A mathematical formulation and an LP-based neighborhood search matheuristic solution method for the integrated train blocking and shipment path problem

This article addresses the integrated train blocking and shipment path (TBSP) problem. The problem aims to route and classify railcar flows while satisfying railway line and station capacity constraints. At the same time, the problem tries to minimize the total operational costs. In this article, a new linear arc-node mathematical model is developed for the TBSP problem. In order to solve the model, a novel matheuristic solution method is proposed, which includes the hybridization of tabu search (TS) metaheuristic as well as mathematical programming techniques. The solution method reduces the search space of the problem by iteratively solving an LP relaxation form of the original model. At each iteration, inspired by the TS, a penalization procedure is applied to the coefficients of the LP objective function according to the solutions. Finally, a restricted MIP model is generated based on the LP solutions. For solving all the LP and the MIP models, a black-box MIP solver is employed. Experimental results confirm that the solution method can solve the problem in a reasonable time and achieve a solution of high quality in terms of the total incurred cost.