# American Institute of Mathematical Sciences

October  2013, 9(4): 827-853. doi: 10.3934/jimo.2013.9.827

## Reordering policy and coordination of a supply chain with a loss-averse retailer

 1 Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, Jiangsu 211100, China 2 School of Management Science and Engineering, Nanjing University, Hankou Road 22, Nanjing, Jiangsu 210093, China

Received  December 2011 Revised  February 2013 Published  August 2013

This paper develops three (re)ordering models of a supply chain consisting of one risk-neutral manufacturer and one loss-averse retailer to study the coordination mechanism and the effects of the reordering policy on the coordination mechanism. The three (re)ordering policies are twice ordering policy with break-even quantity, twice ordering policy without break-even quantity and once ordering policy, respectively. We design a buyback-setup-cost-sharing mechanism to coordinate the supply chain for each policy, and Pareto analysis indicates that both the manufacturer and the retailer will realize a 'win-win' situation. By comparing the models, we find that twice ordering policy with break-even quantity is absolutely dominant for both the retailer and the supply chain. However, only if the break-even quantity is less than the mean quantity to failure, twice ordering policy without break-even quantity is dominant over the once ordering policy. The higher marginal revenue can induce more order quantity of the retailer under both twice ordering policy with break-even quantity and once ordering policy. However, it is interesting that it has no effect on the order plan of centralized decision-maker in twice ordering policy without break-even quantity.
Citation: Kebing Chen, Tiaojun Xiao. Reordering policy and coordination of a supply chain with a loss-averse retailer. Journal of Industrial & Management Optimization, 2013, 9 (4) : 827-853. doi: 10.3934/jimo.2013.9.827
##### References:
 [1] R. Anupindi, Supply contracts with quantity commitments and stochastic demand,, in, (1999), 199. doi: 10.1007/978-1-4615-4949-9_7. [2] F. Bernstein and A. Federgruen, Pricing and replenishment strategies in a distribution system with competing retailers,, Operations Research, 51 (2003), 409. doi: 10.1287/opre.51.3.409.14957. [3] G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue sharing contracts: Strengths and limitations,, Management Science, 51 (2005), 30. doi: 10.1287/mnsc.1040.0215. [4] G. P. Cachon, Supply chain coordination with contracts,, Handbook in Operation Research and Management Science, 11 (2003), 227. doi: 10.1016/S0927-0507(03)11006-7. [5] F. R. Chen, Coordination mechanisms for a distribution system with one supplier and multiple retailers,, Management Science, 47 (2001), 698. doi: 10.1287/mnsc.47.5.693.10484. [6] J. Chen and P. Bell, Coordinating a decentralized supply chain with customer returns and price-dependent stochastic demand using a buyback policy,, European Journal of Operational Research, 212 (2011), 293. doi: 10.1016/j.ejor.2011.01.036. [7] J. Chen, L. Guan and X. Q. Cai, Analysis on Buyers' cooperative strategy under group-buying price mechanism,, Journal of Industrial and Management Optimization, 9 (2013), 291. doi: 10.3934/jimo.2013.9.291. [8] K. B. Chen and T. J. Xiao, Demand disruption and coordination of the supply chain with a dominant retailer,, European Journal of Operational Research, 197 (2009), 225. doi: 10.1016/j.ejor.2008.06.006. [9] K. B. Chen and T. J. Xiao, Ordering policy and coordination of a supply chain with two-period demand uncertainty,, European Journal of Operational Research, 215 (2011), 347. doi: 10.1016/j.ejor.2011.06.015. [10] C. H. Chiu, T. M. Choi and X. Li, Supply chain coordination with risk sensitive retailer under target sales rebate,, Automatica, 47 (2011), 1617. doi: 10.1016/j.automatica.2011.04.012. [11] T. M. Choi, D. Li and H. M. Yan, Optimal returns policy for supply chain with e-marketplace,, International Journal of Production Economics, 88 (2004), 205. doi: 10.1016/S0925-5273(03)00188-9. [12] P. Dutta, D. Chakraborty and A. R. Roy, An inventory model for single-period products with reordering opportunities under fuzzy demand,, Computers & Mathematics with Applications, 53 (2007), 1502. doi: 10.1016/j.camwa.2006.04.029. [13] H. Emmons and S. M. Gilbert, Note: The role of returns policies in pricing and inventory decisions for catalogue goods,, Management Science, 44 (1998), 276. doi: 10.1287/mnsc.44.2.276. [14] M. L. Fisher, J. H. Hammond, W. R. Obermeyer and A. Raman, Making supply meet demand in an uncertain world,, Harvard Business Review, 5-6 (1994), 5. [15] X. Gan, S. Sethi and H. Yan, Channel coordination with a risk neutral supplier and a downside risk-averse retailer,, Production and Operations Management, 14 (2005), 80. doi: 10.1111/j.1937-5956.2005.tb00011.x. [16] G. Hadley and T. M. Whitin, "Analysis of Inventory Systems,", Prentice-Hall, (1963). [17] M. Hervé., "Axioms of Cooperative Decision Making,", Econometric Society Monographs, 15 (1988). [18] Z. S. Hua and S. J. Li, Impacts of demand uncertainty on retailer's dominance and manufacturer -retailer supply chain cooperation,, Omeg, 36 (2008), 697. doi: 10.1016/j.omega.2006.02.005. [19] R. Jarrow and F. Zhao, Downside loss aversion and portfolio management,, Management Science, 52 (2006), 558. [20] H. S. Lau and A. H. L. Lau, Reordering strategies for a newsboy-type product,, European Journal of Operational Research, 103 (1997), 557. doi: 10.1016/S0377-2217(96)00304-9. [21] H. Lee and S. Whang, Decentralized multi-echelon supply chains: Incentives and information,, Management Science, 45 (1999), 633. doi: 10.1287/mnsc.45.5.633. [22] J. Y. Lee and L. B. Schwarz, Lead time reduction in a (Q, r) inventory system: An agency perspective,, International Journal of Production Economics, 105 (2007), 204. [23] L. Q. Liu, A. J. Rettenmaier and T. R. Saving, How much and how often: A model of repeated consumption with endogenous consumption frequency,, Economics Letters, 110 (2011), 186. doi: 10.1016/j.econlet.2010.11.032. [24] J. Mazzola and R. Schantz, Single-facility resourse allocation under capacity-based economies and diseconomies of scope,, Management Science, 41 (1995), 669. doi: 10.1287/mnsc.41.4.669. [25] M. $\ddotO$nal and H. E. Romeijn, Two-echelon requirements planning with pricing decisions,, Journal of Industrial and Management Optimization, 5 (2009), 767. doi: 10.3934/jimo.2009.5.767. [26] V. Padmanabhan and I. P. L. Png, Returns policies: Make money by making good,, Sloan Management Review, 37 (1995), 65. [27] A. Pan, S. Y. S. Leung, K. L. Moon and K. W. Yeung, Optimal reorder decision-making in the agent -based apparel supply chain,, Expert Systems with Applications, 36 (2009), 8571. doi: 10.1016/j.eswa.2008.10.081. [28] M. Parlar and Z. K. Weng, Designing a firm's coordinated manufacturing and supply decisions with short product life cycles,, Management Science, 43 (1997), 1329. doi: 10.1287/mnsc.43.10.1329. [29] M. E. Schweitzer and G. P. Cachon, Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence,, Management Science, 46 (2000), 404. doi: 10.1287/mnsc.46.3.404.12070. [30] K. Shi and T. J. Xiao, Coordination of a supply chain with a loss-averse retailer under two types of contracts,, International Journal of Information and Decision Sciences, 1 (2008), 5. doi: 10.1504/IJIDS.2008.020033. [31] D. Sophia, Design of supply chains for quick response: the case of apparel industry,, 2001. Available from: , (). [32] T. A. Taylor, Supply chain coordination under channel rebates with sales effort effects,, Management Science, 48 (2002), 992. doi: 10.1287/mnsc.48.8.992.168. [33] A. Tsay and N. Agrawal, Channel dynamics under price and service competition,, Manufacturing & Service Operations Management, 2 (2000), 372. doi: 10.1287/msom.2.4.372.12342. [34] B. Tomlin and Y. Wang, On the value of mix flexibility and dual sourcing in unreliable newsvendor networks,, Manufacturing & Service Operations Management, 7 (2005), 37. doi: 10.1287/msom.1040.0063. [35] C. X. Wang and S. Webster, Channel coordination for a supply chain with a risk-neutral manufacturer and a loss-averse retailer,, Decision Sciences, 38 (2007), 361. doi: 10.1111/j.1540-5915.2007.00163.x. [36] Z. K. Weng, Coordinating order quantities between the manufacturer and the buyer: A generalized newsvendor model,, European Journal of Operational Research, 156 (2004), 148. doi: 10.1016/S0377-2217(03)00003-1. [37] J. Wu, J. Li, S. Y. Wang and T. C. E Cheng, Mean-variance analysis of the newsvendor model with stockout cost,, Omega, 37 (2009), 724. doi: 10.1016/j.omega.2008.02.005. [38] T. J. Xiao and D. Q. Yang, Price and service competition of supply chains with risk-averse retailers under demand uncertainty,, International Journal of Production Economics, 114 (2008), 187. doi: 10.1016/j.ijpe.2008.01.006. [39] T. J. Xiao, K. Shi and D. Q. Yang, Coordination of a supply chain with consumer return under demand uncertainty,, International Journal of Production Economics, 124 (2010), 171. doi: 10.1016/j.ijpe.2009.10.021. [40] H. Xiong, B. T. Chen and J. Xie, A composite contract based on buy back and quantity flexibility contracts,, European Journal of Operational Research, 210 (2011), 559. doi: 10.1016/j.ejor.2010.10.010. [41] X. L. Xu and X. Q. Cai, Price and delivery-time competition of perishable products,, Journal of Industrial and Management Optimization, 4 (2008), 843. doi: 10.3934/jimo.2008.4.843. [42] Q. Y. Yan, J. B. Li and J. L. Zhang, Licensing schemes in Stackelberg model under asymmetric information of product costs,, Journal of Industrial and Management Optimization, 3 (2007), 763. doi: 10.3934/jimo.2007.3.763. [43] C. T. Yang, L. Y. Ouyang, H. F. Yen and K. L. Lee, Joint pricing and ordering policies for deteriorating item with retail price-dependent demand in response to announced supply price increase,, Journal of Industrial and Management Optimization, 9 (2013), 437. doi: 10.3934/jimo.2013.9.437. [44] J. Zhang and G. V. Frazier, Strategic alliance via co-opetition: Supply chain partnership with a competitor,, Decision Support Systems, 51 (2011), 853. [45] J. Zhang and J. Chen, Externality of contracts on supply chains with two suppliers and a common retailer,, Journal of Industrial and Management Optimization, 6 (2010), 795. doi: 10.3934/jimo.2010.6.795. [46] Y. W. Zhou and S. D. Wang, Manufacturer-buyer coordination for newsvendor-type- products with two ordering opportunities and partial backorders,, European Journal of Operational Research, 198 (2009), 958. doi: 10.1016/j.ejor.2008.10.026. [47] Y. Zhou and D. H. Li, Coordinating order quantity decisions in the supply chain contract under random demand,, Applied Mathematical Modeling, 31 (2007), 1029. doi: 10.1016/j.apm.2006.02.011.

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##### References:
 [1] R. Anupindi, Supply contracts with quantity commitments and stochastic demand,, in, (1999), 199. doi: 10.1007/978-1-4615-4949-9_7. [2] F. Bernstein and A. Federgruen, Pricing and replenishment strategies in a distribution system with competing retailers,, Operations Research, 51 (2003), 409. doi: 10.1287/opre.51.3.409.14957. [3] G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue sharing contracts: Strengths and limitations,, Management Science, 51 (2005), 30. doi: 10.1287/mnsc.1040.0215. [4] G. P. Cachon, Supply chain coordination with contracts,, Handbook in Operation Research and Management Science, 11 (2003), 227. doi: 10.1016/S0927-0507(03)11006-7. [5] F. R. Chen, Coordination mechanisms for a distribution system with one supplier and multiple retailers,, Management Science, 47 (2001), 698. doi: 10.1287/mnsc.47.5.693.10484. [6] J. Chen and P. Bell, Coordinating a decentralized supply chain with customer returns and price-dependent stochastic demand using a buyback policy,, European Journal of Operational Research, 212 (2011), 293. doi: 10.1016/j.ejor.2011.01.036. [7] J. Chen, L. Guan and X. Q. Cai, Analysis on Buyers' cooperative strategy under group-buying price mechanism,, Journal of Industrial and Management Optimization, 9 (2013), 291. doi: 10.3934/jimo.2013.9.291. [8] K. B. Chen and T. J. Xiao, Demand disruption and coordination of the supply chain with a dominant retailer,, European Journal of Operational Research, 197 (2009), 225. doi: 10.1016/j.ejor.2008.06.006. [9] K. B. Chen and T. J. Xiao, Ordering policy and coordination of a supply chain with two-period demand uncertainty,, European Journal of Operational Research, 215 (2011), 347. doi: 10.1016/j.ejor.2011.06.015. [10] C. H. Chiu, T. M. Choi and X. Li, Supply chain coordination with risk sensitive retailer under target sales rebate,, Automatica, 47 (2011), 1617. doi: 10.1016/j.automatica.2011.04.012. [11] T. M. Choi, D. Li and H. M. Yan, Optimal returns policy for supply chain with e-marketplace,, International Journal of Production Economics, 88 (2004), 205. doi: 10.1016/S0925-5273(03)00188-9. [12] P. Dutta, D. Chakraborty and A. R. Roy, An inventory model for single-period products with reordering opportunities under fuzzy demand,, Computers & Mathematics with Applications, 53 (2007), 1502. doi: 10.1016/j.camwa.2006.04.029. [13] H. Emmons and S. M. Gilbert, Note: The role of returns policies in pricing and inventory decisions for catalogue goods,, Management Science, 44 (1998), 276. doi: 10.1287/mnsc.44.2.276. [14] M. L. Fisher, J. H. Hammond, W. R. Obermeyer and A. Raman, Making supply meet demand in an uncertain world,, Harvard Business Review, 5-6 (1994), 5. [15] X. Gan, S. Sethi and H. Yan, Channel coordination with a risk neutral supplier and a downside risk-averse retailer,, Production and Operations Management, 14 (2005), 80. doi: 10.1111/j.1937-5956.2005.tb00011.x. [16] G. Hadley and T. M. Whitin, "Analysis of Inventory Systems,", Prentice-Hall, (1963). [17] M. Hervé., "Axioms of Cooperative Decision Making,", Econometric Society Monographs, 15 (1988). [18] Z. S. Hua and S. J. Li, Impacts of demand uncertainty on retailer's dominance and manufacturer -retailer supply chain cooperation,, Omeg, 36 (2008), 697. doi: 10.1016/j.omega.2006.02.005. [19] R. Jarrow and F. Zhao, Downside loss aversion and portfolio management,, Management Science, 52 (2006), 558. [20] H. S. Lau and A. H. L. Lau, Reordering strategies for a newsboy-type product,, European Journal of Operational Research, 103 (1997), 557. doi: 10.1016/S0377-2217(96)00304-9. [21] H. Lee and S. Whang, Decentralized multi-echelon supply chains: Incentives and information,, Management Science, 45 (1999), 633. doi: 10.1287/mnsc.45.5.633. [22] J. Y. Lee and L. B. Schwarz, Lead time reduction in a (Q, r) inventory system: An agency perspective,, International Journal of Production Economics, 105 (2007), 204. [23] L. Q. Liu, A. J. Rettenmaier and T. R. Saving, How much and how often: A model of repeated consumption with endogenous consumption frequency,, Economics Letters, 110 (2011), 186. doi: 10.1016/j.econlet.2010.11.032. [24] J. Mazzola and R. Schantz, Single-facility resourse allocation under capacity-based economies and diseconomies of scope,, Management Science, 41 (1995), 669. doi: 10.1287/mnsc.41.4.669. [25] M. $\ddotO$nal and H. E. Romeijn, Two-echelon requirements planning with pricing decisions,, Journal of Industrial and Management Optimization, 5 (2009), 767. doi: 10.3934/jimo.2009.5.767. [26] V. Padmanabhan and I. P. L. Png, Returns policies: Make money by making good,, Sloan Management Review, 37 (1995), 65. [27] A. Pan, S. Y. S. Leung, K. L. Moon and K. W. Yeung, Optimal reorder decision-making in the agent -based apparel supply chain,, Expert Systems with Applications, 36 (2009), 8571. doi: 10.1016/j.eswa.2008.10.081. [28] M. Parlar and Z. K. Weng, Designing a firm's coordinated manufacturing and supply decisions with short product life cycles,, Management Science, 43 (1997), 1329. doi: 10.1287/mnsc.43.10.1329. [29] M. E. Schweitzer and G. P. Cachon, Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence,, Management Science, 46 (2000), 404. doi: 10.1287/mnsc.46.3.404.12070. [30] K. Shi and T. J. Xiao, Coordination of a supply chain with a loss-averse retailer under two types of contracts,, International Journal of Information and Decision Sciences, 1 (2008), 5. doi: 10.1504/IJIDS.2008.020033. [31] D. Sophia, Design of supply chains for quick response: the case of apparel industry,, 2001. Available from: , (). [32] T. A. Taylor, Supply chain coordination under channel rebates with sales effort effects,, Management Science, 48 (2002), 992. doi: 10.1287/mnsc.48.8.992.168. [33] A. Tsay and N. Agrawal, Channel dynamics under price and service competition,, Manufacturing & Service Operations Management, 2 (2000), 372. doi: 10.1287/msom.2.4.372.12342. [34] B. Tomlin and Y. Wang, On the value of mix flexibility and dual sourcing in unreliable newsvendor networks,, Manufacturing & Service Operations Management, 7 (2005), 37. doi: 10.1287/msom.1040.0063. [35] C. X. Wang and S. Webster, Channel coordination for a supply chain with a risk-neutral manufacturer and a loss-averse retailer,, Decision Sciences, 38 (2007), 361. doi: 10.1111/j.1540-5915.2007.00163.x. [36] Z. K. Weng, Coordinating order quantities between the manufacturer and the buyer: A generalized newsvendor model,, European Journal of Operational Research, 156 (2004), 148. doi: 10.1016/S0377-2217(03)00003-1. [37] J. Wu, J. Li, S. Y. Wang and T. C. E Cheng, Mean-variance analysis of the newsvendor model with stockout cost,, Omega, 37 (2009), 724. doi: 10.1016/j.omega.2008.02.005. [38] T. J. Xiao and D. Q. Yang, Price and service competition of supply chains with risk-averse retailers under demand uncertainty,, International Journal of Production Economics, 114 (2008), 187. doi: 10.1016/j.ijpe.2008.01.006. [39] T. J. Xiao, K. Shi and D. Q. Yang, Coordination of a supply chain with consumer return under demand uncertainty,, International Journal of Production Economics, 124 (2010), 171. doi: 10.1016/j.ijpe.2009.10.021. [40] H. Xiong, B. T. Chen and J. Xie, A composite contract based on buy back and quantity flexibility contracts,, European Journal of Operational Research, 210 (2011), 559. doi: 10.1016/j.ejor.2010.10.010. [41] X. L. Xu and X. Q. Cai, Price and delivery-time competition of perishable products,, Journal of Industrial and Management Optimization, 4 (2008), 843. doi: 10.3934/jimo.2008.4.843. [42] Q. Y. Yan, J. B. Li and J. L. Zhang, Licensing schemes in Stackelberg model under asymmetric information of product costs,, Journal of Industrial and Management Optimization, 3 (2007), 763. doi: 10.3934/jimo.2007.3.763. [43] C. T. Yang, L. Y. Ouyang, H. F. Yen and K. L. Lee, Joint pricing and ordering policies for deteriorating item with retail price-dependent demand in response to announced supply price increase,, Journal of Industrial and Management Optimization, 9 (2013), 437. doi: 10.3934/jimo.2013.9.437. [44] J. Zhang and G. V. Frazier, Strategic alliance via co-opetition: Supply chain partnership with a competitor,, Decision Support Systems, 51 (2011), 853. [45] J. Zhang and J. Chen, Externality of contracts on supply chains with two suppliers and a common retailer,, Journal of Industrial and Management Optimization, 6 (2010), 795. doi: 10.3934/jimo.2010.6.795. [46] Y. W. Zhou and S. D. Wang, Manufacturer-buyer coordination for newsvendor-type- products with two ordering opportunities and partial backorders,, European Journal of Operational Research, 198 (2009), 958. doi: 10.1016/j.ejor.2008.10.026. [47] Y. Zhou and D. H. Li, Coordinating order quantity decisions in the supply chain contract under random demand,, Applied Mathematical Modeling, 31 (2007), 1029. doi: 10.1016/j.apm.2006.02.011.
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