The loss-averse newsvendor problem with random supply capacity

Wei Liu; Shiji Song; Ying Qiao; Han Zhao

doi:10.3934/jimo.2016080

Article Contents

2017, Volume 13, Issue 3: 1417-1429. Doi: 10.3934/jimo.2016080

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The loss-averse newsvendor problem with random supply capacity

1.
Department of Basic Science, Military Economics Academy, Wuhan 430035, China
2.
Department of Automation, Tsinghua University, Beijing 100084, China
3.
School of Business Administration, Hubei University of Economics, Wuhan 430205, China

* Corresponding author: Wei Liu
* Corresponding author: Wei Liu

Received: April 2015

Published: September 2017

The paper is supported by Research Fund for the Doctoral Program of Higher Education (No.20120002110035,20130002130010) and Natural Science Foundation of China (No. 61273233).

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Abstract

This paper studies a newsvendor problem with random supply capacity, where the retailer (newsvendor) is loss-averse and the shortage cost is considered. When the retailer orders, the quantity actually received is the minimum between the order quantity and supply capacity, and his objective is to choose an order quantity to maximize the expected utility. It is shown that under different conditions, the loss-averse retailer may order larger than, equal to or less than the risk-neutral one, which is different from the existing result in the case without considering shortage cost. Further, if the shortage cost is less than a critical value, then the loss-averse retailer's optimal order quantity is always less than the risk-neutral retailer's. The numerical experiments are conducted to demonstrate our theoretical results.

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Mathematics Subject Classification: Primary: 90B05; Secondary: 91B42.

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Figure 1. A graphical presentation of demand and capacity outcomes

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Figure 2. Optimal order quantity vs loss aversion level for different levels of demand variation

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Figure 3. Value of $M(h, Q_0)$ vs shortage cost for different levels of demand variation

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Figure 4. Optimal order quantity vs selling price

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Figure 5. Optimal order quantity vs purchasing cost

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