Railroad industry has received tremendous challenges in the world in terms of handling cost and efficiency. For many years, the railroad business lost money in many countries such as Japan until many governments decided to privatize the industry in an attempt to reduce the cost components and to increase the efficiency of various units, significantly. In this paper, we propose a new goal programming technique to handle two objectives of operating cost and the number of passengers travel by train. We consider different types of trains for public transportation of passengers in order to make the proposed model of this paper more realistic. The implementation of the proposed model is demonstrated using some numerical examples to show the effectiveness of the method.

Railroad transportation planning is strategically a long term and an important decision making problem especially in the area of travelling passengers. There have been literally various methods to use in order to provide optimum traveling schedule such as direct or indirect methods. Direct solutions involve the implementation of mixed integer programming, which is often hard to solve for real-world applications. The proposed model of this paper uses a column generation method to decompose a large-scale railroad passenger-scheduling problem into some smaller scale problems, which are easier to solve. The primary concern with the resulted problem is that final solutions of the method need to be integer and this is in contrast with convexity assumption of column generation techniques. We propose heuristic method to handle this problem and apply the proposed model for some examples. The preliminary results indicate that the proposed model of this paper could provide optimal solutions for small-scale problems and it can reach some reasonable solutions for larger problems when direct implementation fails to do in reasonable amount of time.