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An essential issue that a freight transportation system faced is how todeliver shipments (OD pairs) on a capacitated physical network optimally; thatis, to determine the best physical path for each OD pair and assign each ODpair into the most reasonable freight train service sequence. Instead ofpre-specifying or pre-solving the railcar routing beforehand and optimizing thetrain formation plan subsequently, which is a standard practice in Chinarailway system and a widely used method in existing literature to reduce theproblem complexity, this paper proposes a non-linear binary programming modelto address the integrated railcar itinerary and train formation planoptimization problem. The model comprehensively considers various operationalrequirements and a set of capacity constraints, including link capacity, yardreclassification capacity and the maximal number of blocks a yard can beformed, while trying to minimize the total costs of accumulation,reclassification and transportation. An efficient simulated annealing basedheuristic solution approach is developed to solve the mathematical model. Totackle the difficult capacity constraints, we use a penalty function method.Furthermore, a customized heuristics for satisfying the operationalrequirements is designed as well.

Integrating car path optimization with train formation plan: a non-linear binary programming model and simulated annealing based heuristics