Optimal policies for aircraft fleet management in the presence of unscheduled maintenance

This paper presents a fleet management model for military aircraft that generates daily flying and maintenance allocations. This model has two novel features that distinguish it from previous models of fleet management in the literature. Most notably, random unscheduled maintenance is integrated with an optimisation approach. This is important, as unscheduled maintenance is a regular occurrence in day-to-day military aircraft fleet management, thus limiting the ability of deterministic models to provide useful guidance. Furthermore, the model is designed to discover policies that dynamically adapt to random events to deliver optimal fleet serviceability. Other features of the model include flying-hour based phased maintenance with variable induction (day when maintenance begins), day-based regular inspections, and separate phased and flight-line maintenance facilities with both manpower and line capacity constraints. In the model, serviceable aircraft fly up to a specified number of hours per day. Once a certain number of flying hours has been achieved, those aircraft must begin phased maintenance within an allowable induction range. Regular inspections are an additional type of scheduled maintenance based on elapsed time. Phased maintenance typically takes a few hundred maintenance man hours, whereas regular inspections take tens of man hours. Two types of maintenance facilities are included. Phased maintenance can only be undertaken on the phased maintenance line, and regular inspections are typically undertaken on the flight line. If a regular inspection is due at the same time as a phased service, these can be performed concurrently. Unscheduled maintenance is undertaken in flight line maintenance if incurred on serviceable aircraft, or in either facility if discovered during the course of scheduled maintenance. We use Approximate Dynamic Programming (Powell, 2011) to formulate the decision making model. The objective is to find the policy that maximizes the expected value of the contribution function. Our contribution function seeks to maximize the flying hours achieved and maintenance throughput of the fleet over a time period, with a weighting factor balancing these priorities. Decision variables include the allocation of flying hours and maintenance man hours per aircraft per day, and when aircraft are inducted into phased maintenance. The model consists of 75 sets of constraints describing: the allocation of flying hours to serviceable aircraft and maintenance man hours to aircraft in maintenance; the allocation of different maintenance types to aircraft in different maintenance facilities; and state transition tests to determine when aircraft are eligible or required to begin or end types of maintenance. The unscheduled maintenance constraints include an exogenous stochastic variable that represents the daily amount of new unscheduled maintenance generated randomly from a lognormal probability distribution. Aircraft are allowed to carry forward a limited amount of unscheduled maintenance while remaining serviceable. However, once a specified level of unscheduled maintenance is exceeded, the aircraft must undergo maintenance at an appropriate maintenance facility until the outstanding unscheduled maintenance is reduced to a required level. In Approximate Dynamic Programming, a policy is a function that returns a decision, given the current state of the fleet (in the present context). We consider a deterministic look-ahead policy that depends on a discount factor and a look-ahead time horizon. We undertake computational experiments with a squadron of 12 aircraft over a 180 day period, with time horizons ranging from 1 to 14 days and discount factors from 0.8 to 1. Indicative simulation results are presented, where the time horizon substantially dominates the discount factor with respect to influence on the mean total flying hours achieved. While longer time horizons produce larger optimal objective values for a given parameter set and random data, simulation results may not significantly differ when compared with shorter time horizons due to random variation. This is apparent in our results, demonstrating the potential for substantial savings in computational time.