Production Smoothing with Fluctuating Price

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Abstract
The model presented in this paper deals with a firm facing a known price which varies over time during some finite period [0, T]. The firm wishes to determine the production rate at each instant of that interval which will maximize profit, when adjustment of output incurs additional cost. In the paper we characterize the optimal solution and construct a forward algorithm which is shown to converge to the unique optimal solution. We also specify the conditions for planning and forecast horizons, both of which can be identified by the described algorithm. We use control theory to achieve these results.

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