A Goal Programming Approach to Line Planning Problem Considering Multi-type Rolling Stock Constraint

Line planning problem is a strategic and long-term decision in passenger railway planning. A line is a direct railway connection between two stations and is characterized by its origin and destination station, its frequency/day, the route between these two stations and the intermediate stops at passing railway stations. The line plan is the collection of all lines and, finding it, is a very complex problem. Researchers have used linear and non-linear mathematical programming for this problem. In this paper a new multi objective mixed integer linear mathematical model (MOMILP) for line planning problem is presented, in which two conflict objective functions, minimizing total operation costs and maximizing total number of direct passengers, are considered. Total operation costs consist of fixed cost, variable cost and direct passengers are the passengers that can travel from their origin station to their destination station without having to change trains. This model is solved by using goal-programming method. The companies of passenger trains use several kinds of rolling stocks that are different in speed and capacity, and the number of each kind of them is limited. Therefore, in the proposed model, the total number of existing rolling stock is limited by adding a new constraint, and more than one kind of rolling stock can be used for each line. Finally, a numerical example is presented to evaluate the performance of proposed model. The results show that by using goal programming, according to planning conditions and organizational priorities, both objective functions may be optimized simultaneously.