Production scheduling in a flexible manufacturing system under random demand

This paper considers the problem of production scheduling in a Flexible Manufacturing System (FMS) with stochastic demand. With FMS, there is inherent flexibility made available to production. However, it is not always that the entire mix of parts can be processed simultaneously. As such, grouping of the part types is needed. The problem complexity increases when both demand and processing times are random. In this paper, we model the problem as a polling model with the objective of minimizing the total average cost. First, we consider a special cost rate problem whereby the holding cost is assumed proportional to the processing time and inversely proportional to the FMS load factor. Here, three situations are compared: (i) no mixing is allowed among part-families; (ii) a particular part-family, with an independent production schedule, can also be produced with other families; and (iii) a particular part-family with no independent production schedule but can be mixed with all the other families. Under certain conditions of the mixing proportions, we derive conditions for one situation to dominate the others. Next, an optimization model is considered which determines the optimal mixing proportions, if the decision to mix the part-family with other part-families is taken. Specifically, we find that any family with no independent production schedule should always be mixed with the part-family that offers the highest load to the FMS. Finally, we show how the general holding cost rate problem can be analysed using approximate results found in the polling literature.