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doi: 10.3934/jimo.2019008

## Optimal production, pricing and government subsidy policies for a closed loop supply chain with uncertain returns

 1 School of Business, Central South University, The Collaborative Innovation Center for Resource-conserving & Environment-friendly Society and Ecological Civilization, Changsha 410083, China 2 Hunan University of Commerce, Changsha 410205, China 3 School of Business, Central South University, Changsha 410083, China

* Corresponding author: Fuqiang Wang

Received  February 2018 Revised  October 2018 Published  March 2019

This paper studies an original equipment manufacturer's (OEM's) optimal production and pricing decisions and the governments optimal subsidy level when the number of used products returning to the OEM is uncertain. The government aims to minimize its total expenditures but also attempt to achieve a given target collection level. We model the problem as an extended price-setting newsvendor model, which simultaneously incorporates supply uncertainty and external government influence. Moreover, we consider separately the cases of stochastic supplies with additive and multiplicative return uncertainty. We show that under the above settings, the governments optimal strategy is to provide only sufficient subsidies that cause its target to be met exactly. The government subsidies will mitigate the cost of remanufacturing and increase the total collection efforts of the government and the manufacturer. Moreover, the return uncertainty lowers both the manufacturers profits and selling price, whereas its effects on the governments optimal subsidies and the manufacturers optimal return efforts are insignificant. Therefore, the manufacturer is worse off but consumers are better off under the conditions of uncertain returns. By comparing the optimal decisions when the government is a central planner with the case of decentralized decision making, or comparing the arrangement in which the government provides subsidies directly to the manufacturer rather than to consumers, we find that the government subsidies would coordinate the supply chain only when its target collection level is high. Moreover, no essential differences exist between providing subsidies directly to the manufacturer and to consumers. Our results are robust under both the additive and multiplicative uncertainty models.

Citation: Xiaohong Chen, Kui Li, Fuqiang Wang, Xihua Li. Optimal production, pricing and government subsidy policies for a closed loop supply chain with uncertain returns. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019008
##### References:
 [1] D. Aksen, N. Aras and A. G. Karaarslan, Design and analysis of government subsidized collection systems for incentive-dependent returns, Int. J. Prod. Econ., 119 (2009), 308-327. doi: 10.1016/j.ijpe.2009.02.012. [2] A. Atasu, M. Sarvary and L. N. Van Wassenhove, Remanufacturing as a marketing strategy, Manag. Sci., 54 (2008), 1731-1746. doi: 10.1287/mnsc.1080.0893. [3] A. Atasu, Environmentally Responsible Supply Chains, Springer, 2016. doi: 10.1007/978-3-319-30094-8. [4] X. Corporation, Xerox Environmental Report, Xerox Corporation, 2001. [5] R. Ayres, G. Ferrer and T. V. Leynseele, Eco-efficiency, asset recovery and remanufacturing, Eur. Management. J., 15 (1997), 557-574. doi: 10.1016/S0263-2373(97)00035-2. [6] ETBC, Brief Comparison of State E-Waste Laws Electronics TakeBack Coalition, 2013. Available from: http://www.electronicstakeback.com/promote-good-laws/state-legislation-toolkit/. [7] China Auto Review, Remanufacturing Auto Parts to Receive 10 Percent Subsidy, 2015. Available from: http://www.chinaautoreview.com/pub/CARArticle.aspx?ID=11672. [8] Environmental Science and Technology Net, The New Version of E-Waste Recycling Subsidy Standard will be Implemented to Guide Enterprises to Reconstruct the Recycling Interest Chain, 2015. Available from: http://www.cn-hw.net/html/china/201512/51527.html. [9] China Youth Daily, China's Waste Electrical and Electronic Products are More Than 200 Million units each year, 2015. Available from: http://henan.china.com.cn/news/2015/0810/688711.shtml. [10] Australian Bureau of Statistics, Electronic and Electrical Waste, 2013. Available from: http://www.abs.gov.au/ausstats/abs@.nsf/Products/4602.0.55.005~2013~Main+Features~Electronic+and+Electrical+Waste. [11] Industry Information, Recycling of Waste Household Appliances must Establish a Reasonable and Complete Recycling System, 2015. Available from: http://m.feijiu.net/news/zx349338.html. [12] China Enterprise News, The Remanufacturing Industry is Facing Big Opportunities: The Market will Reach 200 Billion in the Future, 2015. Available from: http://finance.sina.com.cn/leadership/mroll/20151109/164823717808.shtml. [13] Europa-Environment, Directive 2012/19/EU of the European Parliament, 2012. Available from: https://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=OJ:L:2012:197:0038:0071:EN:PDF. [14] Meta Economics Consulting Group, National Television and Computer Product Stewardship Scheme: Targets, Trajectories and Implications for Scheme Design, 2011. Available from: http://environment.gov.au/system/files/resources/5107c36d-1456-4958-a361-882a2bd8ffe3/files/ntcrs-targets.pdf. [15] I. S. Bakal and E. Akcali, Effects of random yield in remanufacturing with price-sensitive supply and demand, Production. Oper. Management, 15 (2006), 407-420. doi: 10.1111/j.1937-5956.2006.tb00254.x. [16] M. Bayiz and C. S. Tang, An integrated planning system for managing the refurbishment of thermoluminescent badges, Interfaces., 34 (2004), 331–413. doi: 10.1287/inte.1040.0098. [17] G. P. Cachon, Supply chain coordination with contracts. de Kok AG, Graves SC, eds. Supply Chain Management: Design, Coordination and Operation, Handbooks in Operations Research and Management Science, 11 (2003), 227-339. [18] G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Manag. Sci., 51 (2005), 30-44. doi: 10.1287/mnsc.1040.0215. [19] J. Chen and P. C. Bell, The impact of customer returns on pricing and order decisions, Eur. J. Oper. Res., 195 (2009), 280-295. doi: 10.1016/j.ejor.2008.01.030. [20] S. E. Chick, H. Mamani and D. Simchi-Levi, Supply chain coordination and influenza vaccination, Oper. Res., 56 (2008), 1493-1506. doi: 10.1287/opre.1080.0527. [21] F. W. Ciarallo, R. Akella and T. E. Morton, A periodic review, production planning model with uncertain capacity and uncertain demand-optimality of extended myopic policies, Manag. Sci., 40 (1994), 285-428. doi: 10.1287/mnsc.40.3.320. [22] M. C. Cohen, R. Lobel and G. Perakis, The impact of demand uncertainty on consumer subsidies for green technology adoption, Manag. Sci., 62 (2016), 1235-1258. doi: 10.2139/ssrn.2376662. [23] R. L. Ernst, A Linear Inventory Model of a Monopolistic Firm, Ph.D. dissertation, Department of Economics, University of California, Berkeley, CA, 1970. [24] G. Ferrer and J. M. Swaminathan, Managing new and remanufactured products, Manag. Sci., 52 (2006), 15-26. doi: 10.1287/mnsc.1050.0465. [25] G. Ferrer and D. Whybark, From garbage to goods: Successful remanufacturing systems and skills, Bus. Horizons., 43 (2000), 55-64. doi: 10.1016/S0007-6813(00)80023-3. [26] M. R. Galbreth and J. D. Blackburn, Optimal acquisition quantities in remanufacturing with condition uncertainty, Prod. Oper. Manag., 19 (2010), 61-69. doi: 10.1111/j.1937-5956.2009.01067.x. [27] J. Ginsburg, Manufacturing: Once is not enough, Business. Week., 16 (2001), 128-129. [28] D. Granot and S. Yin, On the effectiveness of returns policies in the price-dependent newsvendor model, Naval. Res. Logist., 52 (2005), 765-779. doi: 10.1002/nav.20114. [29] D. Guide and L. N. Van Wassenhove, The evolution of closed-loop supply chain research, Oper. Res., 57 (2009), 10-18. doi: 10.1287/opre.1080.0628. [30] V. D. Guide, R. H. Teunter and L. N. Van Wassenhove, Matching demand and supply to maximize profits from remanufacturing, Manuf. Serv. Oper. Manag., 5 (2003), 269-374. doi: 10.1287/msom.5.4.303.24883. [31] V. D. R. Guide, Production planning and control for remanufacturing: Industry practice and research needs, J. Oper. Management., 18 (2000), 467-483. doi: 10.1016/S0272-6963(00)00034-6. [32] D. Gupta and W. L. Cooper, Stochastic comparisons in production yield management, Oper. Res., 53 (2005), 377-384. doi: 10.1287/opre.1040.0174. [33] C. Hicks, R. Dietmar and M. Eugster, Therecycling and disposal of electrical and electronic waste in China–legislative and market responses, Environ. Impact. Assess. Rev., 25 (2005), 459-471. doi: 10.1016/j.eiar.2005.04.007. [34] I. H. Hong and J. S. Ke, Determining advanced recycling fees and subsidies in "E-scrap" reverse supply chains, J. Environ. Manag., 92 (2011), 1459-1502. doi: 10.1016/j.jenvman.2010.12.004. [35] C. C. Hsieh and C. H. Wu, Capacity allocation, ordering, and pricing decisions in a supply chain with demand and supply uncertainties, Eur. J. Oper. Res., 184 (2008), 667-684. doi: 10.1016/j.ejor.2006.11.004. [36] O. Kaya, Incentive and production decisions for remanufacturing operations, Eur. J. Oper. Res., 201 (2010), 442-453. doi: 10.1016/j.ejor.2009.03.007. [37] J. Khawam, W. H. Hausman and D. W. Cheng, Warranty inventory optimization for Hitachi Global Storage Technologies, Inc. Interfaces., 37 (2007), 401-499. doi: 10.1287/inte.1070.0299. [38] A. Kocablylkoglu and I. Popescu, An Elasticity Approach to the Newsvendor with Price-Sensitive Demand, Oper. Res., 59 (2011), 301-312. doi: 10.1287/opre.1100.0890. [39] X. Li, Y. J. Li and X. Q. Cai, A note on the random yield from the perspective of the supply chain, Omega., 40 (2012), 601-610. doi: 10.1016/j.omega.2011.12.003. [40] X. Li, Y. J. Li and X. Q. Cai, Double marginalization and coordination in the supply chain with uncertain supply, Eur. J. Oper. Res., 226 (2013), 228-236. doi: 10.1016/j.ejor.2012.10.047. [41] R. Lifset, Take it back: Extended producer responsibility as a form of incentive-based environmental policy, Resour. Manage. Tech., 21 (1993), 163-175. [42] T. Lindhqvist, Extended Producer Responsibility in Cleaner Production, IIIEE. Dissertation., Lund University, 2000. [43] R. Lobel and G. Perakis, Consumer choice model for forecasting demand and designing incentives for solar technology, Working Paper, University of Pennsylvania, Philadelphia, (2015), 36pp. doi: 10.2139/ssrn.1748424. [44] W. M. Ma, Z. Zhao and H. Ke, Dual-channel closed-loop supply chain with government consumption-subsidy, Eur. J. Oper. Res., 226 (2013), 221-227. doi: 10.1016/j.ejor.2012.10.033. [45] G. E. Monahan, N. C. Petruzzi and W. Zhao, The dynamic pricing problem from a newsvendor's perspective, Manuf. Serv. Oper. Manag., 6 (2004), 1-112. doi: 10.1287/msom.1030.0026. [46] A. Mutha, S. Bansal, V. Guide and R. Daniel, Managing demand uncertainty through core acquisition in remanufacturing, Prod. Oper. Manag., 25 (2016), 1449-1464. doi: 10.1111/poms.12554. [47] M. Parlar and D. Perry, Inventory models of future supply uncertainty with single and multiple suppliers, Naval. Res. Logist., 43 (1996), 191-210. doi: 10.1002/(SICI)1520-6750(199603)43:2<191::AID-NAV3>3.0.CO;2-5. [48] B. A. Pasternack, Optimal pricing and return policies for perishable commodities, Mark. Sci., 4 (1985), 93-176. doi: 10.1287/mksc.4.2.166. [49] N. C. Petruzzi and M Dada, Pricing and the newsvendor problem: A review with extensions, Oper. Res., 47 (1999), 175-344. doi: 10.1287/opre.47.2.183. [50] N. C. Petruzzi, K. E. Wee and M. Dada, The newsvendor model with consumer search costs, Prod. Oper. Manag., 18 (2009), 693-704. doi: 10.1111/j.1937-5956.2009.01040.x. [51] G. Raz and A. Ovchinnikov, Coordinating pricing and supply of public interest goods using government rebates and subsidies, IEEE. Trans. Eng. Manag., 62 (2015), 65-79. doi: 10.1109/TEM.2014.2380999. [52] G. Raz and E. L. Porteus, A Fractiles Perspective to the Joint Price/Quantity Newsvendor Model, Manag. Sci., 52 (2006), 1764-1777. doi: 10.1287/mnsc.1060.0584. [53] D. Serel, Inventory and pricing decisions in a single period problem involving risky supply, Int. J. Prod. Econ., 116 (2008), 115-128. doi: 10.1016/j.ijpe.2008.07.012. [54] J. B. Sheu and Y. J. Chen, Impact of government financial intervention on competition among green supply chains, Int. J. Prod. Econ., 138 (2012), 201-213. doi: 10.1016/j.ijpe.2012.03.024. [55] Z. J. Tao, S. X. Zhou and C. S. Tang, Managing a remanufacturing system with random yield: properties, observations, and heuristics, Prod. Oper. Manag., 21 (2012), 797-813. doi: 10.1111/j.1937-5956.2011.01313.x. [56] T. A. Taylor, Supply chain coordination under channel rebates with sales effort effects, Manag. Sci., 48 (2002), 955-1101. doi: 10.1287/mnsc.48.8.992.168. [57] G. T. Thowsen, A dynamic, nonstationary inventory problem for a price/quantity setting firm, Naval. Res. Logist. Quart., 22 (1975), 461-476. doi: 10.1002/nav.3800220306. [58] N. Tojo, Extended Producer Responsibility as a Driver for Design Change - Utopia or Reality?, IIIEE. Dissertations., Lund University, Lund, Sweden, 2004. [59] Wuhan Evening, Nearly 70% of the old mobile phones "lie at home", 2016. Available from: http://e.cjn.cn/whwb/html/2016-04/26/content_5525861.htm. [60] S. Webster and S. Mitra., Competition in remanufacturing and the effects of government subsidies, Int. J. Prod. Econ., 111 (2008), 287-298. doi: 10.1016/j.ijpe.2007.02.042. [61] S. X. Zhou and Y. K. Yu, Optimal product acquisition, pricing, and inventory management for systems with remanufacturing, Oper. Res., 59 (2011), 514-521. doi: 10.1287/opre.1100.0898.

show all references

##### References:
 [1] D. Aksen, N. Aras and A. G. Karaarslan, Design and analysis of government subsidized collection systems for incentive-dependent returns, Int. J. Prod. Econ., 119 (2009), 308-327. doi: 10.1016/j.ijpe.2009.02.012. [2] A. Atasu, M. Sarvary and L. N. Van Wassenhove, Remanufacturing as a marketing strategy, Manag. Sci., 54 (2008), 1731-1746. doi: 10.1287/mnsc.1080.0893. [3] A. Atasu, Environmentally Responsible Supply Chains, Springer, 2016. doi: 10.1007/978-3-319-30094-8. [4] X. Corporation, Xerox Environmental Report, Xerox Corporation, 2001. [5] R. Ayres, G. Ferrer and T. V. Leynseele, Eco-efficiency, asset recovery and remanufacturing, Eur. Management. J., 15 (1997), 557-574. doi: 10.1016/S0263-2373(97)00035-2. [6] ETBC, Brief Comparison of State E-Waste Laws Electronics TakeBack Coalition, 2013. Available from: http://www.electronicstakeback.com/promote-good-laws/state-legislation-toolkit/. [7] China Auto Review, Remanufacturing Auto Parts to Receive 10 Percent Subsidy, 2015. Available from: http://www.chinaautoreview.com/pub/CARArticle.aspx?ID=11672. [8] Environmental Science and Technology Net, The New Version of E-Waste Recycling Subsidy Standard will be Implemented to Guide Enterprises to Reconstruct the Recycling Interest Chain, 2015. Available from: http://www.cn-hw.net/html/china/201512/51527.html. [9] China Youth Daily, China's Waste Electrical and Electronic Products are More Than 200 Million units each year, 2015. Available from: http://henan.china.com.cn/news/2015/0810/688711.shtml. [10] Australian Bureau of Statistics, Electronic and Electrical Waste, 2013. Available from: http://www.abs.gov.au/ausstats/abs@.nsf/Products/4602.0.55.005~2013~Main+Features~Electronic+and+Electrical+Waste. [11] Industry Information, Recycling of Waste Household Appliances must Establish a Reasonable and Complete Recycling System, 2015. Available from: http://m.feijiu.net/news/zx349338.html. [12] China Enterprise News, The Remanufacturing Industry is Facing Big Opportunities: The Market will Reach 200 Billion in the Future, 2015. Available from: http://finance.sina.com.cn/leadership/mroll/20151109/164823717808.shtml. [13] Europa-Environment, Directive 2012/19/EU of the European Parliament, 2012. Available from: https://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=OJ:L:2012:197:0038:0071:EN:PDF. [14] Meta Economics Consulting Group, National Television and Computer Product Stewardship Scheme: Targets, Trajectories and Implications for Scheme Design, 2011. Available from: http://environment.gov.au/system/files/resources/5107c36d-1456-4958-a361-882a2bd8ffe3/files/ntcrs-targets.pdf. [15] I. S. Bakal and E. Akcali, Effects of random yield in remanufacturing with price-sensitive supply and demand, Production. Oper. Management, 15 (2006), 407-420. doi: 10.1111/j.1937-5956.2006.tb00254.x. [16] M. Bayiz and C. S. Tang, An integrated planning system for managing the refurbishment of thermoluminescent badges, Interfaces., 34 (2004), 331–413. doi: 10.1287/inte.1040.0098. [17] G. P. Cachon, Supply chain coordination with contracts. de Kok AG, Graves SC, eds. Supply Chain Management: Design, Coordination and Operation, Handbooks in Operations Research and Management Science, 11 (2003), 227-339. [18] G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Manag. Sci., 51 (2005), 30-44. doi: 10.1287/mnsc.1040.0215. [19] J. Chen and P. C. Bell, The impact of customer returns on pricing and order decisions, Eur. J. Oper. Res., 195 (2009), 280-295. doi: 10.1016/j.ejor.2008.01.030. [20] S. E. Chick, H. Mamani and D. Simchi-Levi, Supply chain coordination and influenza vaccination, Oper. Res., 56 (2008), 1493-1506. doi: 10.1287/opre.1080.0527. [21] F. W. Ciarallo, R. Akella and T. E. Morton, A periodic review, production planning model with uncertain capacity and uncertain demand-optimality of extended myopic policies, Manag. Sci., 40 (1994), 285-428. doi: 10.1287/mnsc.40.3.320. [22] M. C. Cohen, R. Lobel and G. Perakis, The impact of demand uncertainty on consumer subsidies for green technology adoption, Manag. Sci., 62 (2016), 1235-1258. doi: 10.2139/ssrn.2376662. [23] R. L. Ernst, A Linear Inventory Model of a Monopolistic Firm, Ph.D. dissertation, Department of Economics, University of California, Berkeley, CA, 1970. [24] G. Ferrer and J. M. Swaminathan, Managing new and remanufactured products, Manag. Sci., 52 (2006), 15-26. doi: 10.1287/mnsc.1050.0465. [25] G. Ferrer and D. Whybark, From garbage to goods: Successful remanufacturing systems and skills, Bus. Horizons., 43 (2000), 55-64. doi: 10.1016/S0007-6813(00)80023-3. [26] M. R. Galbreth and J. D. Blackburn, Optimal acquisition quantities in remanufacturing with condition uncertainty, Prod. Oper. Manag., 19 (2010), 61-69. doi: 10.1111/j.1937-5956.2009.01067.x. [27] J. Ginsburg, Manufacturing: Once is not enough, Business. Week., 16 (2001), 128-129. [28] D. Granot and S. Yin, On the effectiveness of returns policies in the price-dependent newsvendor model, Naval. Res. Logist., 52 (2005), 765-779. doi: 10.1002/nav.20114. [29] D. Guide and L. N. Van Wassenhove, The evolution of closed-loop supply chain research, Oper. Res., 57 (2009), 10-18. doi: 10.1287/opre.1080.0628. [30] V. D. Guide, R. H. Teunter and L. N. Van Wassenhove, Matching demand and supply to maximize profits from remanufacturing, Manuf. Serv. Oper. Manag., 5 (2003), 269-374. doi: 10.1287/msom.5.4.303.24883. [31] V. D. R. Guide, Production planning and control for remanufacturing: Industry practice and research needs, J. Oper. Management., 18 (2000), 467-483. doi: 10.1016/S0272-6963(00)00034-6. [32] D. Gupta and W. L. Cooper, Stochastic comparisons in production yield management, Oper. Res., 53 (2005), 377-384. doi: 10.1287/opre.1040.0174. [33] C. Hicks, R. Dietmar and M. Eugster, Therecycling and disposal of electrical and electronic waste in China–legislative and market responses, Environ. Impact. Assess. Rev., 25 (2005), 459-471. doi: 10.1016/j.eiar.2005.04.007. [34] I. H. Hong and J. S. Ke, Determining advanced recycling fees and subsidies in "E-scrap" reverse supply chains, J. Environ. Manag., 92 (2011), 1459-1502. doi: 10.1016/j.jenvman.2010.12.004. [35] C. C. Hsieh and C. H. Wu, Capacity allocation, ordering, and pricing decisions in a supply chain with demand and supply uncertainties, Eur. J. Oper. Res., 184 (2008), 667-684. doi: 10.1016/j.ejor.2006.11.004. [36] O. Kaya, Incentive and production decisions for remanufacturing operations, Eur. J. Oper. Res., 201 (2010), 442-453. doi: 10.1016/j.ejor.2009.03.007. [37] J. Khawam, W. H. Hausman and D. W. Cheng, Warranty inventory optimization for Hitachi Global Storage Technologies, Inc. Interfaces., 37 (2007), 401-499. doi: 10.1287/inte.1070.0299. [38] A. Kocablylkoglu and I. Popescu, An Elasticity Approach to the Newsvendor with Price-Sensitive Demand, Oper. Res., 59 (2011), 301-312. doi: 10.1287/opre.1100.0890. [39] X. Li, Y. J. Li and X. Q. Cai, A note on the random yield from the perspective of the supply chain, Omega., 40 (2012), 601-610. doi: 10.1016/j.omega.2011.12.003. [40] X. Li, Y. J. Li and X. Q. Cai, Double marginalization and coordination in the supply chain with uncertain supply, Eur. J. Oper. Res., 226 (2013), 228-236. doi: 10.1016/j.ejor.2012.10.047. [41] R. Lifset, Take it back: Extended producer responsibility as a form of incentive-based environmental policy, Resour. Manage. Tech., 21 (1993), 163-175. [42] T. Lindhqvist, Extended Producer Responsibility in Cleaner Production, IIIEE. Dissertation., Lund University, 2000. [43] R. Lobel and G. Perakis, Consumer choice model for forecasting demand and designing incentives for solar technology, Working Paper, University of Pennsylvania, Philadelphia, (2015), 36pp. doi: 10.2139/ssrn.1748424. [44] W. M. Ma, Z. Zhao and H. Ke, Dual-channel closed-loop supply chain with government consumption-subsidy, Eur. J. Oper. Res., 226 (2013), 221-227. doi: 10.1016/j.ejor.2012.10.033. [45] G. E. Monahan, N. C. Petruzzi and W. Zhao, The dynamic pricing problem from a newsvendor's perspective, Manuf. Serv. Oper. Manag., 6 (2004), 1-112. doi: 10.1287/msom.1030.0026. [46] A. Mutha, S. Bansal, V. Guide and R. Daniel, Managing demand uncertainty through core acquisition in remanufacturing, Prod. Oper. Manag., 25 (2016), 1449-1464. doi: 10.1111/poms.12554. [47] M. Parlar and D. Perry, Inventory models of future supply uncertainty with single and multiple suppliers, Naval. Res. Logist., 43 (1996), 191-210. doi: 10.1002/(SICI)1520-6750(199603)43:2<191::AID-NAV3>3.0.CO;2-5. [48] B. A. Pasternack, Optimal pricing and return policies for perishable commodities, Mark. Sci., 4 (1985), 93-176. doi: 10.1287/mksc.4.2.166. [49] N. C. Petruzzi and M Dada, Pricing and the newsvendor problem: A review with extensions, Oper. Res., 47 (1999), 175-344. doi: 10.1287/opre.47.2.183. [50] N. C. Petruzzi, K. E. Wee and M. Dada, The newsvendor model with consumer search costs, Prod. Oper. Manag., 18 (2009), 693-704. doi: 10.1111/j.1937-5956.2009.01040.x. [51] G. Raz and A. Ovchinnikov, Coordinating pricing and supply of public interest goods using government rebates and subsidies, IEEE. Trans. Eng. Manag., 62 (2015), 65-79. doi: 10.1109/TEM.2014.2380999. [52] G. Raz and E. L. Porteus, A Fractiles Perspective to the Joint Price/Quantity Newsvendor Model, Manag. Sci., 52 (2006), 1764-1777. doi: 10.1287/mnsc.1060.0584. [53] D. Serel, Inventory and pricing decisions in a single period problem involving risky supply, Int. J. Prod. Econ., 116 (2008), 115-128. doi: 10.1016/j.ijpe.2008.07.012. [54] J. B. Sheu and Y. J. Chen, Impact of government financial intervention on competition among green supply chains, Int. J. Prod. Econ., 138 (2012), 201-213. doi: 10.1016/j.ijpe.2012.03.024. [55] Z. J. Tao, S. X. Zhou and C. S. Tang, Managing a remanufacturing system with random yield: properties, observations, and heuristics, Prod. Oper. Manag., 21 (2012), 797-813. doi: 10.1111/j.1937-5956.2011.01313.x. [56] T. A. Taylor, Supply chain coordination under channel rebates with sales effort effects, Manag. Sci., 48 (2002), 955-1101. doi: 10.1287/mnsc.48.8.992.168. [57] G. T. Thowsen, A dynamic, nonstationary inventory problem for a price/quantity setting firm, Naval. Res. Logist. Quart., 22 (1975), 461-476. doi: 10.1002/nav.3800220306. [58] N. Tojo, Extended Producer Responsibility as a Driver for Design Change - Utopia or Reality?, IIIEE. Dissertations., Lund University, Lund, Sweden, 2004. [59] Wuhan Evening, Nearly 70% of the old mobile phones "lie at home", 2016. Available from: http://e.cjn.cn/whwb/html/2016-04/26/content_5525861.htm. [60] S. Webster and S. Mitra., Competition in remanufacturing and the effects of government subsidies, Int. J. Prod. Econ., 111 (2008), 287-298. doi: 10.1016/j.ijpe.2007.02.042. [61] S. X. Zhou and Y. K. Yu, Optimal product acquisition, pricing, and inventory management for systems with remanufacturing, Oper. Res., 59 (2011), 514-521. doi: 10.1287/opre.1100.0898.
Order of events: (1) subsidies; (2) price, quantity and return price; (3) sales
Notations
 $d(p)$ Demand for new products $p$ Selling price $M$ Market size $a$ Price sensitivity factor $q_{n}$ Number of new products produced from raw materials $q_{r}$ Number of new products produced from used products $q$ Total number of products produced $c_{n}$ Unit cost of producing a new product from raw materials $c_{r}$ Unit cost of producing a new product from used products $r$ Price of the returned products $\eta$ Per unit subsidy for returned products the government provides for consumers $\eta^\prime$ Per unit subsidy for returned products the government provides for the manufacturers $z$ Effective price of the returned products $\Gamma$ Target collection level $s$ Salvage value for each unit of unsold product $f_{\epsilon}( \cdot )$ Probability density function of random variable $\epsilon$ $F_{\epsilon}( \cdot )$ Cumulative distribution function of random variable $\epsilon$ $\Pi$ Manufacturer's profit $Exp$ Minimal expected subsidy expenditure
 $d(p)$ Demand for new products $p$ Selling price $M$ Market size $a$ Price sensitivity factor $q_{n}$ Number of new products produced from raw materials $q_{r}$ Number of new products produced from used products $q$ Total number of products produced $c_{n}$ Unit cost of producing a new product from raw materials $c_{r}$ Unit cost of producing a new product from used products $r$ Price of the returned products $\eta$ Per unit subsidy for returned products the government provides for consumers $\eta^\prime$ Per unit subsidy for returned products the government provides for the manufacturers $z$ Effective price of the returned products $\Gamma$ Target collection level $s$ Salvage value for each unit of unsold product $f_{\epsilon}( \cdot )$ Probability density function of random variable $\epsilon$ $F_{\epsilon}( \cdot )$ Cumulative distribution function of random variable $\epsilon$ $\Pi$ Manufacturer's profit $Exp$ Minimal expected subsidy expenditure
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