Perturbation Analysis for Optimal Production Planning Of a Manufacturing System with Subcontracting and Machine Degradation

This paper deals with a manufacturing system M1 which has to satisfy a random demand during a finite horizon given a required service level. To help meet this demand, subcontracting is used through another production system M2 which has a random service level f. The aim of this study is to determine the production plan of the manufacturing system M1 for each period of the horizon taking into account the machine M1 degradation according its production rate. Baring in mind that realistically the subcontractor is not always available to satisfy each demand variation, we assume that we can only order a minimum fixed quantity -defined a priori- during the entire horizon. The optimal production plan then will correspond to the minimum sum of production (M1 and M2), inventory, lost sales cost and degradation cost.