Abstract
In this work, we study the optimization of a production system comprising a multi‐itemsingle machine with piecewise deterministic demands. We present a theoretical characterizationof the solution of the problem as the limit of penalized problems. We prove thatthe solution of the penalized problem is a Lipschitz continuous function that satisfies ageneralized quasi‐variational inequality with boundary conditions. We describe a numericalprocedure to compute this penalized optimal cost function.
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Jean-Marie, A., Tidball, M. Application of the impulsive control of piecewisedeterministic processes to multi‐item single machinestochastic scheduling. Annals of Operations Research 88, 139–159 (1999). https://doi.org/10.1023/A:1018970011223
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DOI: https://doi.org/10.1023/A:1018970011223