A path-based capacitated network flow model for empty railcar distribution


In this paper we develop a novel formulation for the empty railcar distribution problem that considers realistic technical and business requirements while assigning empty cars to customer demands. The proposed model takes block and train capacities into account, while satisfying the supply and demand constraints, and allows car substitutability among pools of the same car type as well as customer preferences towards different pools. Following the practice in US railroads, the proposed model does not combine car routing and car distribution decisions. Those two decisions are separated from each other and they are usually made by different departments in US railroads. The model is implemented in CPLEX Concert Technology using Java and is illustrated in a numerical example. Results show that the proposed model can improve several performance measures over the noncapacitated model which is currently used by industry.

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The authors would like to thank Colombo from Universita degli Studi di Milano, Italia (Team OR at UNIMI) for providing us with their 2011 RAS competition results.

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Correspondence to Ruhollah Heydari.

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Ruhollah Heydari and Emanuel Melachrinoudis state that there are no conflicts of interest.


Appendix 1: An algorithm for returning all permutations of a given word

The returnListOfAllPermutations() reads a given word letter-by-letter. After reading each letter, and before reading the next one, it generates all the words that can be created using the substring traversed so far and saves them in a set called currentSet. Similar to other dynamic programming methods, at each step and after reading each letter, the algorithm uses the substrings created before to generate new substrings of one size more. The algorithm ends when all the letters are traversed.


Appendix 2: An illustrative example for returning all permutations of a given word

Example 1

Generate all permutations of a givenWord \(=\) BIIB


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Heydari, R., Melachrinoudis, E. A path-based capacitated network flow model for empty railcar distribution. Ann Oper Res 253, 773–798 (2017). https://doi.org/10.1007/s10479-016-2259-4

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  • Empty railcar distribution
  • Railroad optimization
  • Transportation planning
  • Rail network