Optimal production scheduling for manufacturing systems with preventive maintenance in an uncertain environment

Consider a manufacturing system in which a single consumable good is fabricated in a process that consists of k stages in an uncertain environment. On each stage, there are a number of workstations that are assumed to have different operating parameters that are subject to failure, repair, and preventive maintenance which generate discrete jumps in the value of the state. A just-in-time manufacturing discipline is assumed for the workstations with running costs that include penalties for shortfall and surplus production. The formulation presented for the optimal production scheduling for the manufacturing system requires extensions to the results of the LQGP problem with state dependent Poisson processes (SDPP) by the inclusion of coefficients for the dynamics and the costs that are parameterized by the value of the state. The cost functional used is fully quadratic which is an enhancement for the LQGP problem. The functionality of this canonical model is demonstrated with a numerical example