (2006). Reverse Channerl Design: The Case of Competing Retailers. Management Science, 52, 1-14.
Smith, J. M., & Price, G. R. (1974). The Theory of Games and the Evolution of Animal Conficts. Journal of Theoretical Biology, 47, 209-221.
Tanimizu, Y., & Shimizu, Y. (2014). A Study on Closed-Loop Supply Chain Model for Parts Reuse with Economic Efficiency. Journal of Advanced Mechanical Design, Systems, and Manufacturing, 8, 1-12.
Teunter, R. H., & Flapper, S. D. P. (2011). Optimal Core Acquisition and Remanufacturing Policies Under Uncertain Core Quality Fractions. European Journal of Operational Research, 210, 241-248.
Walton, S. V., Handfiled, R. B., & Melnyk, S. A. (1998). The Green Supply Chain: Integrating Suppliers into Environmental Management Processes. International Journal of Purchasing and Material Management, 34, 2-11.
Wei, J., Govindan, K., Li, Y., & Zhao, J. (2015). Pricing and Collecting Decisions in A Closed-Loop supply Chain with Symmetric and Asymmetric Information. Computers & Operations Research, 54, 257-265.
Xiao, R., Yu, R., & Zhu, L. (2011). Evolutionary Game on the Utility Decision of the Duopoly Retailers' Marketing Objectives. Advanced Materials Research, 314-316, 2312-2317.
Xiao, T., & Chen, G. (2009). Wholesale pricing and evolutionarily stable strategies of retailers with imperfectly observable objective. European Journal of Operational Research, 196, 1190-1201.
Xiao, T., & Yu, G. (2006). Supply chain disruption management and evolutionarily stable strategies of retailers in the quantity-setting duopoly situation with homogeneous goods. European Journal of Operational Research, 173, 648-668.
Yan, B., Wang, T., Liu, Y.-p., & Liu, Y. (2016). Decision Analysis of Retailer-Dominated Dual-Channel Supply Chain Considering Cost Misreporting. Int. J.ProductionEconomics, 178, 34-41.
Yan, R., Wang, J., & Zhou, B. (2010). Channel Integration and Profit Sharing in the Dynamics of Multi-Channel Firms. Journal of Retailing and Consumer Services, 17, 430-440.
Yi, Y., & Yang, H. (2017a). An evolutionary stable strategy for retailers selling complementary goods subject to indirect network externalities. Economic Modelling, 62, 184-193.
Yi, Y., & Yang, H. (2017b). Wholesale pricing and evolutionary stable strategies of retailers under network externality. European Journal of Operational Research, 259, 37-47.