Inventory and coordination issues with two substitutable products

Abstract

This study considers a two level supply chain in a newsboy setting with two substitutable products. Demands for the two products are assumed independent as long as both are available. If, however, a product stocks out, some of its demand is transferred to the available one with a known probability which ultimately creates a dependence on the amount of purchased items. The retailer is allowed to return some or all of the unsold products to the manufacturer with some credit. The expected chain profit, the retailer’s and the manufacturer’s profit expressions are derived under general conditions. Special cases are inspected to investigate the conditions under which channel coordination is achieved. It is demonstrated that channel coordination can not be achieved if unlimited returns are allowed with full credit, a result that agrees with the findings of Pasternak [B.A. Pasternack, Optimal pricing and return policies for perishable commodities, Market. Sci. 4 (1985) 166– 176] for the single item case. For the cases of unlimited returns with partial credit, the conditions for coordination are derived for one way full substitutions. For exponential demand explicit expressions for the channel and retailer’s expected profit functions are provided. 2009 Elsevier Inc. All rights reserved.