A Survey of Optimization Models for Train

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A Survey of Optimization Models for Train Routing and Scheduling1 JEAN-FRANCOIS CORDEAU ¸
´ GERAD and Ecole Polytechnique de Montreal, 3000, chemin de la Cote-Sainte-Catherine, Montreal H3T 2A7, Canada ´ ˆ ´

PAOLO TOTH and DANIELE VIGO
DEIS, Universita di Bologna, Viale Risorgimento, 2, 40136 Bologna, Italia `

The aim of this paper is to present a survey of recent optimization models for the most commonly studied rail transportation problems. For each group of problems, we propose a classification of models and describe their important characteristics by focusing on model structure and algorithmic aspects. The review mainly concentrates on routing and scheduling problems since they represent the most important portion of the planning activities performed by railways. Routing models surveyed concern the operating policies for freight transportation and railcar fleet management, whereas scheduling models address the dispatching of trains and the assignment of locomotives and cars. A brief discussion of analytical yard and line models is also presented. The emphasis is on recent contributions, but several older yet important works are also cited.

he rail transportation industry is very rich in terms of problems that can be modeled and solved using mathematical optimization techniques. However, the related literature has experienced a slow growth and, until recently, most contributions were dealing with simplified models or small instances failing to incorporate the characteristics of real-life applications. Previous surveys by ASSAD (1980b, 1981) and HAGHANI (1987) suggest that optimization models for rail transportation were not widely used in practice and that carriers often resorted to simulation. This situation is somewhat surprising given the considerable potential savings and performance improvements that may be realized through better resource utilization. It is also contrasting with the rapid penetration of optimization methods in other fields such as air transportation (YU, 1998). In fact, the development of optimization models for train routing and scheduling was for a long time hindered by the large size and the high difficulty of the problems studied. Important computing capabilities were needed to solve the proposed models, and

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even the task of collecting and organizing the relevant data required installations that very few railroads could afford. As a result, practical implementations of optimization models often had a limited success, which deterred both researchers and practitioners from pursuing the effort. In the last decade however, a growing body of advances concerning several aspects of rail freight and passenger transportation has appeared in the operations research literature. The strong competition facing rail carriers, the privatization of many national railroads, deregulation, and the ever increasing speed of computers all motivate the use of optimization models at various levels in the organization. In addition, recently proposed models tend to exhibit an increased level of realism and to incorporate a larger variety of constraints and possibilities. In turn, this convergence of theoretical and practical standpoints results in a growing interest for optimization techniques. Hence, although simulationbased approaches are still widely used to evaluate and compare different scenarios, one witnesses a sustained development of optimization methods capable of producing high-quality solutions to complex problems within short computing times. Problems facing rail transportation planners can 0041-1655 / 98 / 3204-0380 $01.25 © 1998 Institute for Operations Research and the Management Sciences

Transportation Science Vol. 32, No. 4, November 1998

MODELS FOR TRAIN ROUTING AND SCHEDULING

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be grouped into a number of classes according to the facet of the organization that is concerned. The most common approach is to represent the rail...
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