Solving Large Scale Optimization Problems in the Transportation Industry and Beyond Through Column Generation

Abstract

Column Generation is a very powerful class of combinatorial optimization algorithms that has been used successfully to solve a variety of large scale optimization problems. Its application has helped many companies in various industries increase revenue and reduce costs significantly, particularly in transportation, energy, manufacturing, and telecommunication companies. In this chapter, we will first discuss the motivations for column generation, then we will provide an intuitive but rigorous treatment of the mechanisms of column generation – how it works, why it works. We will then give descriptions on the branch and price algorithm and several examples of column generation’s successful applications in one of the world’s largest airlines. We will discuss monthly airline crew schedule optimization for bidlines, crew pairing optimization, and integrated modeling of fleet and routing in the optimization of aircraft scheduling. Part of the focus is on business requirements and priorities in these areas and how the column generation models are built to effectively meet these challenges. Some airline industry domain-specific details are provided to allow the readers to better appreciate the scheduling problems’ complexities that made the master-subproblem approach in column generation essential. We will also discuss the significant run-time speedups for these large scale scheduling problems due to various practical model enhancements, as well as progress in the large scale optimization space made possible by technologies such as parallel processing, big data, and better chips. At last, we will briefly discuss several example variants of column generation and their applications in various industries. We will also review recent applications of optimization techniques to machine learning as well as the future potentials of large scale optimization in this field. This chapter can be used as a primer on the fundamentals of column generation techniques since it clearly addresses essential theoretical concepts that are sometimes elusive to researchers and graduate students who are new to this area. The chapter should also be helpful to practitioners who would like to gain insights into how to build effective column generation models to solve real world large scale optimization problems.