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A study of closed-loop supply chain models with governmental incentives and fees

ProQuest Dissertations and Theses, 2009
Dissertation
Author: Karla B Valenzuela
Abstract:
A rich mixture of government incentives and fees to encourage the collection of used products and the subsequent remanufacturing has been increasingly utilized both domestically and internationally. In this paper, toward a fuller understanding of such government participation in closed-loop supply chains (CLSC's), we construct and analyze a series of game-theoretic CLSC models with remanufacturing. Specifically, we investigate a basic decentralized CLSC model, two government participation models of linear incentives and fees as well as of central coordination via alternative financial instruments, and a revenue-sharing contract model without the government participation. We also analyze the impact of competition among manufacturers in our results. A key differentiating feature in our government participation models is the incorporation of the revenue neutrality requirement from a government's perspective whose financial sources for such incentives must eventually reconcile with the financial sinks for such fees. By comparing and contrasting the equilibrium solutions and the economic consequences of these models, managerial insights and economic implications relevant to academics and practitioners including decision and policy makers are obtained. For example, we show how the government participation can induce an entry or prevent an exit of a CLSC when one or more members are unprofitable.

Table of Contents List of Tables .......................................................................................................................................... v List of Figures ....................................................................................................................................... vi Acknowledgement ................................................................................................................................ vii Abstract ............................................................................................................................................... viii 1. Introduction ........................................................................................................................................ 1 1.1 Research Objectives and Overview ............................................................................................. 1 1.2 Environmental Laws.................................................................................................................... 4 2. Literature Review ............................................................................................................................... 8 3. Closed-loop Supply Chain with One Manufacturer ........................................................................ 11 3.1 Description of the Supply Chain and Assumptions ................................................................... 11 3.2 Basic Model ............................................................................................................................... 14 3.3 Extended Model with Governmental Incentives and Fees ........................................................ 16 3.3.1 Special Cases of Extended Model .................................................................................. 23 3.3.2 Revenue Neutrality Constraint ....................................................................................... 25 3.3.3 Optimal Incentive and Fee for the Extended Model ....................................................... 27 3.4 Centrally Coordinated Model .................................................................................................... 30 3.5 Alternative Financial Instruments ............................................................................................. 31 3.5.1 Allocation Mechanism .................................................................................................... 32 3.6 Entry and Exit Implications of Governmental Participation ..................................................... 33 3.6.1 The Case of the Unprofitable Manufacturer only ........................................................... 34 3.6.2 The Case of the Unprofitable Collector only .................................................................. 37 3.6.3 The Case of the Unprofitable Collector and Unprofitable Manufacturer ....................... 38 3.6.4 Impact of Centrally Coordinated Model on Unprofitability ........................................... 40 3.7 Revenue-Sharing Contract Model ............................................................................................. 41 3.8 Comparative Examinations ....................................................................................................... 44 3.9 Distributive Issues ..................................................................................................................... 45 3.10 Discussion of Results ............................................................................................................... 49 4. Closed-loop Supply Chain with Multiple Manufacturers ............................................................... 50 4.1 Description of the Supply Chain and Assumptions ................................................................... 50 4.2 Basic Model ............................................................................................................................... 52

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4.2.1 The Case of Homogeneous Products with Symmetric Cost ........................................... 54 4.3 Extended Model with Governmental Incentives and Fees ...................................................... 56 4.3.1Homogeneous Products with Symmetric Costs ............................................................... 61 4.3.2 Multiple Manufacturers .................................................................................................. 63 4.4 Centrally Coordinated Model: Extended Model ...................................................................... 66 4.4.1 Centrally Coordinated Model: Homogeneous products with symmetric cost ........................ 67 4.4.3 Approximation for Extended Model ............................................................................... 69 4.5 Discussion of the Results .......................................................................................................... 73 5. Extension to Some Current Policies Mexico ................................................................................... 74 6. Concluding Remarks and Future Research ..................................................................................... 76 Appendix A. Concavity and Optimality of Profit Functions in Basic and Extended Model ................ 81 Appendix B. Expression for * α , its Uniqueness and Bounds.............................................................. 82 Appendix C. Relationships among the Total Surpluses and the Collection Rates of Basic, Extended, Alternative Financial Instruments, and Revenue-Sharing Contract Models ........................................ 84 Appendix D. Relationships among Collector Profits, Manufacturer Profits, and Consumer Surpluses for Basic, Extended, Alternative Financial Instrument, and Revenue-Sharing Contract Models ........ 85 Appendix E. Optimality of the Total Surplus Function in Centrally Coordinated Model and Derivation of Financial Instruments ..................................................................................................... 87 Appendix F. Concavity and Optimality of the Forward only Supply Chain and the Revenue-Sharing Contract Model ..................................................................................................................................... 88 Appendix G. Concavity and Optimality of Profit Functions in Basic and Extended Model with Competition .......................................................................................................................................... 89 Appendix H. Expression for * α its Uniqueness and Bounds for Homogeneous Products ................. 93 Appendix I. Relationships among the Total Surpluses as well as the Collection Rates of Basic Model, Extended Model, and Centrally Coordinated Model for the case of Homogeneous Products ............. 95 Appendix J. Derivation of Boundaries for * M α .................................................................................... 97 Appendix K. Optimality of Total Surplus in Centrally Coordinated Model with Competition and Derivation of Instruments ..................................................................................................................... 98 References .......................................................................................................................................... 100

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List of Tables Table 1. Comparison of Environmental Legislation in US………………………………………….....5 Table 2. Extended Model with Governmental Incentives and Fees…………………………………..23 Table 3. Special Cases Equilibrium Solutions of Extended Model…………………………………...24 Table 4. Extended Model Results with Revenue Neutrality………………………………………….25 Table 5. Special Cases Equilibrium Solutions of Extended Model with Revenue Neutrality………..26 Table 6. Results for Basic and Extended Models……………………………………………………..29 Table 7. Profits and Decision Variables for the Allocation Mechanism………………………….…..32 Table 8. Unprofitability with * CC TS …………………………………………………………………..40 Table 9. Ranges for Fixed Costs under Alternative Financial Instruments where m A c δ β = − and 2 B k β = …………………………………………………………………………………………….41 Table 10. Initial Allocation Results and the Distributive Actions…………………………………….46 Table 11. Results for numerical example for Basic, Extended, AFI, Revenue-Sharing Contract…...49 Table 12. Results for Basic and Extended model with Competition...………………………………..60 Table 13. Results for the new Scheme of Incentives and Fees in the Model with Competition….…..68 Table 14. Results of the numerical example for the Alternative Incentives and Fees in the Model with Competition..………………………………………………………………………………….…69

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List of Figures Figure 1. Basic Model………………………………………………………………………………...11 Figure 2. Extended Model with Governmental Incentives and Fees (E)……………………………...17 Figure 3. Special Cases of Extended Model…………………………………………………………..24 Figure 4. E TS vs. α…………………………………………………………………………………...29 Figure. 5. Total surplus for the Basic Model, Extended Model, Alternative Financial Instruments, Revenue- Sharing contract……………………………………………………….……………………48 Figure 6. Basic Model with Competition…...………………………………………………………...50 Figure 7. Extended Model with Governmental Incentives and Fees (G) and Competition…………..56 Figure 8. TS vs α for Basic Model and Extended Model with competition…………………………..60 Figure 9. TS for Basic, Extended and Centrally Coordinated Model with Homogeneous Products....65 Figure 10. Ratio vs 2 ………………………………………………………………………………...71 Figure 11. Ratio vs β 2 …………………………………………………………………………………71 Figure 12. Ratio vs k 2 …………………………………………………………………………………72 Figure 13. Ratio vs δ 2 …………………………………………………………………………………72

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Acknowledgement “To accomplish great things, we must not only act, but also dream, not only plan, but also believe.” Anatole France.

I feel truly blessed with this accomplishment in my life, and I’d like to take this opportunity to thank each and everyone who made it possible. I would like to thank God for all His blessings. I would like to thank Dr. Min for all his support. From the beginning of my journey he helped me in every possible way. He taught me what research is and how it must be done. His guidelines will help me through my entire future career. I could not have asked for a better advisor. I would like to thank my committee members Dr. Gaytan, Dr. Jackman, Dr. Marasinghe, Dr. Wang, Dr. Olafsson and Dr. Serrato for their suggestions and thoughtful comments. I would also like to thank José Carlos Miranda and Roberto Villaseñor for their support for the last years. I would like to thank Lori Bushore for everything she has done for me. Her kindness shown since the very first emails made me feel confident about starting this adventure. I would like to thank Carlos, he has encouraged me in so many ways to achieve this goal: First with his passion to teach and to learn; then by encouraging me to start my studies at Tec de Monterrey and by pushing me to continue at ISU. And finally, by giving me the most beautiful present I could ever ask for. I would like to thank Karla for her friendship and support; for all the Starbucks coffee and talks that made this journey more enjoyable. I would like to thank my parents and siblings for their support, prayers and unconditional love through all my life and during my studies. Specially, I would like to thank my mother, for loving my daughter as her own and for taking care of her while I was working. Last, but definitely not the least I would like to thank Valeria, my daughter. Her laughs, her smile and her hugs gave me the courage and the strength to go through the long nights and weekends of endless work. Her love was what kept me going and made me finish. This is for you my baby.

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Abstract

A rich mixture of government incentives and fees to encourage the collection of used products and the subsequent remanufacturing has been increasingly utilized both domestically and internationally. In this paper, toward a fuller understanding of such government participation in closed-loop supply chains (CLSC’s), we construct and analyze a series of game-theoretic CLSC models with remanufacturing. Specifically, we investigate a basic decentralized CLSC model, two government participation models of linear incentives and fees as well as of central coordination via alternative financial instruments, and a revenue-sharing contract model without the government participation. We also analyze the impact of competition among manufacturers in our results. A key differentiating feature in our government participation models is the incorporation of the revenue neutrality requirement from a government’s perspective whose financial sources for such incentives must eventually reconcile with the financial sinks for such fees. By comparing and contrasting the equilibrium solutions and the economic consequences of these models, managerial insights and economic implications relevant to academics and practitioners including decision and policy makers are obtained. For example, we show how the government participation can induce an entry or prevent an exit of a CLSC when one or more members are unprofitable.

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1. Introduction 1.1 Research Objectives and Overview This research is motivated by the concurrent practices and plans of a heterogeneous and sometimes seemingly unrelated mixture of incentives and fees that are theoretically difficult to collectively analyze, compare, and produce policy and decision implications and guidelines for. They are often practically difficult to implement due to the complexity and ambiguity of the legislations as well. This research provides guidelines to those involved in the process of designing and analyzing the environmental laws and regulations. To our best knowledge, however, there have been few papers that address the implications from a government’s perspective whose financial sources for such incentives must eventually reconcile with the financial sinks for such fees. Under these circumstances, as a first step toward a fuller understanding of such government participation, in this paper, we construct four CLSC models with remanfuacturing, and utilize these models to obtain insights and implications including policy and decision guidelines. The specific research objectives are: (1) To analyze the impact of governmental participation via incentives and fees in the economic efficiency of a closed-loop supply chain. (2) To investigate alternative mechanism that can improve the economic efficiency of a closed-loop supply chain. (3) To analyze the impact of competition among manufacturers in the efficiency of a closed-loop supply chain with governmental participation. The outlines and the background information of each model derived in this paper are as follows: First, we construct a basic decentralized CLSC model without government participation consisting of a manufacturer who manufactures as well as remanufactures her product of a single kind, customers who directly purchase from the manufacturer, and a collector who collects the used products from customers and sells them back to the manufacturer. In the basic model as well as all the

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other subsequent models, we assume that the manufacturer sells directly to the customers. For example, Chiang et al. (2003) report that 42% of top suppliers like IBM, Estee Lauder, and Nike have begun to sell directly to customers over the Internet. Furthermore, companies such as Dell, Sony, and HP have long been offering their products directly to their customers via the Internet. Also, we assume that the manufacturer has sufficient channel power over the collector to act as a Stackelberg leader (hence, the collector is the follower; see e.g., Savaskan et al. 2004). This is a reasonable assumption as major manufacturers who also remanufactures such as Kodak, BMW, IBM, DEC, and Xerox (Atasu et al. 2008b) do seem to have more than sufficient channel power relative to collectors of their products. In addition, in this paper, by remanufacturing we mean restoring used products to their original performance standards based on Section 3102-e(1)(b)(5) of the Public Authorities Law in the state of New York (New York State Department of Taxation and Finance 1999b). The scope in this paper is restricted to the products described in this law, such as: facsimile machines, photocopiers, printers, duplication equipment, magnetic ink cartridges, toner cartridges, inkjet cartridges and printer cartridges. Following the formulation of the basic model, our analyses of the basic model include the economic efficiency and the collection rate at the equilibrium, which also serve as the benchmark reference points later. By economic efficiency, we mean the total surplus or the sum of all profits of the manufacturer, collector, and customers (i.e., consumer surplus), and it is often referred to as the social welfare from a social planner or a government perspective. Also, we note that the collection rate is an important environmental measure because some critical legislations such as the Waste Electrical and Electronic Equipment (WEEE) Directive contains the minimum target that must be met (Atasu et al. 2009) even though there certainly are other environmental measures. Based on the basic model, we next propose two new models of the government participation with the revenue neutrality requirement. By revenue neutrality, we mean that all the incentives must be financed by all the fees without any external financial source or sink (i.e., all the fees and

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incentives are endogenously raised and spent, and the net gain to the government is zero). This revenue neutrality requirement allows us to concentrate on the economic efficiency of the incentives and fees without the distraction of financial sources to fund the incentives or financial sinks to apply the fees that are external to the CLSC models (Mrozek 2000). In the first extension, we simultaneously consider a remanufacturing incentive for the manufacturer and a collecting incentive for the collector as well as a manufacturing fee for the manufacturer and a consumption fee for the customers where all incentives and fees are linear in product quantity. We note that the linear incentives and fees are easy to understand and implement, and have been widely used in the literature (e.g. Baker 1992). Also they are of importance on their own right and as a first order approximation - especially in the absence of more sophisticated previous studies in the context of this paper. In this way, fairly large classes of linear incentives and fees are incorporated within a single framework and we are able to concurrently address a wide variety of scenarios, which may first appear different and separate, and provide a unified analysis on the equilibrium solutions and the economic efficiencies. We also note that, a priori, the improvement of the economic efficiency may be unclear due to the revenue neutrality requirement. For this extended model, through the analysis of various bounds, we demonstrate that the economic efficiency does improve – if the government sets the incentives and fees at the optimal levels. Otherwise, the economic efficiency may deteriorate relative to the decentralized model. In the second extension, we assume that there exists a social planner (see e.g., Carraro and Topa 1995) who centrally coordinates the forward and the reverse flows of products so as to maximize the total surplus. This leads to the upper bound of the total surplus that is theoretically achievable. We then show how the government can achieve this theoretically maximal total surplus via alternative financial instruments under the revenue neutrality requirement. With these government participation models, we proceed to the basic model cases where one or more of the CLSC members are unprofitable. In the context of recycling, there have been

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numerous documents indicating that government incentives should be utilized when the recycling efforts are not profitable (Evans 1994). On the other hand, in the context of remanufacturing, there seem to be few quantitative papers addressing either the cases of unprofitable CLSC’s or the government participation in such cases. As the same logic of unprofitability and incentives is easily extendable to the case of remanufacturing, under the extended and centrally coordinated model framework, we will show how the government participation may induce an entry of a new CLSC or prevent an exit of an existing CLSC. We will also provide concrete guidelines for the government efforts regarding these aspects. In this paper, in addition, we examine how the manufacturer and the collector can coordinate themselves without the government by constructing a revenue-sharing contract model (see e.g., Cachon and Lariviere 2005). In this model, the sum of the CLSC member profits is maximized, but not the total surplus. Next, we proceed to compare and contrast all the models studied in this paper focusing on the economic efficiencies as well as the collection rate. Finally, we show how the economic distribution issues may be addressed in order to implement the proposed CLSC models of the linear incentives and fees, central coordination, and revenue-sharing contract as some initial allocation may not be agreeable to one or more members of the CLSC’s. We then extend our analysis to the case where two manufacturers act as the leaders in a Stackelberg-Cournot game. 1.2 Environmental Laws In recent years, the usage of government incentives and fees to facilitate the collection of used products and the subsequent remanufacturing has significantly increased at all of local, state, national, as well as international levels. At the same time, the types of incentives and fees vary greatly from a community to a community. For example, in New York, remanufacturers receive tax credits that are commensurate with the number of employees and/or the durability of capital investment (New York State Department of Taxation and Finance 1999a). Also, in 2008, a federal bill was introduced to

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allow a credit against income tax for remanufacturing or recycling equipment. It, however, is unclear if the federal definition of the remanufacturing or recycling is consistent with those of states (H.R. 5659-Government Relations: The Remanufacturing Institute, 2009). Furthermore, in the context of recycling, in California, customers pay an advance recovery fee for numerous video display devices (Electronic Waste Recycling Act California 2003) while collectors are reimbursed for the costs of collection per pound (Council of State Governments 2009). In addition, in Minnesota, certain electronics manufacturers pay a fee that is commensurate with their sales quantities. Table 1 shows some of the states that currently have an environmental legislation as well as their characteristics. Table 1. Comparison of environmental legislation in US. State Incentive Fee Product California A key element of the act that affects e-waste collectors and recyclers is the availability of recovery and recycling payments to approved participants for certain collection and recycling activities ARF (Advance Recycling Fee) charged to customers at point of sale. The fee depends on the size of the device: • between 4 and 15 inches $8; • between 15 and 35 inches $16; • 35 inches and larger $25 Cathode ray tube, televisions and computer monitors; LCD desktop monitors, laptop computers with LCD displays; LCD televisions; plasma televisions; portable DVD Connecticut The state will use the fees to administer a recycling program. Manufacturers must register with the state Department of Environmental Protection and pay an annual fee. Desktop or personal computers, computer monitors, portable computers, televisions. Illinois All registration fees are deposited in the Electronics Recycling Fund Manufacturers must register with the state and pay an annual fee of $5,000. Computer, computer monitor, television, printer. Maryland Fees are deposited in a fund to make grants to counties and municipalities to implement local collection plans. The manufacturer registration fee is$10,000 for the initial registration Computer or video display devices with a screen greater than four inches. Minnesota As an incentive to increase collection. Recyclers, collectors, and manufacturers can multiply the actual weight collected by 1.5.

Manufacturer pays a registration fee for year one. • $1,250 for companies manufacturing fewer than 100 units per year for sale •$5000 for manufacturers producing more than 100 units per year Regulated video display devices (VDDs):televisions, laptop computers and computer monitors with displays larger than nine inches, measured diagonally. New Jersey The department shall make payments to the county or municipality,based upon the costs incurred municipality IT companies will include payments with their annual fees, calculated as weight times 50 cents per pound of product sold. Desktop or personal computer, computer monitor, television

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Considering these examples, it is highly desirable to understand what the managerial insights and economic implications of the government participation through incentives and fees may be on closed-loop supply chains (CLSC’s). To our knowledge, this is the first paper that, in the context of CLSC’s, formulates the government participation models subject to the revenue neutrality requirement via active and creative pricing of incentives and fees, and analyzes the economic efficiencies and collection rates relative to benchmark models without the government. From a broader perspective, this paper contributes to a fuller understanding of the impact of the government incentives and fees in the context of CLSC’s that are nowadays ubiquitous across the U.S. and certain international regions such as the European Union. That is, this paper strongly argues that the government incentives and fees do have major ramifications on CLSC’s in terms of economic efficiency and collection rate. Accordingly, various guidelines with respect to economic parameters are provided for the decision and policy makers to determine deliberate and purposeful choices on the kinds of financial instruments and the levels of incentives and fees to each member of CLSC’s. The rest of this paper is organized as follows. In Chapter 2, we provide a brief review of the relevant literature. Next, in Chapter 3, we elaborate on the major assumptions, and present the basic decentralized CLSC model with one manufacturer and one collector. We then extend the basic model by incorporating the government participation subject to the revenue neutrality requirement via the linear incentives and fees. Additionally we construct a centrally coordinated model, and show how the theoretically maximal economic efficiency can be achieved via the alternative financial instruments. We also examine the cases where one or more members of the CLSC are unprofitable, and the government participation and its policy and decision implications on the entry and exit of CLSC’s. Finally, we present the revenue-sharing contract model without the government as well as the economic comparisons, and address the distributive issues of all the models. In Chapter 4, we derive the basic model that presents competition among manufacturers. We extend the basic model by

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incorporating the governmental participation via incentives and fees. We show how the optimal levels of the incentives and fees can be determined under the requirement of revenue neutrality when the firms have symmetric costs and they sell a homogeneous product. We derive a centrally coordinated model and present the theoretical upper bound of the total surplus. We generate a mechanism that achieves the upper bound for the case of homogeneous products and symmetric costs and then present an approximation for the case of heterogeneous products. In Chapter 5, we discuss the implications of our findings for some current policies in Mexico. Finally, in Chapter 6, we make concluding remarks and comment on future research.

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2. Literature Review In this section, we briefly review the most pertinent publications to this paper in the existing literature. The study of CLSC’s is a relatively new field of research, and there exist numerous challenging managerial problems (Atasu et al. 2008a, Guide and Van Wassenhove 2006). Within this study of CLSC’s, a game-theoretic framework has been widely utilized so as to gain insights about the decisions of CLSC members and their economic consequences (see e.g., Webster and Mitra 2007). Moreover, within the game-theoretic framework for collection and remanufacturing, Savaskan et al. (2004) examine various collection strategies with respect to channel structures under a Stackelberg game for a manufacturer/remanufacturer, a retailer, customers, and a collector. In contrast, in this paper, the channel structure is simpler and fixed, but the increasingly ubiquitous governmental participation via incentives and fees is investigated for economic and environmental consequences. In both cases, we note that the fundamental driver of remanufacturing is the cost savings for the maximization of profits, and not a requirement by the government or corporate wishes for better image. In the context of closed-loop supply chains with competition, Savaskan and Wassenhove (2006) described a supply chain consisting of one manufacturer that sells his product to two competing retailers. The objective was to analyze the reverse channel that would improve the collection rate and total profit. In contrast, in this paper, we examine the competition among manufacturers while they sell directly to the customer. Ferguson and Toktay (2006) analyze the competition that the original manufacturer faces from the remanufacturer. In this paper the game is played in a two-stage period, where the new product is introduced in the first period and the remanufactured product enters the market in the second period. In this paper we analyze competition among manufacturers which are also remanufacturers, so the competition appears at the initial stage of the game. Choi (1991) analyzed a channel structure with two competing manufacturers and one intermediary (a common retailer) that sells both manufacturers' products. This paper studied different

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noncooperative games of different power structures between the two manufacturers and the retailer, i.e., two Stackelberg and one Nash games. This is the approach in this paper. In the area of governmental participation as a social planner, the use of taxes and subsidies as a tool to improve social welfare has been widely studied (Galiana et al. 2003). Carraro and Topa (1995) analyze the impact of environmental regulation in the form of taxation on the innovation activity of firms. In that paper, the regulation problem is modeled as a two-stage game. In the first stage, the government sets its policy instruments. In the second stage, the firms decide whether and when to innovate. The regulator’s objective function is the sum of the consumer surplus and industry profits, which is the total surplus. The governmental participation through a scheme of incentives and fees that aims to align different objectives is similar to the principal’s problem in the economic theory of agency (Ross 1973). As in Mirrlees (1976), the members in our CLSC models have different objectives, and behave in accordance with their own interest. Hence, we can view that the government in our models will need an incentive contract in the form of incentives and fees so as to maximize the total surplus, which is the principal’s objective. Once the government participates through incentives and fees, for cash flow issues in practice and for completeness issues in theory, it is highly desirable to address how these incentives are financed or the collected fees get utilized eventually. For this, Mrozek (2000) argues that deposit/refund systems must be implemented in a way that the revenue is neutral. That is, the amount of incentives disbursed is equal to the amount of fees collected within a closed system without a source or a sink for cash flow that is external to the model under consideration. In this paper, as in Carraro and Topa (1995), the economic efficiency is measured in total surplus while, as in Mrozek (2000), the revenue neutrality is exploited in several applicable sections. In the area of environmental regulations on supply chains, Webster and Mitra (2007) examine the impact of take-back laws when a manufacturer and a remanufacturer compete. In their study, two

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possible implementations of a take-back law are analyzed based on the degree of control that the manufacturer has on returns sold to the remanufacturer. Also, in Mitra and Webster (2008), the impact of governmental subsidies for remanufacturing is examined and a mechanism to distribute subsidies to benefit both manufacturer and remanufacturer is presented. Furthermore, Hammond and Beullens (2007) investigate a CLSC network with governmental participation through the Waste Electrical and Electronic Equipment (WEEE) directive. This investigation shows how the manufacturer’s and consumer’s behavior under different schemes of environmental regulations can be quantitatively modeled and analyzed. Also, Atasu et al. (2009) examine a series of efficient take-back legislation models with subsidies. We note that these papers explicitly or implicitly assume that the government financial instruments are exogenous factors or external to their models subject to no limitation (i.e., no upper bound or budget). In addition, the need of government participation to create a viable environmental supply chain has been well described in the literature. For example, Evans (1994) analyzes the impact of the Resource Recovery Act that encourages private recycling operators to undertake operations that were first unprofitable. In this paper, in the context of CLSC’s, we formalize various conditions under which the government can influence the entry and exit of CLSC’s, clarifying the relevance of the government participation.

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3. Closed-loop Supply Chain with One Manufacturer 3.1 Description of the Supply Chain and Assumptions In this section, we formulate and analyze a basic closed loop supply chain consisting of a manufacturer who manufactures as well as remanufactures her product of a single kind, customers who directly purchase from the manufacturer and a collector who collects the used products from customers and sells them back to the manufacturer. We incorporate the participation of a collector since a third party collector can be more technically advanced in collection and recovery of returned products (see Hamza et al. 2007). We assume that there are no governmental incentives or fees. Figure 1 depicts the configuration of the basic model.

Figure 1. Basic Model We denote the manufacturer’s per unit selling price as w. Given w, we assume that the manufacturer faces a demand of D(w) = δ – βw where δ > 0 is the maximal demand of the product and β > 0 denotes the decrease in demand for a unit increase in price w. We note that the linear demand functions have been widely utilized in economic models (Dobbs 1991, Gutiérrez-Alcaraz and Sheblé 2005). In order for the manufacturer to manufacture and remanufacture she incurs in a fixed cost of M k . We also assume that, after consuming the products, the customers are willing to return them to the collector and that the collector incurs a cost e per unit collected representing his level of

Full document contains 111 pages
Abstract: A rich mixture of government incentives and fees to encourage the collection of used products and the subsequent remanufacturing has been increasingly utilized both domestically and internationally. In this paper, toward a fuller understanding of such government participation in closed-loop supply chains (CLSC's), we construct and analyze a series of game-theoretic CLSC models with remanufacturing. Specifically, we investigate a basic decentralized CLSC model, two government participation models of linear incentives and fees as well as of central coordination via alternative financial instruments, and a revenue-sharing contract model without the government participation. We also analyze the impact of competition among manufacturers in our results. A key differentiating feature in our government participation models is the incorporation of the revenue neutrality requirement from a government's perspective whose financial sources for such incentives must eventually reconcile with the financial sinks for such fees. By comparing and contrasting the equilibrium solutions and the economic consequences of these models, managerial insights and economic implications relevant to academics and practitioners including decision and policy makers are obtained. For example, we show how the government participation can induce an entry or prevent an exit of a CLSC when one or more members are unprofitable.