Hedging Risks in the Loss-Averse Newsvendor Problem with Backlogging

Xiaoqing Liu,Xinsheng Xu,Felix T S Chan

doi:10.3390/math7050429

Abstract

This paper studies the optimal order decisions for the loss-averse newsvendor problem with backordering and contributes to the risk hedging issue in the newsvendor model. The Conditional Value-at-Risk (CVaR) measure is applied to quantify the potential risks for the loss-averse newsvendor in a backordering setting, and we obtain the optimal order quantity for a loss-averse newsvendor to maximize the CVaR of utility. It is found that the optimal order quantity to maximize the CVaR objective could be bigger or smaller than the expected profit maximization (EPM) order quantity, which provides an alternative explanation on decision bias in the newsvendor model. This study also reveals that the optimal order quantity for a loss-averse newsvendor to maximize expected utility with backordering is smaller than the EPM order quantity, which implies that backordering encourages the loss-averse newsvendor to order fewer items. Sensitivity analyses are performed to investigate the properties of the optimal order quantities and managerial insights are suggested. This paper provides a novel method for the risk management of the loss-averse newsvendor model and presents several new ordering policies for the retailers in practice.

Highlights

Evidence-based practice has proven that stockouts always bring the retailer great supply risks, and the shortage cost ranging from profit loss to goodwill loss of the unsatisfied customers has an important influence on the benefit of the retailer
When loss aversion and shortage cost are considered, the optimal order quantity may be decreasing in the retail price p and increasing in the wholesale price c, which is different from those results in the classical newsvendor model
To hedge against potential risks, we introduce the Conditional Value-at-Risk (CVaR) measure and obtain the optimal order quantity for a loss-averse newsvendor to maximize CVaR about utility

Summary

Introduction

Evidence-based practice has proven that stockouts always bring the retailer great supply risks, and the shortage cost ranging from profit loss to goodwill loss of the unsatisfied customers has an important influence on the benefit of the retailer. Consumer Response of Europe, 15% of customers will accept the backorder invitation of the retailer in a stockout situation (Gruen and Corsten [1]) As another example, there was a worldwide study of more than 71,000 customers, which was conducted in a series of 29 studies across 20 countries. There was a worldwide study of more than 71,000 customers, which was conducted in a series of 29 studies across 20 countries It showed that about 20% of the unsatisfied customers would like to accept the backorders in a stockout situation (Gruen and Corsten [1]). Lodree et al [5,6]

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