Stochastic production systems: production and maintenance scheduling with finite buffers

Consider the production of a single consumable product that is fabricated in a process of k stages that is subject to an uncertain environment. There are a number of workstations on each stage that have different operating parameters. The workstations are subject to the discrete events of repair, failure, and preventive maintenance that generate a jump in the state of the system. Between each stage of the manufacturing process is a finite buffer that holds pieces before they can be processed by the next stage. If a buffer is full, then the preceding stage cannot produce pieces since there will be no place for them to go. This formulation of a manufacturing system is a hybrid system consisting of the meeting the global production demand while locally managing the operational status of the workstations. This formulation of the optimal scheduling of production is a quasi-LQGP problem whose jumps are generated by state dependent Poisson processes. A numerical example is presented to illustrate the model