Copyright © 2013 Yancong Zhou and Junqing Sun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Substitution behaviors happen frequently when demands are uncertain in a production inventory system, and it has attracted enough attention from firms. Related researches can be clearly classified into firm-driven substitution and customer-driven substitution. However, if production inventory is stock-out when a firm updates its product, the firm may use a new generation product to satisfy the customer’s demand of old generation product or use updated component to substitute old component to satisfy production demand. Obviously, two cases of substitution exist simultaneously in the product-updated system when an emergent shortage happens. In this paper, we consider a component order problem with component substitution and product substitution simultaneously in a product-updated system, where the case of firm-driven substitution or customer-driven substitution can be reached by setting different values for two system parameters. Firstly, we formulate the problem into a two-stage dynamic programming. Secondly, we give the optimal decisions about assembled quantities of different types of products. Next, we prove that the expected profit function is jointly concave in order quantities and decrease the feasible domain by determining some bounds for decision variables. Finally, some management insights about component substitution and product substitution are investigated by theoretical analysis method.