Mixed integer biobjective quadratic programming for maximum-value minimum-variability fleet availability of a unit of mission aircraft

- We address the problem of issuing a flight and maintenance plan for an aircraft unit.
- The aim is to maximize the fleet availability over a multi-period planning horizon.
- We develop a biobjective quadratic model that also balances the availability.
- We develop two solution algorithms that obtain the non-dominated frontier.
- Computational results demonstrate the high efficiency of these algorithms.

We consider the FMP problem encountered in the Hellenic Air Force (HAF), that is, the problem of issuing individual flight and maintenance plans for a group of aircraft comprising a unit, so as to maximize the fleet availability of the unit over a multi-period planning horizon while also satisfying various flight and maintenance related restrictions. The optimization models that have been developed to tackle this problem often perform unsatisfactorily, providing solutions for which the fleet availability exhibits significant variability. In order to handle this difficulty, in this work we develop a mixed integer programming model, which, besides the typical objective maximizing the fleet availability, also includes an additional objective that minimizes its variability. Motivated by the substantial computational difficulties the typical ε-constraint reduced feasible region approach is faced with, as a result of the solution complexity of the optimization models involved, we also develop two specialized solution methodologies for this problem. Both methodologies identify the entire frontier of non-dominated solutions, utilizing suitable relaxations of the original model and exploiting the fact that the domain comprising possible fleet availability values is a discrete set. The first one disaggregates the original FMP model into smaller subproblems whose solution is attained much more efficiently. The second one is a variant of the ε-constraint method, applied to a suitable relaxation of the original FMP model. We present extensive computational results assessing the efficiency of the proposed solution methodologies and demonstrating that their performance is significantly superior to that of the typical ε-constraint method applied directly to the original biobjective model.