A Production/Inventory System Subject to Failure with Limited Repair Capacity

We consider a production/inventory system consisting of M machines and K (K(le)M) repair crews in which machines are subject to time dependent failures. The repair operations on each machine require one repair crew during the whole operation. In this production/inventory system, each machine is assigned to produce a different item according to a make-to-stock routine. Inventories of each item service a Poisson demand process, and 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 (1) allocating the limited number of repairmen 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 base-stock policies in systems with identical machines, where first break first repair (FBFR) or preemptive priority (PPRI) repair policies are used. Then we present two heuristics to perform the same optimization analysis in systems with different machines. Finally, we compare the combination of the optimal base-stock policy (as the production policy) and the FBFR and PPRI policies (as the repair policies) to the optimal dynamic policy, and through numerical examples we show that this integration creates a solution that is close to the optimal dynamic policy. The results indicate that simple policies for determining finished goods inventory levels and repair crew assignment to failed machines can work well as long as the two problems are addressed in a coordinated manner.