# American Institute of Mathematical Sciences

July  2012, 8(3): 577-590. doi: 10.3934/jimo.2012.8.577

## Single-period inventory model with discrete stochastic demand based on prospect theory

 1 Department of Automation, Tsinghua University, Beijing 100084, China, China, China

Received  March 2011 Revised  November 2011 Published  June 2012

This paper studies a single-period inventory (newsvendor) problem with discrete stochastic demand. In general, most of the previous works are based on the expected profit/cost criterion or expected utility criterion. We consider the effect of irrational factor under uncertainty and therefore incorporate prospect theory into inventory model. Our objective is to maximize the overall value of the prospect, which can be calculated by using the value function and the weighting function. For any given initial inventory level, it can be shown that a state-dependent order-up-to policy is optimal. Further, the optimal policy has a simple structure, and the retailer can easily decide whether to place an order or not. Moreover, the impacts of parameters on the optimal policy are illustrated through numerical experiments.
Citation: Wei Liu, Shiji Song, Cheng Wu. Single-period inventory model with discrete stochastic demand based on prospect theory. Journal of Industrial & Management Optimization, 2012, 8 (3) : 577-590. doi: 10.3934/jimo.2012.8.577
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