Optimal Pricing and Inventory Decisions for Fashion Retailers under Value-At-Risk Objective: Applications and Review

Introduction

The fashion retailing problem and the newsvendor problem share many common features. The fashion retailer faces uncertain demands in selling fashion products. The purchase cost of a specific fashion product is fixed, the selling season is short, the end-of-season markdown will clear the unsold leftover, and the fashion retailer needs to determine the order quantity of the fashion product from his supplier before the selling season starts. If we check the classical newsvendor problem (see, e.g., Lau, 1980), we can see that the problem faced by a fashion retailer is very close to the newsvendor problem. As a result, there are quite a number of studies which employ the newsvendor model to investigate supply chain management problems in fashion retailing. Examples include an investigation of trade promotion scan-back rebate scheme in fashion supply chains (Kurata & Yue, 2008), a mean-variance analysis of quick response fashion supply chains (Choi & Chow, 2008), and a study on risk hedging problem in multi-product fashion supply chains (Vaagen & Wallace, 2008).

Over the past few years, there are extensive studies of inventory models with the consideration of risk in the literature (see, e.g., Wu et al., 2009; Tapiero, 2005; Choi and Ruszczyriski, 2008). However, most of these studies do not consider pricing and only explore the corresponding optimal inventory policies. In addition, for those which include both inventory and pricing decisions, they only illustrate the technical details but do not show the applications of the algorithms (e.g. Chiu & Choi 2010). Since retail pricing is undoubtedly a crucial decision for fashion retailers and applications are important, we explore in this chapter the joint optimal pricing and stocking algorithms with an optimization objective based on the Value-at-Risk (VaR) function for a single-period product with price-dependent demand. We propose detailed algorithms to illustrate how the optimal pricing and stocking policies can be determined for different forms of price-dependent demand functions. This chapter can be taken as a review plus extended works supplementing the related literature (such as Gotoh & Takano, 2007; Chiu & Choi, 2010) with detailed algorithms, numerical analysis and discussions on channel coordination challenge.

The rest of the chapter is organized as follows. A literature review is first provided. The basic model is then discussed. Afterwards, the solution schemes are proposed and numerical examples are provided to further illustrate the findings. The performance of pure buyback contract and pure wholesale pricing contract in enhancing supply chain efficiency is examined. We finally conclude with a discussion on probable future research directions.