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The main difference between locomotive schedule of heavy haul railways and that of regular rail transportation is the number of locomotives utilized for one train. One heavy-loaded train usually has more than one locomotive, but a regular train only has one. This paper develops an optimization model for the multilocomotive scheduling problem (MLSP) through analyzing the current locomotive schedule of Da-qin Railway. The objective function of our paper is to minimize the total number of utilized locomotives. The MLSP is nondeterministic polynomial (NP) hard. Therefore, we convert the multilocomotive traction problem into a single-locomotive traction problem. Then, the single-locomotive traction problem (SLTP) can be converted into an assignment problem. The Hungarian algorithm is applied to solve the model and obtain the optimal locomotive schedule. We use the variance of detention time of locomotives at stations to evaluate the stability of locomotive schedule. In order to evaluate the effectiveness of the proposed optimization model, case studies for 20 kt and 30 kt heavy-loaded combined trains on Da-qin Railway are both conducted. Compared to the current schedules, the optimal schedules from the proposed models can save 62 and 47 locomotives for 20 kt and 30 kt heavy-loaded combined trains, respectively. Therefore, the effectiveness of the proposed model and its solution algorithm are both valid

Locomotive Schedule Optimization for Da-qin Heavy Haul Railway