A Nonlinear Continuous Time Optimal Control Model of Dynamic Pricing and Inventory Control with No Backorders

In this paper, we present a continuous time optimal control model for studying a dynamic pricing and inventory control problem for a make-to-stock manufacturing system. We consider a multiproduct capacitated, dynamic setting. We introduce a demand-based model where the demand is a linear function of the price, the inventory cost is linear, the production cost is an increasing strictly convex function of the production rate, and all coefficients are time-dependent. A key part of the model is that no backorders are allowed. We introduce and study an algorithm that computes the optimal production and pricing policy as a function of the time on a finite time horizon, and discuss some insights. Our results illustrate the role of capacity and the effects of the dynamic nature of demand in the model. © 2007 Wiley Periodicals, Inc. Naval Research Logistics 54: 767–795, 2007