Abstract
In this paper, we address the route planning problem in fourth party logistics (4PL). The problem calls for the selection of the logistics companies by a 4PL provider to optimize the routes of delivering goods through a transportation network. The concept of 4PL emerged in response to the shortfall in services capabilities of traditional third party logistics and has been proven to be capable of integrating logistics resources in order to fulfill complex transportation demands. A mixed-integer programming model is established for the planning problem with setup cost and edge cost discount policies which are commonly seen in practice. We propose a column generation approach combined with graph search heuristic to efficiently solve the problem. The good performance in terms of the solution quality and computational efficiency of our approach is shown through extensive numerical experiments on various scales of test instances. Impacts of cost policies on routing decision are also investigated and managerial insights are drawn.
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Acknowledgments
Dr. Yi Tao was supported by the Natural Science Foundation of Guangdong Province, China, under Grant 2016A030313700.
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Appendices
Appendix A
Effects of graph search heuristic
Preliminary experiments have been conducted to evaluate the effect of the graph search heuristic. Detailed results are presented in Table A1. It can be seen that if graph search heuristic is not involved to solve the subproblems and exact method is used instead, the average solution value is slightly improved compared to the one obtained from the CGH approach. However, the average running time is significantly longer because exact method for solving each subproblem can be quite time consuming especially when the scale of cases becomes large. Because the route planning problem faced by the 4PL provider is usually complex and efficient solution is expected, we use graph search heuristic to solve the subproblems.
Appendix B
Numerical experiment with various numbers of nodes
This section presents the detailed results for MIP and CGH on the 3 sets of instances (ie, 1a, 1b, and 1c), resulting in the following three tables (Tables B1, B2, B3).
Appendix C
Numerical experiment with various numbers of tasks
This section contains the detailed results for MIP and CGH on the three sets of instances (ie, 2a, 2b, and 2c), resulting in the following three tables (Tables C1, C2, C3).
Appendix D
Numerical experiment with varying levels of setup cost
This section contains the detailed results for MIP and CGH on the 3 sets of instances (ie, 3a, 3b, and 3c), resulting in the following three tables (Tables D1, D2, D3).
Appendix E
Numerical experiment with varying levels of edge cost discount
This section contains the detailed results for MIP and CGH on the 3 sets of instances (ie, 4a, 4b, and 4c), resulting in the following three tables (Tables E1, E2, E3).
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Tao, Y., Chew, E.P., Lee, L.H. et al. A column generation approach for the route planning problem in fourth party logistics. J Oper Res Soc 68, 165–181 (2017). https://doi.org/10.1057/s41274-016-0024-3
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DOI: https://doi.org/10.1057/s41274-016-0024-3