Stock rationing in an M/Er/1 multi-class make-to-stock queue with backorders

A model of a single-item make-to-stock production system is presented. The item is demanded by several classes of customers arriving according to Poisson processes with different backorder costs. Item processing times have an Erlang distribution. It is shown that certain structural properties of optimal stock and capacity allocation policies exist for the case where production may be interrupted and restarted. Also, a complete characterization of the optimal policy in the case of uninterrupted production when excess production can be diverted to a salvage market is presented. A heuristic policy is developed and assessed based on the results obtained in the analysis. Finally the value of production status information and the effects of processing time variability are investigated.