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doi: 10.3934/jimo.2018121

## Coordination of VMI supply chain with a loss-averse manufacturer under quality-dependency and marketing-dependency

 1 Institute of Transportation Development Strategy & Planning of Sichuan Province, Chengdu 610041, China 2 School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610036, China 3 School of Economics and Management, Jiang Su University of Science and Technology, Zhenjiang 212003, China

* Corresponding author: Juan He

Received  July 2017 Revised  March 2018 Published  August 2018

Fund Project: The paper is supported by the National Natural Science Foundation of China (Grant No.71273214) and the Philosophy and Social Science Research Grand of Sichuan Province (Grant No.SKA13-01)

This paper addresses a vendor-managed inventory (VMI) supply chain with a loss-averse manufacturer and a risk-neutral retailer. Market demand faced by the retailer is stochastic and dependent on product quality level and marketing effort level. We propose a combined contract composed of option and cost-sharing to investigate coordination and profit allocation issues of the supply chain. To model loss aversion of the manufacturer, we employ multiple mental accounts and apply the utility function to upside and downside potentials of manufacturer's production decision separately. We derive the optimal strategy for each member with a Stackelberg game in which the retailer acts as the leader. It is proved that both coordination of the supply chain and Pareto-improvement can be achieved synchronously by the combined contract. In the premise of coordination, the system-wide profit can be allocated arbitrarily only by option price. Through negotiation, the retailer and the manufacturer just need to confirm an appropriate option price to obtain that neither of them becomes worse off. We also find that the manufacturer's loss aversion is a significant element for contract design and profit allocation, and the manufacturer could benefit from its own loss aversion behavior under certain condition.

Citation: Fuyou Huang, Juan He, Jian Wang. Coordination of VMI supply chain with a loss-averse manufacturer under quality-dependency and marketing-dependency. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018121
##### References:
 [1] D. Barnes-Schuster, Y. Bassok and R. Anupindi, Coordination and flexibility in supply contracts with options, Manufacturing & Service Operations Management, 4 (2002), 171-207. doi: 10.1287/msom.4.3.171.7754. [2] M. Becker-Peth, E. Katok and U. W. Thonemann, Designing buyback contracts for irrational but predictable newsvendors, Management Science, 59 (2013), 1800-1816. doi: 10.1287/mnsc.1120.1662. [3] G. P. Cachon, Supply chain coordination with contracts, Handbooks in Operations Research and Management Science, 11 (2003), 227-339. doi: 10.1016/S0927-0507(03)11006-7. [4] J. Cai, X. Hu, Y. Han, H. Cheng and W. Huang, Supply chain coordination with an option contract under vendor-managed inventory, International Transactions in Operational Research, 23 (2016), 1163-1183. doi: 10.1111/itor.12172. [5] J. Cai, X. Hu, P. R. Tadikamalla and J. Shang, Flexible contract design for VMI supply chain with service-sensitive demand: Revenue-sharing and supplier subsidy, European Journal of Operational Research, 261 (2017), 143-153. doi: 10.1016/j.ejor.2017.01.043. [6] J. Cai, M. Zhong, J. Shang and W. Huang, Coordinating VMI supply chain under yield uncertainty: Option contract, subsidy contract, and replenishment tactic, International Journal of Production Economics, 185 (2017), 196-210. doi: 10.1016/j.ijpe.2016.12.032. [7] G. H. Chao, S. M. R. Iravani and R. C. Savaskan, Quality improvement incentives and product recall cost sharing contracts, Management Science, 55 (2009), 1122-1138. doi: 10.1287/mnsc.1090.1008. [8] J. Chen, L. Liang, D. Q. Yao and S. Sun, Price and quality decisions in dual-channel supply chains, European Journal of Operational Research, 259 (2017), 935-948. doi: 10.1016/j.ejor.2016.11.016. [9] K. Chen and T. Xiao, Reordering policy and coordination of a supply chain with a loss-averse retailer, Journal of Industrial and Management Optimization, 9 (2013), 827-853. doi: 10.3934/jimo.2013.9.827. [10] X. Chen, G. Hao and L. Li, Channel coordination with a loss-averse retailer and option contracts, International Journal of Production Economics, 150 (2014), 52-57. doi: 10.1016/j.ijpe.2013.12.004. [11] X. Chen and Z. Shen, An analysis on supply chain with options contracts and service requirement, IIE Transactions, 44 (2012), 805-819. doi: 10.1080/0740817X.2011.649383. [12] J. Dai and W. Meng, A risk-averse newsvendor model under marketing-dependency and price-dependency, International Journal of Production Economics, 160 (2015), 220-229. doi: 10.1016/j.ijpe.2014.11.006. [13] Y. Dai, S. X. Zhou and Y. Xu, Competitive and collaborative quality and warranty management in supply chains, Production and Operations management, 21 (2012), 129-144. doi: 10.1111/j.1937-5956.2011.01217.x. [14] M. A. Darwish and O. M. Odah, Vendor managed inventory model for single-vendor multi-retailer supply chains, European Journal of Operational Research, 204 (2010), 473-484. doi: 10.1016/j.ejor.2009.11.023. [15] A. M. Davis, E. Katok and N. Santamaría, Push, pull, or both? A behavioral study of how the allocation of inventory risk affects channel efficiency, Management Science, 60 (2014), 2666-2683. doi: 10.1287/mnsc.2014.1940. [16] X. Deng, J. Xie and H. Xiong, Manufacturer-retailer contracting with asymmetric information on retailer's degree of loss aversion, International Journal of Production Economics, 142 (2013), 372-380. doi: 10.1016/j.ijpe.2012.12.013. [17] Y. Dong, M. Dresner and Y. Yao, Beyond information sharing: An empirical analysis of vendor-managed inventory, Production and Operations Management, 23 (2014), 817-828. doi: 10.1111/poms.12085. [18] T. Feng, L. R. Keller and X. Zheng, Decision making in the newsvendor problem: A cross-national laboratory study, Omega, 39 (2011), 41-50. doi: 10.1016/j.omega.2010.02.003. [19] R. Guan and X. Zhao, On contracts for VMI program with continuous review (r, Q) policy, European Journal of Operational Research, 207 (2010), 656-667. doi: 10.1016/j.ejor.2010.04.037. [20] H. Gurnani and M. Erkoc, Supply contracts in manufacturer-retailer interactions with manufacturer-quality and retailer effort-induced demand, Naval Research Logistics, 55 (2008), 200-217. doi: 10.1002/nav.20277. [21] H. Gurnani, M. Erkoc and Y. Luo, Impact of product pricing and timing of investment decisions on supply chain co-opetition, European Journal of Operational Research, 180 (2007), 228-248. doi: 10.1016/j.ejor.2006.02.047. [22] M. Hariga, M. Gumus and A. Daghfous, Storage constrained vendor managed inventory models with unequal shipment frequencies, Omega, 48 (2014), 94-106. doi: 10.1016/j.omega.2013.11.003. [23] J. He, C. Ma and K. Pan, Capacity investment in supply chain with risk averse supplier under risk diversification contract, Transportation Research Part E: Logistics and Transportation Review, 106 (2017), 255-275. doi: 10.1016/j.tre.2017.08.005. [24] X. He, A. Krishnamoorthy, A. Prasad and S. P. Sethi, Retail competition and cooperative advertising, Operations Research Letters, 39 (2011), 11-16. doi: 10.1016/j.orl.2010.10.006. [25] Y. He and X. Zhao, Contracts and coordination: Supply chains with uncertain demand and supply, Naval Research Logistics, 63 (2016), 305-319. doi: 10.1002/nav.21695. [26] T. H. Ho and J. Zhang, Designing pricing contracts for boundedly rational customers: does the framing of the fixed fee matter?, Management Science, 54 (2008), 686-700. [27] D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-291. [28] R. Lal, Improving channel coordination through franchising, Marketing Science, 9 (1990), 299-318. doi: 10.1287/mksc.9.4.299. [29] J. Y. Lee, R. K. Cho and S. K. Paik, Supply chain coordination in vendor-managed inventory systems with stockout-cost sharing under limited storage capacity, European Journal of Operational Research, 248 (2016), 95-106. doi: 10.1016/j.ejor.2015.06.080. [30] W. Liu, S. Song, Y. Qiao and H. Zhao, The loss-averse newsvendor problem with random supply capacity, Journal of Industrial and Management Optimization, 13 (2017), 1417-1429. doi: 10.3934/jimo.2016080. [31] X. Liu, Q. Gou, L. Alwan and L. Liang, Option contracts: A solution for overloading problems in the delivery service supply chain, Journal of the Operational Research Society, 67 (2016), 187-197. doi: 10.1057/jors.2014.133. [32] P. Ma, H. Wang and J. Shang, Supply chain channel strategies with quality and marketing effort-dependent demand, International Journal of Production Economics, 144 (2013), 572-581. doi: 10.1016/j.ijpe.2013.04.020. [33] S. P. Sarmah, D. Acharya and S. K. Goyal, Coordination of a single-manufacturer/multi-buyer supply chain with credit option, International Journal of Production Economics, 111 (2008), 676-685. doi: 10.1016/j.ijpe.2007.04.003. [34] M. E. Schweitzer and G. P. Cachon, Decision bias in the newsvendor problem with a known demand distribution: experimental evidence, Management Science, 46 (2000), 404-420. doi: 10.1287/mnsc.46.3.404.12070. [35] Y. C. Tsao and G. J. Sheen, Effects of promotion cost sharing policy with the sales learning curve on supply chain coordination, Computers & Operations Research, 39 (2012), 1872-1878. doi: 10.1016/j.cor.2011.07.009. [36] N. K. Verma, A. Chakraborty and A. K. Chatterjee, Joint replenishment of multi retailer with variable replenishment cycle under VMI, European Journal of Operational Research, 233 (2014), 787-789. doi: 10.1016/j.ejor.2013.10.001. [37] M. Waller, M. E. Johnson and T. Davis, Vendor-managed inventory in the retail supply chain, Journal of Business Logistics, 20 (1999), 183-204. [38] 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), 361-389. doi: 10.1111/j.1540-5915.2007.00163.x. [39] C. X. Wang and S. Webster, The loss-averse newsvendor problem, Omega, 37 (2009), 93-105. doi: 10.1016/j.omega.2006.08.003. [40] X. Wang and L. Liu, Coordination in a retailer-led supply chain through option contract, International Journal of Production Economics, 110 (2007), 115-127. doi: 10.1016/j.ijpe.2007.02.022. [41] X. Wang, F. Li, L. Liang, Z. Huang and A. Ashley, Pre-purchasing with option contract and coordination in a relief supply chain, International Journal of Production Economics, 167 (2015), 170-176. doi: 10.1016/j.ijpe.2015.05.031. [42] D. J. Wu and P. R. Kleindorfer, Competitive options, supply contracting, and electronic markets, Management Science, 51 (2005), 452-466. doi: 10.1287/mnsc.1040.0341. [43] T. Xiao, Y. Xia and G. P. Zhang, Strategic outsourcing decisions for manufacturers competing on product quality, IIE Transactions, 46 (2014), 313-329. doi: 10.1080/0740817X.2012.761368. [44] Y. Yu and G. Q. Huang, Nash game model for optimizing market strategies, configuration of platform products in a vendor managed inventory (VMI) supply chain for a product family, European Journal of Operational Research, 206 (2010), 361-373. doi: 10.1016/j.ejor.2010.02.039. [45] J. Zhang, Coordination of supply chain with buyer's promotion, Journal of Industrial and Management Optimization, 3 (2007), 715-726. doi: 10.3934/jimo.2007.3.715. [46] Y. Zhao, S. Wang, T. C. E. Cheng, X. Yang and Z. Huang, Coordination of supply chains by option contracts: A cooperative game theory approach, European Journal of Operational Research, 207 (2010), 668-675. doi: 10.1016/j.ejor.2010.05.017.

show all references

##### References:
 [1] D. Barnes-Schuster, Y. Bassok and R. Anupindi, Coordination and flexibility in supply contracts with options, Manufacturing & Service Operations Management, 4 (2002), 171-207. doi: 10.1287/msom.4.3.171.7754. [2] M. Becker-Peth, E. Katok and U. W. Thonemann, Designing buyback contracts for irrational but predictable newsvendors, Management Science, 59 (2013), 1800-1816. doi: 10.1287/mnsc.1120.1662. [3] G. P. Cachon, Supply chain coordination with contracts, Handbooks in Operations Research and Management Science, 11 (2003), 227-339. doi: 10.1016/S0927-0507(03)11006-7. [4] J. Cai, X. Hu, Y. Han, H. Cheng and W. Huang, Supply chain coordination with an option contract under vendor-managed inventory, International Transactions in Operational Research, 23 (2016), 1163-1183. doi: 10.1111/itor.12172. [5] J. Cai, X. Hu, P. R. Tadikamalla and J. Shang, Flexible contract design for VMI supply chain with service-sensitive demand: Revenue-sharing and supplier subsidy, European Journal of Operational Research, 261 (2017), 143-153. doi: 10.1016/j.ejor.2017.01.043. [6] J. Cai, M. Zhong, J. Shang and W. Huang, Coordinating VMI supply chain under yield uncertainty: Option contract, subsidy contract, and replenishment tactic, International Journal of Production Economics, 185 (2017), 196-210. doi: 10.1016/j.ijpe.2016.12.032. [7] G. H. Chao, S. M. R. Iravani and R. C. Savaskan, Quality improvement incentives and product recall cost sharing contracts, Management Science, 55 (2009), 1122-1138. doi: 10.1287/mnsc.1090.1008. [8] J. Chen, L. Liang, D. Q. Yao and S. Sun, Price and quality decisions in dual-channel supply chains, European Journal of Operational Research, 259 (2017), 935-948. doi: 10.1016/j.ejor.2016.11.016. [9] K. Chen and T. Xiao, Reordering policy and coordination of a supply chain with a loss-averse retailer, Journal of Industrial and Management Optimization, 9 (2013), 827-853. doi: 10.3934/jimo.2013.9.827. [10] X. Chen, G. Hao and L. Li, Channel coordination with a loss-averse retailer and option contracts, International Journal of Production Economics, 150 (2014), 52-57. doi: 10.1016/j.ijpe.2013.12.004. [11] X. Chen and Z. Shen, An analysis on supply chain with options contracts and service requirement, IIE Transactions, 44 (2012), 805-819. doi: 10.1080/0740817X.2011.649383. [12] J. Dai and W. Meng, A risk-averse newsvendor model under marketing-dependency and price-dependency, International Journal of Production Economics, 160 (2015), 220-229. doi: 10.1016/j.ijpe.2014.11.006. [13] Y. Dai, S. X. Zhou and Y. Xu, Competitive and collaborative quality and warranty management in supply chains, Production and Operations management, 21 (2012), 129-144. doi: 10.1111/j.1937-5956.2011.01217.x. [14] M. A. Darwish and O. M. Odah, Vendor managed inventory model for single-vendor multi-retailer supply chains, European Journal of Operational Research, 204 (2010), 473-484. doi: 10.1016/j.ejor.2009.11.023. [15] A. M. Davis, E. Katok and N. Santamaría, Push, pull, or both? A behavioral study of how the allocation of inventory risk affects channel efficiency, Management Science, 60 (2014), 2666-2683. doi: 10.1287/mnsc.2014.1940. [16] X. Deng, J. Xie and H. Xiong, Manufacturer-retailer contracting with asymmetric information on retailer's degree of loss aversion, International Journal of Production Economics, 142 (2013), 372-380. doi: 10.1016/j.ijpe.2012.12.013. [17] Y. Dong, M. Dresner and Y. Yao, Beyond information sharing: An empirical analysis of vendor-managed inventory, Production and Operations Management, 23 (2014), 817-828. doi: 10.1111/poms.12085. [18] T. Feng, L. R. Keller and X. Zheng, Decision making in the newsvendor problem: A cross-national laboratory study, Omega, 39 (2011), 41-50. doi: 10.1016/j.omega.2010.02.003. [19] R. Guan and X. Zhao, On contracts for VMI program with continuous review (r, Q) policy, European Journal of Operational Research, 207 (2010), 656-667. doi: 10.1016/j.ejor.2010.04.037. [20] H. Gurnani and M. Erkoc, Supply contracts in manufacturer-retailer interactions with manufacturer-quality and retailer effort-induced demand, Naval Research Logistics, 55 (2008), 200-217. doi: 10.1002/nav.20277. [21] H. Gurnani, M. Erkoc and Y. Luo, Impact of product pricing and timing of investment decisions on supply chain co-opetition, European Journal of Operational Research, 180 (2007), 228-248. doi: 10.1016/j.ejor.2006.02.047. [22] M. Hariga, M. Gumus and A. Daghfous, Storage constrained vendor managed inventory models with unequal shipment frequencies, Omega, 48 (2014), 94-106. doi: 10.1016/j.omega.2013.11.003. [23] J. He, C. Ma and K. Pan, Capacity investment in supply chain with risk averse supplier under risk diversification contract, Transportation Research Part E: Logistics and Transportation Review, 106 (2017), 255-275. doi: 10.1016/j.tre.2017.08.005. [24] X. He, A. Krishnamoorthy, A. Prasad and S. P. Sethi, Retail competition and cooperative advertising, Operations Research Letters, 39 (2011), 11-16. doi: 10.1016/j.orl.2010.10.006. [25] Y. He and X. Zhao, Contracts and coordination: Supply chains with uncertain demand and supply, Naval Research Logistics, 63 (2016), 305-319. doi: 10.1002/nav.21695. [26] T. H. Ho and J. Zhang, Designing pricing contracts for boundedly rational customers: does the framing of the fixed fee matter?, Management Science, 54 (2008), 686-700. [27] D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-291. [28] R. Lal, Improving channel coordination through franchising, Marketing Science, 9 (1990), 299-318. doi: 10.1287/mksc.9.4.299. [29] J. Y. Lee, R. K. Cho and S. K. Paik, Supply chain coordination in vendor-managed inventory systems with stockout-cost sharing under limited storage capacity, European Journal of Operational Research, 248 (2016), 95-106. doi: 10.1016/j.ejor.2015.06.080. [30] W. Liu, S. Song, Y. Qiao and H. Zhao, The loss-averse newsvendor problem with random supply capacity, Journal of Industrial and Management Optimization, 13 (2017), 1417-1429. doi: 10.3934/jimo.2016080. [31] X. Liu, Q. Gou, L. Alwan and L. Liang, Option contracts: A solution for overloading problems in the delivery service supply chain, Journal of the Operational Research Society, 67 (2016), 187-197. doi: 10.1057/jors.2014.133. [32] P. Ma, H. Wang and J. Shang, Supply chain channel strategies with quality and marketing effort-dependent demand, International Journal of Production Economics, 144 (2013), 572-581. doi: 10.1016/j.ijpe.2013.04.020. [33] S. P. Sarmah, D. Acharya and S. K. Goyal, Coordination of a single-manufacturer/multi-buyer supply chain with credit option, International Journal of Production Economics, 111 (2008), 676-685. doi: 10.1016/j.ijpe.2007.04.003. [34] M. E. Schweitzer and G. P. Cachon, Decision bias in the newsvendor problem with a known demand distribution: experimental evidence, Management Science, 46 (2000), 404-420. doi: 10.1287/mnsc.46.3.404.12070. [35] Y. C. Tsao and G. J. Sheen, Effects of promotion cost sharing policy with the sales learning curve on supply chain coordination, Computers & Operations Research, 39 (2012), 1872-1878. doi: 10.1016/j.cor.2011.07.009. [36] N. K. Verma, A. Chakraborty and A. K. Chatterjee, Joint replenishment of multi retailer with variable replenishment cycle under VMI, European Journal of Operational Research, 233 (2014), 787-789. doi: 10.1016/j.ejor.2013.10.001. [37] M. Waller, M. E. Johnson and T. Davis, Vendor-managed inventory in the retail supply chain, Journal of Business Logistics, 20 (1999), 183-204. [38] 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), 361-389. doi: 10.1111/j.1540-5915.2007.00163.x. [39] C. X. Wang and S. Webster, The loss-averse newsvendor problem, Omega, 37 (2009), 93-105. doi: 10.1016/j.omega.2006.08.003. [40] X. Wang and L. Liu, Coordination in a retailer-led supply chain through option contract, International Journal of Production Economics, 110 (2007), 115-127. doi: 10.1016/j.ijpe.2007.02.022. [41] X. Wang, F. Li, L. Liang, Z. Huang and A. Ashley, Pre-purchasing with option contract and coordination in a relief supply chain, International Journal of Production Economics, 167 (2015), 170-176. doi: 10.1016/j.ijpe.2015.05.031. [42] D. J. Wu and P. R. Kleindorfer, Competitive options, supply contracting, and electronic markets, Management Science, 51 (2005), 452-466. doi: 10.1287/mnsc.1040.0341. [43] T. Xiao, Y. Xia and G. P. Zhang, Strategic outsourcing decisions for manufacturers competing on product quality, IIE Transactions, 46 (2014), 313-329. doi: 10.1080/0740817X.2012.761368. [44] Y. Yu and G. Q. Huang, Nash game model for optimizing market strategies, configuration of platform products in a vendor managed inventory (VMI) supply chain for a product family, European Journal of Operational Research, 206 (2010), 361-373. doi: 10.1016/j.ejor.2010.02.039. [45] J. Zhang, Coordination of supply chain with buyer's promotion, Journal of Industrial and Management Optimization, 3 (2007), 715-726. doi: 10.3934/jimo.2007.3.715. [46] Y. Zhao, S. Wang, T. C. E. Cheng, X. Yang and Z. Huang, Coordination of supply chains by option contracts: A cooperative game theory approach, European Journal of Operational Research, 207 (2010), 668-675. doi: 10.1016/j.ejor.2010.05.017.
Effect of the loss aversion coefficient on the optimal production quantity
Effects of the loss aversion coefficient on the expected profits of both parties
Expected profits with respect to option price under coordination ($\lambda = 2$)
Expected profits with respect to option price under coordination ($\lambda = 3$)
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