Optimizing the operation of rolling stock in organizing cargo transportation at a railway network segment

We propose a mathematical model for the assignment of locomotives to transport freight trains. We consider various objective functions. One of the optimization objectives in our model is to minimize the number of locomotives involved in transportation by choosing the routes of trains and locomotives given that the daily transportation plan is fulfilled. The model is capable to account for different types of locomotives as well as different types of their technical maintenance. We propose a new heuristic algorithm for finding an approximate solution for this problem. The main tool of the proposed algorithm is a heuristic utility function that takes into account the topology of the railway network, restrictions imposed on the movement of locomotives, and also the need for technical inspection and repair of locomotives. Results of numerical simulation are presented with the example of real data regarding the movement of freight trains on a section of the Moscow Railway. We pay special attention to performing a qualitative analysis of the resulting solution, in particular, in order to reveal the dependencies between the values of the main qualitative characteristics of the motion and coefficients in front of the variables in the utility function. We assume that it is possible to control the total number of locomotives involved by changing the percentage of admissible idle and auxiliary runs.