Demand Management and Inventory Control for Substitutable Products

This paper studies dynamic inventory and pricing decisions for a set of substitutable products over a finite planning horizon. We present a general stochastic, price-dependent demand model that unifies many commonly used demand models in the literature. Unsatisfied demands are backlogged. There are linear purchasing, inventory-holding, and backordering costs. The objective is to maximize the total expected discounted profit. The original formulation is not jointly concave in the decision variables and is therefore intractable. One key observation here is that the problem becomes jointly concave if we work with the inverse of the price vector – the market share vector. We characterize the optimal policy and develop algorithms to compute it. We establish conditions under which the optimal policy demonstrates certain monotonicity property, which, in turn, can greatly enhance computation. We also analyze the myopic policy and its optimality, and present a numerical study to illustrate the interplay of the pricing and inventory decisions.