System design for express airlines

Abstract

In this thesis we investigate and analyze express airlines for the purpose of system design. Chapter 1 contains a taxonomy for express carriers that is built around elemental system components, distinguishable from one another with a two-variable classification scheme. We describe how overnight carriers operate, what their basic philosophy of operation is, and how they might choose to develop their networks to best serve that philosophy. In addition, we present mathematical formulations for several systems. Chapter 2 is a review of research into similar problems and of solution techniques that might be applicable to express system design problems. In Chapter 3 we focus on the simplest express network problem, the Single- Hub, Single-Turn System Design Problem, SHP. We develop several models for SHP, both to expose the structure of the problem and to find a tractable formulation. The emergent concept of the chapter is the route complex. Using this approach to route expression, we choose a formulation that is essentially a set partitioning problem with side constraints. In Chapter 4 we explore the dualization of the side constraints and develop a solution procedure. There are three types of complicating constraints: aircraft availability, placement (for ferry flights), and columnjoining (for transforming a pure set partitioning problem into a nonbipartite matching problem with side constraints). We use a minimum weight, nonbipartite matching problem as the core of our solution procedure for SHP, focusing on obtaining feasible solutions directly from a Lagrangian relaxation, rather than using branch-and-bound. In Chapter 5 we report our computational results and offer suggestions for further research.