Inventory management under price-based and stockout-based substitution

We examine a stochastic inventory and pricing problem for a firm that sells two vertically differentiated products. The demands for the two products are determined by total (random) market size and the customers' net utility from buying the two products, which is determined by the products' quality attributes, the individual quality valuation (unknown to the firm), and the selling prices. In case the preferred product is out of stock, customers may be willing to buy a substitute instead, if their net utility is non-negative. Therefore, we analyze an inventory and pricing model, considering price-based and stockout-based substitution. We show that the demand function is not continuous in price. By decomposing the profit function into different price regimes, we are able to derive closed-form expressions for the stockout-based substitution rates (upward and downward substitution) and the optimal inventory levels under exogenous pricing. Under endogenous pricing, we find that the profit function is not necessarily unimodal. However, we show that a unique solution exists for the integrated price and inventory problem under price-based substitution only. Numerical results reveal that not considering stockout-based substitution (i) leads to lower profit margins for high-quality products and (ii) may cause severe supply-demand mismatches throughout the entire assortment. Finally, we show the performance of two approximated pricing policies. (C) 2017 Elsevier B.V. All rights reserved.