Solution techniques for periodic control problems: A case study in production planning

Solution techniques for periodic control problems: A case study in production planning

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Article ID: iaor2000993
Country: United Kingdom
Volume: 19
Issue: 3
Start Page Number: 185
End Page Number: 203
Publication Date: May 1998
Journal: Optimal Control Applications & Methods
Authors: , ,
Keywords: production
Abstract:

Two numerical techniques for solving optimal periodic control problems with a free period are developed. The first method uses shooting techniques for solving an appropriate boundary value problem associated with the necessary conditions of the minimum principle. A convenient form of the transversality condition for the free period is incorporated. The second method is a direct optimization method that applies non-linear programming techniques to a discretized version of the control problem. Both numerical methods are illustrated in detail by a non-convex economic production planning problem. In this model, the π-test reveals that the steady-state operation is not optimal. The optimal periodic control is computed such that a complete set of necessary conditions is verified. The solution techniques are extended to obtain the optimal periodic control under various state constraints. A sensitivity analysis of the optimal solution is performed with respect to a specific parameter in the model.

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