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.

A Survey of Optimization Models for Train Routing and Scheduling

Computational methods for rostering and personnel scheduling has been a subject of continued research and commercial interest since the 1950s. This annotated bibliography puts together a comprehensive collection of some 700 references in this area, focusing mainly on algorithms for generating rosters and personnel schedules but also covering related areas such as workforce planning and estimating staffing requirements. We classify these papers according to the type of problem addressed, the application areas covered and the methods used. In addition, a short summary is provided for each paper.

http://www3.eng.cam.ac.uk/~hj231/Papers/AORRosteringPaper.pdf

An Annotated Bibliography of Personnel Scheduling and Rostering

One of the many problems faced by rail transportation companies is to optimize the utilization of the available stock of locomotives and cars. In this paper, we describe a decomposition method for the simultaneous assignment of locomotives and cars in the context of passenger transportation. Given a list of train legs and a fleet composed of several types of equipment, the problem is to determine a set of minimum cost equipment cycles such that every leg is covered using appropriate equipment. Linking constraints, which appear when both locomotives and cars are treated simultaneously, lead to a large integer programming formulation. We propose an exact algorithm, based on the Benders decomposition approach, that exploits the separability of the problem. Computational experiments carried on a number of real-life instances indicate that the method finds optimal solutions within short computing times. It also outperforms other approaches based on Lagrangian relaxation or Dantzig--Wolfe decomposition, as well as a simplex-based branch-and-bound method.

A Benders Decomposition Approach for the Locomotive and Car Assignment Problem

Locomotive assignment with heterogeneous consists at CN North America

A method is described for finding a minimum cost set of schedules for railway locomotives to work a given set of trains. The times at which the trains start may be fixed or variable. A heuristic method, based on a linear programming model, is described. This gives good integer solutions to the problem.

The Solution of a Railway Locomotive Scheduling Problem

A previously published integer linear programming model for finding a minimum cost schedule for railway locomotives to work a given set of trains is considered. Lagrangean relaxation is suggested as a effective means of solving the model.

https://link.springer.com/content/pdf/10.1057%2Fjors.1995.13.pdf

A Note on the Use of Lagrangean Relaxation in Railway Scheduling

The method discussed provides an allocation of jobs to men in a transportation system. Each man is assigned a prespecified shift, associated with a base station, and returned to his base station at the end of his shift. The total number of men required is minimized, subject to a minimum time between jobs, a suitable lunch break, and the performance of all the jobs, employing the decomposition principle of linear programming.

J. M. P. Booler

Papers

The Solution of a Railway Locomotive Scheduling Problem

A Note on the Use of Lagrangean Relaxation in Railway Scheduling

A Method for Solving Crew Scheduling Problems