Two-Parameter Approximations For Multi-Echelon Repairable Inventory Models With Batch Ordering Policy

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Abstract
In this paper we present a model for multi-echelon repairable systems with batch ordering policy at the bases. Such an ordering policy is desirable when demand rates and/or the set up cost for ordering are relatively high. Operating characteristics of such a system are analyzed. A two-parameter approximation scheme for the distribution of the number of orders outstanding and consequently backorders is developed, and its performance evaluated. It is found that, under a variety of scenarios including both finite and infinite servers at the repair facility, the approximation scheme is very effective in providing a relatively simple means to determine the stocking levels at both the depot and the bases to minimize the cost of inventory holding and backorders. For the special case when the batch size is one, we confirm the effectiveness of the use of the negative binomial distribution as an approximation for the distribution of orders outstanding, as suggested by recent studies, under a much more general setting.