Queueing analysis on a single-station make-to-stock/make-to-order inventory-production system

We consider a one-station production system that produces standard products for ordinary demands and custom products for specific demands. In this system, the workstation has two manufacturing modes. In mode 1, it produces standard products and, in mode 2, it produces custom products by performing the additional alternating works on one existing finished standard product. Base-stock control policy is applied to control the production of standard products. The fill rate of the ordinary demand and the on-time-delivery-rate of the specific demand are considered as the measures of the qualities of service. By assuming an Markovian system, qualities of service under base-stock policy are obtained; furthermore, the optimal base-stock level can be obtained numerically under the requirements on the qualities of services.