Capacity Design for Unreliable M/M/m Production-Inventory Systems Considering Spares

Capacity Design for Unreliable M/M/m Production-Inventory Systems Considering Spares

In this paper we consider spare, inventory, and external demand simultaneously, in which a failure prone M/M/m production-inventory system considering spares was proposed to investigate the interaction of capacity investment on system performance. Transient analysis and queueing theory were first employed for obtaining reliability related measures of the proposed production-inventory system and waiting time analysis of repair jobs respectively. Using a quasi-birth-death (QBD) method we derived several other measures related to system-wide performance. Direct search and mixed variable genetic algorithm are used to optimize the single server (m = 1) and multi-server cases respectively. We found patterns between operating costs, as well as spare and inventory investments in the single server case. For the multiple server case, we verify the viability of the proposed mixed variable genetic algorithm approach for optimizing the studied problem. Finally, we provide sensitivity analysis for the multi-server case.