Complementarity analysis of a multi‐item inventory model with leading product pricing

Our research investigates a joint inventory replenishment and pricing problem, where a seller controls the price of a leading product while restocking for all the products. We demonstrate that the seller's expected value functions present an L♮-concave$L^\natural \text{-concave}$ structure, recommending an optimal order‐up‐to inventory‐level and list‐price policy. Our findings reveal divergent economic relationships between products from the seller's and customer's perspectives, suggesting managers broaden their strategies beyond customer viewpoints. We extend the pricing and inventory analysis to scenarios involving three substitute products under both price and inventory control. In these situations, we further reveal that sellers and customers uniformly view product inventories as substitutes, and the corresponding value functions are submodular and mutually diagonally dominant.