A production/inventory system subject to failure with limited repair capacity

We consider a production/inventory system consisting of M machines and K (K less than or equal toM) repair crews in which machines are subject to time -dependent failures. The repair operations an each machine require one repa ir crew during the whole operation. In this production/inventory system, ea ch machine is assigned to produce a different item according to a make-to-s tock routine. Inventories of each item service a Poisson demand process, an d the unsatisfied demands are lost. The objective is to minimize the sum of the average holding and lost-sales penalty costs. We formulate the joint problem of(I) allocating the limited number of repai rmen to failed machines and (2) deciding how much finished goods inventory to keep as a Markov decision process. We show that the optimal policy has a very complicated structure. We introduce two models to compute optimal bas e-stock policies in systems with identical machines, where first break firs t repair (FBFR) or preemptive priority (PPRI) repair policies are used. The n we present two heuristics to perform the same optimization analysis in sy stems with different machines. Finally, we compare the combination of the o ptimal base-stack policy (as the production policy) and the FBFR and PPRI p olicies (as the repair policies) to the optimal dynamic policy, and through numerical examples we show that this integration creates a solution that i s close to the optimal dynamic policy. The results indicate that simple pol icies for determining finished goods inventory levels and repair crew assig nment to failed machines can work well as long as the two problems are addr essed in a coordinated manner.