A train makeup problem specifies the frequency of freight trains and allocates the shipment to trains based on the desired shipment-to-train allocation scheme. In this study, a multi-objective model is presented for train makeup, taking into account the locomotive limitations on a railway network. The objective functions include maximization of the total profit and the customers' satisfaction level as well as minimization of the total number of shunting operations in yards, the unused capacity of trains, the total lost demand, the transfer time of trains and the total fuel consumed. The main constraints of the model are the establishment of flow balance for each yard and each demand, the upper and lower limits of the train length, and the upper limit of the following: train makeup in each yard, shunting operations in each yard, capacity of each train and locomotive utilization in each period. Goal programming and Lp metric methods are used for the multi-objective problem considered. For solving this problem, a hybrid firefly algorithm is also proposed. A number of test problems based on the simulation are generated and solved by using the proposed algorithm. Furthermore, a real-time case study based on the Iranian Railway Network is used. The results show the potential of the presented model and the efficiency of the hybrid algorithm, which can be used for real-time railway problems.
Abstract. Train formation planning faces two types of challenges; namely, the determination of the quantity of cargo trains run known as the frequency of cargo trains and the formation of desired allocations of demands to a freight train. To investigate the issues of train makeup and train routing simultaneously, this multiobjective model optimizes the total profit, satisfaction level of customers, yard activities in terms of the total size of a shunting operation, and underutilized train capacity. It also considers the guarantee for the yard-demand balance of flow, maximum and minimum limitations for the length of trains, maximum yard limitation for train formation, maximum yard limitation for operations related to shunting, maximum limitation for the train capacity, and upper limit of the capacity of each arc in passing trains. In this paper, a goal programming approach and an Lp norm method are applied to the problem. Furthermore, a simulated annealing (SA) algorithm is designed. Some test problems are also carried out via simulation and solved using the SA algorithm. Furthermore, a sample investigation is carried out in a railway company in Iran. The findings show the capability and performance of the proposed approach to solve the problems in a real rail network.
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