Stock Rationing in a Multi-class Make-to-stock Queue with Information on the Production Status

We consider a single-item make-to-stock production system. The item is demanded by several classes of customers with different backorder costs. The item can also satisfy demands from a salvage market without a backorder cost. Item processing times have an Erlang distribution. This allows us to model the information on the production status in a tractable way. We fully characterize the optimal stock allocation policy and we provide an effective heuristic procedure to evaluate the corresponding optimal parameters. In addition, we study the influence of processing time variability on the performance of the system. Finally, we extend our study to the case where there is no salvage market.