Production Batching with Machine Breakdowns and Safety Stocks

We study the problem of selecting the economic lot size for an unreliable manufacturing facility with a constant failure rate and general randomly distributed repair times. Safety stocks must be used to meet the managerially prescribed service level (the fraction of lost sales) because these stochastic interventions reduce the effective production capacity. We develop bounds on the range of feasible service levels and investigate the impact of several system parameters on this range. We introduce an easily implementable production control policy (but do not establish the optimality of its structure) and prove that under this policy the safety stock dynamics can be characterized fully by a renewal process analogous to the workload process of a special single server queueing system. This analogy is exploited in deriving exact and approximate expressions for the safety stock holding costs. Several operational insights are revealed by experimenting with the models developed here. We show how the results can be incorporated in a broader management framework for evaluating resource allocation decisions aimed at reducing the failure rate of the machines. A clear tradeoff is shown to exist between the overall investment in increasing the maintenance level and the resulting savings in safety stocks and repair costs.