A Bi-objective model and a branch-and-price-and-cut solution method for the railroad blocking problem in hazardous material transportation

One of the most important railway transportation problems is the railroad blocking problem (RBP). To our knowledge, no works consider the costs and risks of hazmat transportation in the RBP literature. In this paper, a bi-objective mathematical model is proposed for the RBP considering the risk of hazmat transportation and operating costs. The objective functions are (1) minimizing the cost of delivering commodities while observing limits on the number and aggregate volume of the blocks assembled at each terminal in freight railroads, and (2) minimizing the risk of hazmat transportation in terminals and en route. The ε-constraint method and a presented branch-and-price-and-cut (B&P&C) algorithm are used to solve the proposed bi-objective model. To evaluate the model and the solution method, seventeen experimental instances based on real-world conditions are generated and solved. Modeling and solving the experimental instances and the case study revealed the proposed model's capability and the solution method's efficiency. In addition, as a case study, the proposed model and algorithm are implemented in the Iranian railway network.