Network Models in Railroad Planning and Scheduling

The past few decades have witnessed numerous applications of operations research in logistics, and these applications have resulted in substantial cost savings. However, the U.S. railroad industry has not benefited from the advances, and most of the planning and scheduling processes do not use modeling and optimization. Indeed, most of the planning and scheduling problems arising in railroads, which involve billions of dollars of resources annually, are currently being solved manually. The main reason for not using OR models and methodologies is the mathematical difficulty of these problems, which prevented the development of decision tools that railroads can use to obtain implementable solutions. However, now this situation is gradually changing. We are developing cutting-edge operations research algorithms, by using state-of-the-art ideas from linear and integer programming, network flows, discrete optimization, heuristics, and very large-scale neighborhood (VLSN) search, that railroads have already started using and from which they have started deriving immense benefits. This chapter gives an overview of the railroad planning and scheduling problems, including the railroad blocking problem, train scheduling problem, yard location problem, train dispatching problem, locomotive scheduling problem, and crew scheduling problem. Some of these problems are very large-scale integer programming problems containing billions or even trillions of integer variables. We will describe algorithms that can solve these problems to near-optimality within one to two hours of computational time. We present computational results of these algorithms on the data provided by several U.S. railroads, demonstrating potential benefits from tens to hundreds of millions annually.