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

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

Reza Ghasemy Yaghin (Amirkabir University of Technology, Iran), Hadi Mosadegh (Amirkabir University of Technology, Iran) and S. M. T. Fatemi Ghomi (Amirkabir University of Technology, Iran)
DOI: 10.4018/978-1-5225-2944-6.ch009
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A two-echelon supply chain is studied that involves a retailer who faces demand from two or more market segments and enable to set different prices and marketing expenditures and a supplier who desires to find optimal number of shipments through an integrated system. A new mixed-integer non-linear fractional programming (MINLFP) model is developed. In order to solve the resultant MINLFP model, the constrained non-linear programming model is reformulated as an unconstrained one using penalty terms. Two meta-heuristics, namely simulated annealing (SA) and imperialist competitive algorithm (ICA), are applied to solve the relaxed unconstrained model. Numerical results show that ICA can reach better solutions in comparison with SA. However, SA has the ability of providing more robust solutions which are converged to a good solution. The chapter concludes with superiority of SA.
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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.

Key Terms in this Chapter

Marketing: Marketing’s primary focus is to identify and satisfy customers in a way that helps build a solid and, hopefully, sustained relationship that encourages customers to continue doing business with the marketer.

Return on Inventory Investment: The ratio of profit to investment, and is a widely utilized economic performance measure dealing with finished goods inventories.

Inventory: Materials and components that businesses hold in stock.

Pricing: The method a company uses to set the price its product. Pricing is one of the four aspects of marketing. The other three parts of the marketing mix are product management, promotion, and distribution.

Mathematical Optimization: The selection of a best element (with regard to some criterion) from some set of available alternatives based on mathematical formulation.

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