This paper aims to study the locomotive assignment problem which is very important for railway companies, in view of high cost of operating locomotives. This problem is to determine the minimum cost assignment of homogeneous locomotives located in some central depots to a set of pre-scheduled trains in order to provide sufficient power to pull the trains from their origins to their destinations. These trains have different degrees of priority for servicing, and the high class of trains should be serviced earlier than others. This problem is modeled using vehicle routing and scheduling problem where trains representing the customers are supposed to be serviced in pre-specified hard/soft fuzzy time windows.A two-phase approach is used which, in the first phase, the multi-depot locomotive assignment is converted to a set of single depot problems, and after that, each single depot problem is solved heuristically by a hybrid genetic algorithm. In the genetic algorithm, various heuristics and efficient operators are used in the evolutionary search. The suggested algorithm is applied to solve the medium sized numerical example to check capabilities of the model and algorithm. Moreover, some of the results are compared with those solutions produced by branch-and-bound technique to determine validity and quality of the model. Results show that suggested approach is rather effective in respect of quality and time.
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