Dynamic Pricing and Inventory Control of Substitute Products

We study dynamic pricing and inventory control of substitute products for a retailer who faces a long supply lead time and a short selling season. Within a multinomial logit model of consumer choice over substitutes, we develop a stochastic dynamic programming formulation and derive the optimal dynamic pricing policy. We prove that dynamic pricing converges to static pricing as inventory levels of all variates approach the number of remaining selling periods (assuming at most one customer arrival within each period). Our extensive numerical study of the effects of time and inventory depletion on the optimal pricing reveals two fundamental underlying driving forces of the complex price behavior: the level of inventory scarcity and the quality difference among products. We also compare the performance of three restricted pricing strategies: static, unified dynamic, and mixed dynamic pricing. We find that full-scale dynamic pricing is of great value in the presence of inventory scarcity, and initial inventory decisions are quite robust in the pricing scheme employed in the selling season. Based on the above insights, we propose a computationally efficient approach to the initial inventory decision, which delivers close-to-optimal inventory levels for all testing cases.