The objective of the locomotive assignment problem (LAP) is to assign a fleet of locomotives to a set of trains while satisfying a rich set of operational and budget constraints and optimizing one or more crucial objectives. This paper presents a survey on optimization models for this class of scheduling problems. Depending on the context of application, the kind of model used to solve the LAP varies; accordingly, this influences the solution methodology and algorithms used. In this paper, we review and also suggest a classification of the various models.

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