VARI-METRIC: Improved Approximations for Multi-Indenture, Multi-Echelon Availability Models

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Abstract
Multi-indenture models for (s − 1, s) inventory policies, such as mod-metric and the Logistics Management Institute (LMI) Aircraft Availability Model, understate the delay in the repair of a higher indenture item caused by backorders on the item's lower indenture components. These models also understate the multi-echelon delay in the resupply of a base from a depot that has backorders. Consequently, the models tend to understate expected backorders and overstate expected availability of repair items. We show that it is possible to improve the accuracy of multi-indenture models in a manner similar to the way in which the metric approximation for multi-echelon availability has been improved. We do so by showing that the multi-indenture improvement for a single echelon is valid for compound Poisson demand and arbitrary repair distributions, and that the new approximation is easy to incorporate. Simulation shows that the new approximation provides a much more accurate estimate of the expected backorders. We then present the improved approximation for the combination of multi-indenture and multi-echelon, using the vari-metric model. The vari-metric estimate of backorders is very close to the “true” value from simulation, and the allocation of investment across one item group consisting of a first indenture item and its second indenture components is better than mod-metric when there is a difference.

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