Column generation approaches to the military airlift scheduling problem

Abstract

In this thesis, we develop methods to address airlift scheduling, and in particular the problem of scheduling military aircraft capacity to meet ad hoc demand. Network optimization methods typically applied to scheduling problems do not sufficiently capture all necessary characteristics of this problem. Thus, we develop a new method that uses integer linear programming (IP) with column generation to make the problem more tractable while incorporating the relevant characteristics. In our method, we decompose the problem into two steps: generating feasible aircraft routes, and solving the optimization model. By ensuring that routes are feasible with respect to travel time, ground time, crew rest, and requirement restrictions when we build them, we do not need to encode these characteristics within the IP optimization model, thus reducing the number of constraints. Further, we reduce the number of decision variables by generating only the fraction of feasible aircraft routes needed to find near-optimal solutions. We propose two methods for generating routes to include in the IP model: explicit column generation and selective column generation. In explicit column generation, all aircraft routes that we could potentially consider including in the model are generated first. Starting with a subset of these routes, we iteratively use reduced cost information obtained by solving a relaxed version of the IP model to choose more routes to add from the original set of routes. In selective column generation, we first generate a small set of feasible aircraft routes. Starting with this set of routes, we iteratively generate more routes by solving a relaxed version of the IP model and then combine routes in the solution together and add those that are feasible to the route set. In both methods, we iterate until there are either no other routes to include or the solution stops improving. Last, we solve the IP model with the final set of routes to obtain an integer solution. We test the two approaches by varying the number of locations in the network, the number of locations that are wings, and the number of requirements. We show that selective column generation produces a solution with an objective value similar to that of explicit column generation in a fraction of the time. In our experiments, we solve problems with up to 100 requirements using selective column generation. In addition, we test the impact of integrating lines of business while scheduling airlift and show a significant improvement over the current process.