Parseh Designers Transportation Research Institute Quarterly Journal of Transportation Engineering 2008-6598 Articles in Press 2022 07 31 Employing multi-objective simulated annealing algorithm to solve the developed model for determining the size of freight cars in rail transportation industry Employing multi-objective simulated annealing algorithm to solve the developed model for determining the size of freight cars in rail transportation industry 154265 10.22119/jte.2022.154265 FA Zahra Mafakheri Faculty of Industrial and Systems Engineering, Tarbiat Modarres University Majid Skeikhmohammady Tarbiat Modarres University Faculty of Industrial and Systems Engineering Ali Husseinzadeh Kashan Faculty of Industrial and Systems Engineering, Tarbiat Modarres University Journal Article 2015 11 22 Determining the fleet size is one of the most important issues of the shipping industry. In this study, a mathematical model is proposed for the dynamic problem of determining the number of rail freight wagons in conformity with the real-world conditions and restrictions. In the proposed model, the demands for wagon and due time for start have been considered deterministic. In addition to the revenue, another objective function has been considered for more productivity which reduces the number of delays in responding the demands during planning. Also, in accordance with the actual conditions in a railway network, freight wagons have been heterogeneously taken into consideration. In the proposed model, the vehicle capacity constraints, vehicle delivery, and the line capacity have been taken into account for the first time. Here, specifying empty wagons in order to increase productivity of the available wagons in the network; as a result, reducing a large expense of fleet ownership and maintenance has been considered. After defining the problem in the form of a mathematical model, a method based on the multi-objective simulated annealing algorithm has been proposed to find the Pareto solutions. Finally, a numerical example has been given from the Islamic Republic of Iran's Railway Transportation Industry and the solution has been discussed. Determining the fleet size is one of the most important issues of the shipping industry. In this study, a mathematical model is proposed for the dynamic problem of determining the number of rail freight wagons in conformity with the real-world conditions and restrictions. In the proposed model, the demands for wagon and due time for start have been considered deterministic. In addition to the revenue, another objective function has been considered for more productivity which reduces the number of delays in responding the demands during planning. Also, in accordance with the actual conditions in a railway network, freight wagons have been heterogeneously taken into consideration. In the proposed model, the vehicle capacity constraints, vehicle delivery, and the line capacity have been taken into account for the first time. Here, specifying empty wagons in order to increase productivity of the available wagons in the network; as a result, reducing a large expense of fleet ownership and maintenance has been considered. After defining the problem in the form of a mathematical model, a method based on the multi-objective simulated annealing algorithm has been proposed to find the Pareto solutions. Finally, a numerical example has been given from the Islamic Republic of Iran's Railway Transportation Industry and the solution has been discussed.