Abstract
In this paper, we consider a minimax production planning model of a flexible manufacturing system with machines that are subject to random breakdown and repair. The objective is to choose the rate of production that minimizes the related minimax cost of production and inventory/shortage. The value function is shown to be the unique viscosity solution to the associated Hamilton-Jacobi-Isaacs equation. Under certain conditions, it is shown that the value function is continuously differentiable. A verification theorem is given to provide a sufficient condition for optimal control. Finally, two examples are solved explicitly.
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Communicated by C. T. Leondes
This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grants OGP0036444 and A4169.
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Boukas, E.K., Yang, H. & Zhang, Q. Minimax production planning in failure-prone manufacturing systems. J Optim Theory Appl 87, 269–286 (1995). https://doi.org/10.1007/BF02192564
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DOI: https://doi.org/10.1007/BF02192564