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

Xiaohong Chen; Kui Li; Fuqiang Wang; Xihua Li

doi:10.3934/jimo.2019008

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May 2020, 16(3): 1389-1414. doi: 10.3934/jimo.2019008

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

Xiaohong Chen ^1,2, , Kui Li ^3, , Fuqiang Wang ^3,, and Xihua Li ^3,

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.

Keywords: Price-setting newsvendor model, return uncertainty, remanufacturing, government subsidies.

Mathematics Subject Classification: Primary: 91A40, 97M40.

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, 2020, 16 (3) : 1389-1414. doi: 10.3934/jimo.2019008

References:

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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. Google Scholar
[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. Google Scholar
[3]	A. Atasu, Environmentally Responsible Supply Chains, Springer, 2016. doi: 10.1007/978-3-319-30094-8. Google Scholar
[4]	X. Corporation, Xerox Environmental Report, Xerox Corporation, 2001. Google Scholar
[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. Google Scholar
[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/. Google Scholar
[7]	China Auto Review, Remanufacturing Auto Parts to Receive 10 Percent Subsidy, 2015. Available from: http://www.chinaautoreview.com/pub/CARArticle.aspx?ID=11672. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[23]	R. L. Ernst, A Linear Inventory Model of a Monopolistic Firm, Ph.D. dissertation, Department of Economics, University of California, Berkeley, CA, 1970. Google Scholar
[24]	G. Ferrer and J. M. Swaminathan, Managing new and remanufactured products, Manag. Sci., 52 (2006), 15-26. doi: 10.1287/mnsc.1050.0465. Google Scholar
[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. Google Scholar
[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. Google Scholar
[27]	J. Ginsburg, Manufacturing: Once is not enough, Business. Week., 16 (2001), 128-129. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[41]	R. Lifset, Take it back: Extended producer responsibility as a form of incentive-based environmental policy, Resour. Manage. Tech., 21 (1993), 163-175. Google Scholar
[42]	T. Lindhqvist, Extended Producer Responsibility in Cleaner Production, IIIEE. Dissertation., Lund University, 2000. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
[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. Google Scholar
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Figure 1. Order of events: (1) subsidies; (2) price, quantity and return price; (3) sales

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Table 1. 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

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$ 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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2019 Impact Factor: 1.366

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2019 Impact Factor: 1.366

American Institute of Mathematical Sciences

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

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

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