Metric: A Multi-Echelon Technique for Recoverable Item Control

TLDR

Metric is a mathematical model of a base‑depot supply system with compound‑Poisson demand whose mean is estimated via Bayesian inference. The program is designed to minimize expected backorders for any system investment while evaluating stock distributions and computing optimal redistribution. The model assumes unit failures at the base with repair probability r and arbitrary repair‑time distributions, otherwise returns to the depot, with the base issuing resupply requests; the program implements this framework, providing cost‑effectiveness trade‑offs and analytic solutions based on mean repair times. For high‑cost, low‑demand items the optimal policy is (s−1, s), meaning no batching of repair or resupply requests, and the problem admits a simple analytic solution that depends only on mean repair times, eliminating the need for arbitrary backorder or holding‑cost estimates.

Abstract

Metric is a mathematical model of a base-depot supply system in which item demand is compound Poisson with a mean value estimated by a Bayesian procedure. When a unit fails at base level there is a probability r that it can be repaired at the base according to an arbitrary probability distribution of repair time, and a probability 1 − r that it must be returned to the depot for repair according to some other arbitrary distribution. In the latter case the base levies a resupply request on depot. No lateral resupply between bases is considered in the model. For high-cost, low-demand items the appropriate policy is (s − 1, s), which means that items are not batched for repair or resupply requests. This problem has a simple analytic solution that is a function of the mean repair times rather than the repair time distributions. A practical and efficient computer program has been designed to show the cost-effectiveness tradeoff for a large group of recoverable items. In addition to minimizing expected backorders for any system investment, the program can evaluate any distribution of stock and it can compute the optimal redistribution of stock. No arbitrary estimates of backorder cost or holding cost are required.