Optimal Production Planning for a Multi Part-type Manufacturing System with Production Rate Dependent Failure Rates

This study deals with the problem of dependence between production and failure rates within the context of multi part-type production system. It gives an answer about how to produce, i.e. the production rates, and what to produce, i.e. the part-type selection, over a finite horizon of H periods of equal length. We consider a single randomly failing and repairable machine that produces a multi part-type. The first part-type is produced to meet a strategic demand d(k) via a buffer stock S, each period k (k=1, 2, ..., H) . The second part-type is considered as a secondary demand in order to maximize the profits the production system. It is produced during an interval at the end of each period k of the horizon H. Our objective is to determine the production planning that maximizes the total profit. This optimal planning includes the optimal production rate during each period and the optimal duration of the production interval of the second part-type.