Joint pricing and inventory control models with long lead times
Thursday, October 4, 2018 - 2:00pm - 2:45pm
We consider a joint pricing and inventory control problem with positive replenishment lead times. Although this fundamental problem has been extensively studied in the literature, the structure of the optimal policy remains poorly understood. In this work, we propose a class of so-called constant-order contingent pricing policies with provable performance. Under such a policy, a constant-order amount of new inventory is ordered every period and a pricing decision is made based on the on-hand inventory. We prove that the best constant-order and contingent pricing policy is asymptotically optimal as the lead time grows large, which is exactly the setting in which the problem becomes computationally intractable due to the curse of dimensionality. As a key technical contribution, we establish the convergence of a discounted infinite horizon inventory model with two-sided ordering constraints and random yields to its long-run average counterpart as the discount factor goes to one. We will touch upon its extension to more general Markovian decision processes and some implications on data-driven models.