An application of shortest path algorithm: optimal assortments for network goods with vertical differentiation

School of Management, Fudan University, Shanghai 200433, China

^* e-mail: yinbofeng13@fudan.edu.cn

Abstract

This paper presents an efficient algorithm based on the shortest path algorithm for a directed weighted graph where all arc cots depend on which node is thought of as the source node. This approach can be applied well to the optimal assortment problem for a network good industry with vertical differentiation. The assortment problem was introduced for decision-makers to select what products to be produced or stocked from a large product category when it is not desirable to stock all of them. A network good is a good with network effect—the effect that the consumption of a good by one has an impact on the value of that product to others. Vertical differentiation occurs when the several goods can be ordered according to their objective quality in the sense that a high-quality good is “better” than the low-quality one. It is shown that an optimal assortment plan can be identified in a polynomial time by our algorithms. The theoretical results also provide qualitative managerial insights into the optimal assortment plan for decision-makers.