A discrete-time Markov production-inventory model with machine breakdowns

A machine produces an item at a constant rate, which is assumed to be great er than the demand rate, and the demand is assumed to be known and constant . While operating, the machine can fail, and upon failure it requires servi ce. The machine times-to-failure and repair times are random, and during re pairs, demand is backordered as long as the backordering level does not exc eed a prescribed amount, after which demand is lost. By considering time to be of discrete units and the times-to-failure and repair times to be geome trically distributed, we model the production-inventory system as a Markov chain and develop an efficient algorithm to compute the potentials that are used to formulate the cost function. The model results are then compared t o simulation results where time is treated as a continuous parameter. (C) 2 001 Elsevier Science Ltd. All rights reserved.