Mixed integer least squares optimization for flight and maintenance planning of mission aircraft

We address the problem of generating a joint flight and maintenance plan for a unit of mission aircraft. The objective is to establish a balanced allocation of the flight load and the maintenance capacity to the individual aircraft of the unit, so that its long-term availability is kept at a high and steady level. We propose a mixed integer nonlinear model to formulate the problem, the objective function of which minimizes a least squares index expressing the total deviation of the individual aircraft flight and maintenance times from their corresponding target values. Using the model's special structure and properties, we develop an exact search algorithm for its solution. We analyze the computational complexity of this algorithm, and we present computational results comparing its performance against that of a commercial optimization package. Besides demonstrating the superiority of the proposed algorithm, these results reveal that the total computational effort required for the solution of the problem depends mainly on two crucial parameters: the size of the unit (i.e., the number of aircraft that comprise it) and the space capacity of the maintenance station. (c) 2012 Wiley Periodicals, Inc. Naval Research Logistics, 2012