An Evaluator for the Number of Operationally Ready Aircraft in a Multilevel Supply System

This paper develops an analytic model that evaluates the expected number of aircraft not operationally ready at a random point in time because of supply (NORS). The model was developed for application to the F-111 aircraft for a multilevel problem, where demand on a first-level line replaceable unit (LRU) eventually causes second-level demands for one or more modules that are components of the LRU. The model is for a single base. Since it is evaluative in nature, the inputs include item stock levels as well as item demand rates, average repair times, and resupply times. An optimization model to determine stock levels that minimize the number of NORS aircraft subject to a budget constraint would be preferable to the evaluation model. The paper shows, however, that an optimization model is not mathematically tractable because the criterion function is not separable into independent item calculations. But an example using F-111 data indicates that if the METRIC model [see Opns. Res. 16, 122–141 (1968)] is used to optimize stock levels, the resulting number of aircraft NORS is within 1 percent of the minimum number of aircraft achievable with the same budget. Finally, the well-known formula of Erlang for the M/G/s service system with no queue allowed is generalized to the case where demand rates and repair rates may be a function of the number of units already in repair. This enables us to examine the sensitivity of the optimal allocation of budget across a group of items when expediting may take place. Though expediting improves system performance, the conclusion is that the optimal allocation is virtually the same as the METRIC allocation.