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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.

90B05Inventory, storage, reservoirs
49N90Applications of optimal control and differential games
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