Long Haul Fleet Assignment: Models, Methods and Applications

The fleet assignment problem is an integral part of the airline planning process. Given a schedule of international flights and certain maintenance criteria required by the Federal Aviation Administration (FAA), the objective of the long haul fleet assignment problem is to assign aircraft of different fleet types to different flights such that operating costs are minimized. We develop a new formulation for this problem with the decision variables modeled as sets of flights originating and terminating at maintenance stations. This variable definition enables explicit incorporation of aircraft maintenance constraints in the model. Maintenance requirements need to be considered explicitly in the international problem since opportunities for maintenance are fewer than in domestic operations. Using this variable definition, the long haul fleet assignment problem is formulated as an integer multi-commodity flow problem with side constraints, defined on a timeline network. The model is solved using a branch and bound procedure in which the bounds are provided by solving a linear program at each node of the branch and bound tree. The definition of the decision variable as a string of flights precludes explicit enumeration of the constraint matrix since it is possible that billions of strings exist. Hence the root node linear programming relaxation of the problem is solved using column generation techniques. Using the data and international schedule of a long-haul airline, near-optimal solutions have been determined. Significant savings in operating costs are achieved by our solution procedure. Thesis Supervisor: Cynthia Barnhart Title: Assistant Professor of Civil and Environmental Engineering