A Mathematical Model for Train Routing and Scheduling Problem with Fuzzy Approach

Routing and Makeup problems, determine the routing and frequency of trains & the assignment of blocks to trains, but do not take scheduling into consideration. Consequently later on, it may be difficult to find a timetable accommodating all planned trains and satisfying line and station capacity. As an attempt to settle this issue, both the routing & the scheduling of freight transportation have been merged in the present paper. The proposed model embodies three different objectives of: the cost of train formation, the cost of idle time of waiting wagons in stations, & the cost of wagon classifications in shunting stations. It is assumed that, the maximum tonnage and length of trains in each block-section is finite, and is dependent on the critical gradient of the route and also maximum length of internal tracks of stations. In real world application, it is out of reality to assign crisp values to the admissible maximum tonnage of trains in the planning stage. A more applicable method is to consider this parameter as a fuzzy number. The paper intends to present a pure 0-1 model with fuzzy approach, & offers a decomposition-based heuristic algorithm to solve the large-scale problems in a limited amount of time.