Application of the impulsive control of piecewise deterministic processes to multi-item single machine stochastic scheduling

In this work, we study the optimization of a production system comprising a multi-item single machine with piecewise deterministic demands. We present a theoretical characterization of the solution of the problem as the limit of penalized problems. We prove that the solution of the penalized problem is a Lipschitz continuous function that satisfies a generalized quasi-variational inequality with boundary conditions. We describe a numerical procedure to compute this penalized optimal cost function.