Derivations of Formulas for Measures of Effectiveness, Safety Stock, and Min-Cost Order and Repair Quantities for a Readiness-Based Repairable Item Inventory Model for the U.S. Navy

摘要

A new wholesale level replenishment model is being developed for managing the Navy's inventories of repairable items. It is a readiness-based model that seeks to determine the depths of items of a weapon system which minimize the system's Mean Supply Response Time subject to budget constraint. The model incorporates both a batch procurement and batch repair of the items. Required inputs to this model are the specified values of each. Basic to the development of this model are the derivations of formulas for the probability of being out of stock at any instant of time and the expected number of backorders at any instant of time. Formulas for these measures are presented for the assumptions of both Poisson and Normal demand during the aggregate lead time. The model also needs a formula for the safety stock. Therefore approximate formulas for safety stock have been derived through the use of a simulation model of the repairable inventory management process. Finally, because the batch procurement and repair quantities are required inputs to the proposed model, formulas for approximate least cost values have been derived as part of a study of possible candidate values for these inputs.