Heuristics for flight and maintenance planning of mission aircraft

Flight and Maintenance Planning (FMP) of mission aircraft addresses the question of which available aircraft to fly and for how long, and which grounded aircraft to perform maintenance operations on, in a group of aircraft that comprise a unit. The objective is to achieve maximum fleet availability of the unit over a given planning horizon, while also satisfying certain flight and maintenance requirements. The application of exact methodologies for the solution of the problem is quite limited, as a result of their excessive computational requirements. In this work, we prove several important properties of the FMP problem, and we use them to develop two heuristic procedures for solving large-scale FMP instances. The first heuristic is based on a graphical procedure which is currently used for generating flight and maintenance plans of mission aircraft by many Air Force organizations worldwide. The second heuristic is based on the idea of splitting the original problem into smaller sub-problems and solving each sub-problem separately. Both heuristics have been roughly sketched in earlier works that have appeared in the related literature. The present paper develops the theoretical background on which these heuristics are based, provides in detail the algorithmic steps required for their implementation, analyzes their worst-case computational complexity, presents computational results illustrating their computational performance on random problem instances, and evaluates the quality of the solutions that they produce. The size and parameter values of some of the randomly tested problem instances are quite realistic, making it possible to infer the performance of the heuristics on real world problem instances. Our computational results demonstrate that, under careful consideration, even large FMP instances can be handled quite effectively. The theoretical results and insights that we develop establish a fundamental background that can be very useful for future theoretical and practical developments related to the FMP problem.