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An inventory system with quasi-hyperbolic discounting rate

Xiaobo Zhao, Yun Zhou and Jinxing Xie

IISE Transactions, 2017, vol. 49, issue 6, 593-602

Abstract: In this article, we consider a periodic-review inventory system with stochastic demands for an infinite horizon, where the manager has a time-inconsistent preference with a quasi-hyperbolic discounting rate. We model the inventory system as an intra-personal sequential decision problem. It is shown that the ordering decision follows a base-stock policy but has a systematic bias in that the base-stock level is lower than the standard optimal level. We extend our analysis to a supply chain that is composed of a perfectly rational supplier and a quasi-hyperbolic retailer. The results show that the time-inconsistent preference of the retailer can cause considerable loss in system performance. We propose a contract with a delay-in-payment and income-sharing for such a supply chain. The results show that the contract can effectively un-bias the ordering decision of the retailer and can reach the goal of coordinating the supply chain to improve the performance.

Date: 2017
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DOI: 10.1080/24725854.2017.1303763

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