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A nonlinear continuous time optimal control model of dynamic pricing and inventory control with no backorders. (English) Zbl 1137.90302
Summary: 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.
MSC:
90B05Inventory, storage, reservoirs
49N90Applications of optimal control and differential games