Risk-Averse Newsvendor Model with Strategic Consumer Behavior

Qiying Hu,Tie Wang

doi:10.1155/2013/636259

Abstract

The classic newsvendor problem focuses on maximizing the expected profit or minimizing the expected cost when the newsvendor faces myopic customers. However, it ignores the customer’s bargain-hunting behavior and risk preference measure of the newsvendor. As a result, we carry out the rational expectation (RE) equilibrium analysis for risk-averse newsvendor facing forward-looking customers who anticipate future sales and choose purchasing timing to maximize their expected surplus. We propose the equations satisfied by the RE equilibrium price and quantity for the risk-averse retailer in general setting and the explicit equilibrium decisions for the case where demand follows the uniform distribution and utility is a general power function. We identify the impacts of the system parameters on the RE equilibrium for this specific situation. In particular, we show that the RE equilibrium price for some risk-averse newsvendors is lower than for a risk-neutral retailer and the RE equilibrium stocking quantity for some risk-averse newsvendors is higher than for a risk-neutral retailer. We also find that the RE equilibrium sale price for a risk-averse newsvendor is decreasing in salvage price in some situations.

Highlights

Product cost Customer valuation Retail price rational expectation (RE) equilibrium price for risk-neutral retailer RE equilibrium price for risk-averse retailer Salvage price Order quantity Optimal ordering quantity for risk-averse newsvendor model with myopic customers RE equilibrium ordering quantity for risk-neutral retailer RE equilibrium ordering quantity for risk-averse retailer pdf and cdf of the distribution of stochastic demand ξ Profit function Newsvendor’s utility function sale price in RE equilibrium for risk-averse newsvendor is decreasing in salvage price
To derive structural results and generate managerial insights into the equilibrium decisions of the risk-averse newsvendor problem with strategic consumers, we present specific results for the situation in which demand is a uniformly distributed and utility is a general power function
We obtain the analytical representations for the RE equilibrium price and quantity and perform the sensitivity analysis to investigate the impacts of ordering cost, salvage price, and degree of risk-aversion on the equilibrium

Summary

Introduction

Khouja and Robbins [15] extended the model presented by Gerchak and Parlar [14] to three cases of demand variation as a function of advertising expenditure: (1) demand has constant variance, (2) demand has constant coefficient variation, and (3) demand has an increasing coefficient variation They investigated the newsvendor problem with advertising under multiplicative demand and obtained the optimal advertising premium and ordering quantity by maximizing the expected profit or maximizing the probability of achieving a target profit under the previous three situations using particular mean demand and discussed that the optimal advertising decisions for maximizing profit is increased with the profit margin. We obtain an analytical solution for a specific situation where demand follows the uniform distribution and utility is a power function to illustrate the combined impacts of strategic consumer behavior and risk aversion on newsvendor’s decisions.

The General Model

Rational Expectation Equilibrium for Power Utility and Uniform Distribution

Numerical Examples

Conclusions