Differential Return on Investment Optimization: Pricing, Lotsizing, and Shipment Considerations in a Two-Echelon Supply Chain

Introduction And Background

An up-to-date review by Chen and Simchi-Levi (2012) reveals there is a growing literature in presenting and analyzing optimization models integrating pricing and lotsizing policies. In today’s global markets, the revenue management (RM) models are becoming a powerful instrument, where a retail industry desires to provide different levels of marketing mix (named four P’s: price, product, promotion and place) to different market segmentations (i.e. channels). Since the pioneering review research of Kleijn and Dekker (1998), the concept of inventories’ price differentiation has been one of the most pervasive activities in both the marketing and operations academic literature and practice.

One of the underlying principles of RM is to divide a single market into multiple sub-markets/segments and then set different prices in each sub-market. Price differentiation is a powerful way for sellers to improve their profitability (Phillips, 2005). Sen and Zhang (1999) considered the newsboy problem with multiple demand classes, where demands were realized sequentially and demand dependency was modeled through the diversion. Zhang and Bell (2007) extended the newsvendor problem with backlogged demand to the case where the single product can be sold to different demand classes at different prices. Zhang et al. (2010) evaluated the simultaneous determination of price and inventory replenishment in a two-segment market with a fence. All of these research papers focus on profit aspects of the retailer/manufacturer without any other criterion.

Ghasemy Yaghin et al. (2013) presented a joint pricing and lot-sizing model with multiple demand classes to set different prices and marketing expenditure in each sub-market. Traditionally, numerous papers have employed the profit maximization or cost minimization as their objective in designing and analyzing inventory models. Many researchers also optimized the inventory systems under return on investment (ROI) maximization. As Lenskold (2003) mentions, it is completely reasonable, and highly beneficial, to expect a return on investment for each incremental marketing dollar spent. An inventory model using the criterion of ROI maximization is proposed by Schroeder and Krishnan (1976). Also, Rosenberg (1991) compares and contrasts profit maximization versus return on inventory investment with respect to logarithmic concave demand functions. Otake et al. (1999) proposed an ROI maximization model with the lot size and setup cost reduction investment as the strategic joint decision variables. Otake and Min (2001) constructed and analyzed inventory and investment in quality improvement policies under ROI maximization.