# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020125

## Coordination of a supply chain with a loss-averse retailer under supply uncertainty and marketing effort

 1 School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610036, China 2 Institute of Transportation Development Strategy & Planning of Sichuan Province, Chengdu 610041, China 3 School of Transportation and Logistics, Southwest Jiaotong University, Chengdu 610036, China

* Corresponding author: Fuyou Huang

Received  January 2020 Revised  May 2020 Early access  June 2020

Fund Project: The paper is supported by the National Natural Science Foundation of China (Grant No.71273214), the Humanities and Social Sciences of Education Ministry of China (Grant No. 18YJAZH024), the Science and Technology Project of Sichuan Province (Grant No. 20CXTD0081) and the Science and Technology Project of Transportation Department of Sichuan Province (Grant No. 2019-D-05)

This paper deals with a one-period two-stage supply chain, in which a loss-averse retailer facing stochastic demand orders products from a risk-neutral supplier subject to yield uncertainty. Marketing effort exerted by the retailer is employed to enhance the final market demand. We first establish a performance benchmark, and show that the wholesale price contract fails to coordinate the supply chain due to the effects of double marginalization and loss aversion. Then we propose a revenue-cost-sharing contract in order to achieve supply chain coordination. It is verified that a properly designed revenue-cost-sharing contract can achieve perfect coordination and a win-win outcome synchronously. Our results reveal that it is simple to implement and arbitrarily allocate the total channel profit between the retailer and the supplier. In addition, we examine the effect of the retailer's loss aversion degree on contract parameters and profit allocation, and we show that both the retailer and the supplier can benefit from marketing effort.

Citation: Wenying Xie, Bin Chen, Fuyou Huang, Juan He. Coordination of a supply chain with a loss-averse retailer under supply uncertainty and marketing effort. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020125
##### References:
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Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-291.  doi: 10.2307/1914185.  Google Scholar [26] B. Kazaz, Production planning under yield and demand uncertainty with yield-dependent cost and price, Manufacturing & Service Operations Management, 6 (2004), 209-224.  doi: 10.1287/msom.1030.0024.  Google Scholar [27] B. Kazaz and S. Webster, The impact of yield-dependent trading costs on pricing and production planning under supply and demand uncertainty, Manufacturing & Service Operations Management, 13 (2011), 404-417.   Google Scholar [28] H. Krishnan, R. Kapuscinski and D. A. Butz, Coordinating contracts for decentralized supply chains with retailer promotional effort, Management Science, 50 (2004), 48-63.   Google Scholar [29] M. Kunter, Coordination via cost and revenue sharing in manufacturercretailer channels, European Journal of Operational Research, 216 (2012), 477-486.  doi: 10.1016/j.ejor.2011.07.001.  Google Scholar [30] X. Li, Y. Li and X. Cai, Double marginalization and coordination in the supply chain with uncertain supply, European Journal of Operational Research, 226 (2013), 228-236.  doi: 10.1016/j.ejor.2012.10.047.  Google Scholar [31] P. Liao, F. Ye and X. Wu, A comparison of the merchant and agency models in the hotel industry, International Transactions in Operational Research, 26 (2019), 1052-1073.  doi: 10.1111/itor.12365.  Google Scholar [32] W. Liu, S. Song, Y. Qiao and H. Zhao, The loss-averse newsvendor problem with random supply capacity, Journal of Industrial & Management Optimization, 13 (2017), 1417-1429.  doi: 10.3934/jimo.2016080.  Google Scholar [33] S. K. Mukhopadhyay, X. Su and S. Ghose, Motivating retail marketing effort: Optimal contract design, Production and Operations Management, 18 (2009), 197-211.  doi: 10.1111/j.1937-5956.2009.01014.x.  Google Scholar [34] S. Ray, S. Li and Y. Song, Tailored supply chain decision making under price-sensitive stochastic demand and delivery uncertainty, Management Science, 51 (2005), 1733-1902.  doi: 10.1287/mnsc.1050.0452.  Google Scholar [35] A. N. Sadigh, S. K. Chaharsooghi and M. Sheikhmohammady, A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain, Journal of Industrial & Management Optimization, 12 (2016), 337-355.  doi: 10.3934/jimo.2016.12.337.  Google Scholar [36] M. E. Schweitzer and G. P. Cachon, Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence, Management Science, 46 (2000), 333-450.  doi: 10.1287/mnsc.46.3.404.12070.  Google Scholar [37] K. Taaffe, J. Geunes and H. E. Romeijn, Target market selection and marketing effort under uncertainty: The selective newsvendor, European Journal of Operational Research, 189 (2008), 987-1003.  doi: 10.1016/j.ejor.2006.11.049.  Google Scholar [38] T. A. Taylor, Sale timing in a supply chain: When to sell to the retailer, Manufacturing & Service Operations Management, 8 (2006), 23-42.  doi: 10.1287/msom.1050.0089.  Google Scholar [39] 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.  Google Scholar [40] C. X. Wang, Random yield and uncertain demand in decentralised supply chains under the traditional and VMI arrangements, International Journal of Production Research, 47 (2009), 1955-1968.  doi: 10.1080/00207540701666220.  Google Scholar [41] 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.  Google Scholar [42] X. Xu, C. K. Chan and A. Langevin, Coping with risk management and fill rate in the loss-averse newsvendor model, International Journal of Production Economics, 195 (2018), 296-310.  doi: 10.1016/j.ijpe.2017.10.024.  Google Scholar [43] X. Xu, F. T. S. Chan and C. K. Chan, Optimal option purchase decision of a loss-averse retailer under emergent replenishment, International Journal of Production Research, 57 (2019), 4594-4620.  doi: 10.1080/00207543.2019.1579935.  Google Scholar [44] X. Xu and Z. Meng, Coordination between a supplier and a retailer in terms of profit concession for a two-stage supply chain, International Journal of Production Research, 52 (2014), 2122-2133.  doi: 10.1080/00207543.2013.854940.  Google Scholar [45] X. Xu, Z. Meng, P. Ji, C. Dang and H. Wang, On the newsvendor model with conditional Value-at-Risk of opportunity loss, International Journal of Production Research, 54 (2016), 2449-2458.  doi: 10.1080/00207543.2015.1100765.  Google Scholar [46] X. Xu, H. Wang, C. Dang and P. Ji, The loss-averse newsvendor model with backordering, International Journal of Production Economics, 188 (2017), 1-10.  doi: 10.1016/j.ijpe.2017.03.005.  Google Scholar [47] Z. Yao, S. C. H. Leung and K. K. Lai, Manufacturer's revenue-sharing contract and retail competition, European Journal of Operational Research, 186 (2008), 637-651.  doi: 10.1016/j.ejor.2007.01.049.  Google Scholar [48] J. Zhang, Coordination of supply chain with buyer's promotion, Journal of Industrial & Management Optimization, 3 (2007), 715-726.  doi: 10.3934/jimo.2007.3.715.  Google Scholar [49] Y. Zhou, Z. Shen, R. Ying and X. Xu, A loss-averse two-product ordering model with information updating in two-echelon inventory system, Journal of Industrial & Management Optimization, 14 (2018), 687-705.  doi: 10.3934/jimo.2017069.  Google Scholar

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##### References:
 [1] M. Becker-Peth, E. Katok and U. W. Thonemann, Designing buyback contracts for irrational but predictable newsvendors, Management Science, 59 (2013), 1800-1816.   Google Scholar [2] G. P. Cachon and M. A. Lariviere, Supply chain coordination with revenue-sharing contracts: Strengths and limitations, Management Science, 51 (2005), 1-150.  doi: 10.1287/mnsc.1040.0215.  Google Scholar [3] B. Chen, W. Xie, F. Huang and J. He, Quality competition and coordination in a vendor-managed inventory supply chain with two risk-averse manufacturers, Journal of Industrial & Management Optimization, http://dx.doi.org/10.3934/jimo.2020100. Google Scholar [4] K. Chen and T. Xiao, Reordering policy and coordination of a supply chain with a loss-averse retailer, Journal of Industrial & Management Optimization, 9 (2013), 827-853.  doi: 10.3934/jimo.2013.9.827.  Google Scholar [5] K. Chen and L. Yang, Random yield and coordination mechanisms of a supply chain with emergency backup sourcing, International Journal of Production Research, 52 (2014), 4747-4767.  doi: 10.1080/00207543.2014.886790.  Google Scholar [6] 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.  Google Scholar [7] Y. Gerchak and Y. Wang, Revenue-sharing vs. wholesale-price contracts in assembly systems with random demand, Production & Operations Management, 13 (2004), 23-33.   Google Scholar [8] I. Giannoccaro and P. Pontrandolfo, Supply chain coordination by revenue sharing contracts, International Journal of Production Economics, 89 (2004), 131-139.   Google Scholar [9] B. C. Giri and S. Bardhan, Coordinating a supply chain under uncertain demand and random yield in presence of supply disruption, International Journal of Production Research, 53 (2015), 5070-5084.  doi: 10.1080/00207543.2015.1030469.  Google Scholar [10] A. Golmohammadi and E. Hassini, Capacity, pricing and production under supply and demand uncertainties with an application in agriculture, European Journal of Operational Research, 275 (2019), 1037-1049.  doi: 10.1016/j.ejor.2018.12.027.  Google Scholar [11] K. Govindan and M. N. Popiuc, Reverse supply chain coordination by revenue sharing contract: A case for the personal computers industry, European Journal of Operational Research, 233 (2014), 326-336.  doi: 10.1016/j.ejor.2013.03.023.  Google Scholar [12] S. E. Grasman, T. L. Olsen and J. R. Birge, Setting basestock levels in multi-product systems with setups and random yield, IIE Transactions, 40 (2008), 1158-1170.  doi: 10.1080/07408170801967062.  Google Scholar [13] M. G. G$\ddot{u}$ler and M. E. Keski, On coordination under random yield and random demand, Expert Systems with Applications, 40 (2013), 3688-3695.   Google Scholar [14] H. Gurnani and Y. Gerchak, Coordination in decentralized assembly systems with uncertain component yields, European Journal of Operational Research, 176 (2007), 1559-1576.  doi: 10.1016/j.ejor.2005.09.036.  Google Scholar [15] Y. He and X. Zhao, Contracts and coordination: Supply chains with uncertain demand and supply: Contracts and coordination, Naval Research Logistics, 63 (2016), 305-319.  doi: 10.1002/nav.21695.  Google Scholar [16] Y. He, X. Zhao, L. Zhao and J. He, Coordinating a supply chain with effort and price dependent stochastic demand, Applied Mathematical Modelling, 33 (2009), 2777-2790.  doi: 10.1016/j.apm.2008.08.016.  Google Scholar [17] T. H. Ho, N. Lim and T. H. Cui, Reference dependence in multilocation newsvendor models: A structural analysis, Management Science, 56 (2010), 1891-1910.  doi: 10.1287/mnsc.1100.1225.  Google Scholar [18] B. Hu, M. Chao, X. Dong and Y. J. Son, Three-echelon supply chain coordination with a loss-averse retailer and revenue sharing contracts, International Journal of Production Economics, 179 (2016), 192-202.   Google Scholar [19] F. Hu, C. C. Lim and Z. Lu, Coordination of supply chains with a flexible ordering policy under yield and demand uncertainty, International Journal of Production Economics, 146 (2013), 686-693.  doi: 10.1016/j.ijpe.2013.08.024.  Google Scholar [20] F. Huang, J. He and Q. Lei, Coordination in a retailer-dominated supply chain with a risk-averse manufacturer under marketing dependency, International Transactions in Operational Research, https://doi.org/10.1111/itor.12520. doi: 10.1111/itor.12520.  Google Scholar [21] F. Huang, J. He and J. Wang, Coordination of VMI supply chain with a loss-averse manufacturer under quality-dependency and marketing-dependency, Journal of Industrial & Management Optimization, 15 (2019), 1753-1772.  doi: 10.3934/jimo.2018121.  Google Scholar [22] K. Inderfurth and J. Clemens, Supply chain coordination by risk sharing contracts under random production yield and deterministic demand, OR Spectrum, 36 (2014), 525-556.  doi: 10.1007/s00291-012-0314-3.  Google Scholar [23] K. Inderfurth and S. Vogelgesang, Concepts for safety stock determination under stochastic demand and different types of random production yield, European Journal of Operational Research, 224 (2013), 293-301.  doi: 10.1016/j.ejor.2012.07.040.  Google Scholar [24] P. C. Jones, T. J. Lowe and R. D. Traub, Matching supply and demand: The value of a second chance in producing seed corn, Manufacturing & Service Operations Management, 24 (2002), 222-238.   Google Scholar [25] D. Kahneman and A. Tversky, Prospect theory: An analysis of decision under risk, Econometrica, 47 (1979), 263-291.  doi: 10.2307/1914185.  Google Scholar [26] B. Kazaz, Production planning under yield and demand uncertainty with yield-dependent cost and price, Manufacturing & Service Operations Management, 6 (2004), 209-224.  doi: 10.1287/msom.1030.0024.  Google Scholar [27] B. Kazaz and S. Webster, The impact of yield-dependent trading costs on pricing and production planning under supply and demand uncertainty, Manufacturing & Service Operations Management, 13 (2011), 404-417.   Google Scholar [28] H. Krishnan, R. Kapuscinski and D. A. Butz, Coordinating contracts for decentralized supply chains with retailer promotional effort, Management Science, 50 (2004), 48-63.   Google Scholar [29] M. Kunter, Coordination via cost and revenue sharing in manufacturercretailer channels, European Journal of Operational Research, 216 (2012), 477-486.  doi: 10.1016/j.ejor.2011.07.001.  Google Scholar [30] X. Li, Y. Li and X. Cai, Double marginalization and coordination in the supply chain with uncertain supply, European Journal of Operational Research, 226 (2013), 228-236.  doi: 10.1016/j.ejor.2012.10.047.  Google Scholar [31] P. Liao, F. Ye and X. Wu, A comparison of the merchant and agency models in the hotel industry, International Transactions in Operational Research, 26 (2019), 1052-1073.  doi: 10.1111/itor.12365.  Google Scholar [32] W. Liu, S. Song, Y. Qiao and H. Zhao, The loss-averse newsvendor problem with random supply capacity, Journal of Industrial & Management Optimization, 13 (2017), 1417-1429.  doi: 10.3934/jimo.2016080.  Google Scholar [33] S. K. Mukhopadhyay, X. Su and S. Ghose, Motivating retail marketing effort: Optimal contract design, Production and Operations Management, 18 (2009), 197-211.  doi: 10.1111/j.1937-5956.2009.01014.x.  Google Scholar [34] S. Ray, S. Li and Y. Song, Tailored supply chain decision making under price-sensitive stochastic demand and delivery uncertainty, Management Science, 51 (2005), 1733-1902.  doi: 10.1287/mnsc.1050.0452.  Google Scholar [35] A. N. Sadigh, S. K. Chaharsooghi and M. Sheikhmohammady, A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain, Journal of Industrial & Management Optimization, 12 (2016), 337-355.  doi: 10.3934/jimo.2016.12.337.  Google Scholar [36] M. E. Schweitzer and G. P. Cachon, Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence, Management Science, 46 (2000), 333-450.  doi: 10.1287/mnsc.46.3.404.12070.  Google Scholar [37] K. Taaffe, J. Geunes and H. E. Romeijn, Target market selection and marketing effort under uncertainty: The selective newsvendor, European Journal of Operational Research, 189 (2008), 987-1003.  doi: 10.1016/j.ejor.2006.11.049.  Google Scholar [38] T. A. Taylor, Sale timing in a supply chain: When to sell to the retailer, Manufacturing & Service Operations Management, 8 (2006), 23-42.  doi: 10.1287/msom.1050.0089.  Google Scholar [39] 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.  Google Scholar [40] C. X. Wang, Random yield and uncertain demand in decentralised supply chains under the traditional and VMI arrangements, International Journal of Production Research, 47 (2009), 1955-1968.  doi: 10.1080/00207540701666220.  Google Scholar [41] 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.  Google Scholar [42] X. Xu, C. K. Chan and A. Langevin, Coping with risk management and fill rate in the loss-averse newsvendor model, International Journal of Production Economics, 195 (2018), 296-310.  doi: 10.1016/j.ijpe.2017.10.024.  Google Scholar [43] X. Xu, F. T. S. Chan and C. K. Chan, Optimal option purchase decision of a loss-averse retailer under emergent replenishment, International Journal of Production Research, 57 (2019), 4594-4620.  doi: 10.1080/00207543.2019.1579935.  Google Scholar [44] X. Xu and Z. Meng, Coordination between a supplier and a retailer in terms of profit concession for a two-stage supply chain, International Journal of Production Research, 52 (2014), 2122-2133.  doi: 10.1080/00207543.2013.854940.  Google Scholar [45] X. Xu, Z. Meng, P. Ji, C. Dang and H. Wang, On the newsvendor model with conditional Value-at-Risk of opportunity loss, International Journal of Production Research, 54 (2016), 2449-2458.  doi: 10.1080/00207543.2015.1100765.  Google Scholar [46] X. Xu, H. Wang, C. Dang and P. Ji, The loss-averse newsvendor model with backordering, International Journal of Production Economics, 188 (2017), 1-10.  doi: 10.1016/j.ijpe.2017.03.005.  Google Scholar [47] Z. Yao, S. C. H. Leung and K. K. Lai, Manufacturer's revenue-sharing contract and retail competition, European Journal of Operational Research, 186 (2008), 637-651.  doi: 10.1016/j.ejor.2007.01.049.  Google Scholar [48] J. Zhang, Coordination of supply chain with buyer's promotion, Journal of Industrial & Management Optimization, 3 (2007), 715-726.  doi: 10.3934/jimo.2007.3.715.  Google Scholar [49] Y. Zhou, Z. Shen, R. Ying and X. Xu, A loss-averse two-product ordering model with information updating in two-echelon inventory system, Journal of Industrial & Management Optimization, 14 (2018), 687-705.  doi: 10.3934/jimo.2017069.  Google Scholar
Wholesale price with respect to revenue-sharing coefficient under different loss aversion degrees
Cost-sharing coefficient with respect to wholesale price under different loss aversion degrees
Allocation of additional expected profit under coordination
Effect of loss aversion on order quantity
Effect of loss aversion on marketing effort level
Effect of loss aversion on expected profit
Effect of loss aversion on profit allocation
Production quantity with respect to $k$
Marketing effort level with respect to $k$
Expected profit with respect to $k$
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