# American Institute of Mathematical Sciences

October  2019, 15(4): 1753-1772. 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, 2019, 15 (4) : 1753-1772. doi: 10.3934/jimo.2018121
##### References:

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##### References:
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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