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Abstract. In inventory control and production planning one is tempted to use one of two strategies: produce all demand to stock or produce all demand to order. The disadvantages are well-known. In the 'make everything to order' case (MTO) the response times may become quite long if the load is high, in the 'make everything to stock' case (MTS) one gets an enormous inventory if the number of different products is large. In this paper we study two simple models which combine MTO and MTS, and investigate the effect of combining MTO and MTS on the production lead times.

We consider a memoryless single server queue in which users can purchase relative priority so as to reduce their expected waiting costs which are linear with time. Relative priority is given in proportion to a price paid by customers present in the system. For two service disciplines, (weighted) processor sharing and (weighted) random entrance, we find the unique pure and symmetric Nash equilibrium price paid by the customers.

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