Inventory management with simultaneously horizontal and vertical substitution

In this study, we focus on inventory management issues under simultaneously horizontal (equivalently inter-brand) and vertical (equivalently intra-brand) substitution. The analysis is divided into two distinct scenarios: centralized inventory management, where all brands are managed by a central decision maker; and decentralized inventory management, where each brand is managed by an independent decision maker. For the two situations, the optimal and the equilibrium order quantities are developed. Moreover, we find that there exist situations when the order quantities are greater in the centralized setting than in the competitive setting for some products.