Applications of Optimal Control to Production Planning
Keywords:optimal control, controllability, Pontryagin Maximum Principle, Hamilton-Jacobi-Bellman equations, production planning, inventory and production
In this paper we solve a problem of optimization and production planning using the optimal control methods and Pontryagin Maximum Principle. We propose an economic model and find an optimal plan of production for n products, to ensure the required quantity at specified delivery data with minimum cost of inventory and production. We prove that the economic system is not controllable, in the sense that we cannot reach any final stock quantity. Finally, we justify this construction with a numerical example.
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