Abstract
The Scheduled Service Network Design Problem (SSNDP) models a wide range of tactical planning issues in the operation of freight transportation networks. Most variants of the problem model transportation costs that follow a step function that represents constant per-vehicle costs. However, piecewise linear functions have also been used to model cases where transportation costs are quoted on a per-unit-of-flow basis, with the rate decreasing in the amount of flow. We present a formulation strategy for the SSNDP that can be used for cost functions of any structure as it is based on encoding cost functions in data. With an extensive computational study we study the performance of solving instances of these formulations with an off-the-shelf solver.
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References
Arslan, O., Archetti, C., Jabali, O., Laporte, G., & Speranza, M. G. (2020). Minimum cost network design in strategic alliances. Omega, 96, 102079.
Bakir, I., Erera, A., & Savelsbergh, M. (2021). Motor carrier service network design. In: T. G. Crainic, M. Gendreau, & B. Gendron (Eds.), Network design with applications to transportation and logistics (pp. 427–467). Springer.
Balakrishnan, A., & Graves, S. C. (1989). A composite algorithm for a concave-cost network flow problem. Networks, 19(2), 175–202.
Boland, N., Hewitt, M., Marshall, L., & Savelsbergh, M. (2017). The continuous-time service network design problem. Operations Research, 65(5), 1303–1321.
Chabot, T., Bouchard, F., Legault-Michaud, A., Renaud, J., & Coelho, L. C. (2018). Service level, cost and environmental optimization of collaborative transportation. Transportation Research Part E: Logistics and Transportation Review, 110, 1–14.
Crainic, T. G., & Hewitt, M. (2021). Service network design. In: T. G. Crainic, M. Gendreau, & B. Gendron (Eds.), Network design with applications to transportation and logistics (pp. 347–382). Springer.
Crainic, T. G., Gendreau, M., & Gendron, B. (2021). Network design with applications to transportation and logistics. Springer Nature.
Croxton, K. L., Gendron, B., & Magnanti, T. L. (2003). Models and methods for merge-in-transit operations. Transportation Science, 37(1), 1–22.
Croxton, K. L., Gendron, B., & Magnanti, T. L. (2007). Variable disaggregation in network flow problems with piecewise linear costs. Operations Research 55(1), 146–157.
Ford, L. R., & Fulkerson, D. R. (1958). Constructing maximal dynamic flows from static flows. Operations Research, 6(3), 419–433.
Ford, L. R., & Fulkerson, D. R. (1962). Flows in networks. Princeton University Press.
Fortz, B., Gouveia, L., & Joyce-Moniz, M. (2017). Models for the piecewise linear unsplittable multicommodity flow problems. European Journal of Operational Research, 261(1), 30–42.
Frangioni, A., & Gendron, B. (2009). 0–1 reformulations of the multicommodity capacitated network design problem. Discrete Applied Mathematics 157(6), 1229–1241.
Frangioni, A., & Gendron, B. (2021) Piecewise linear cost network design. In: T. G. Crainic, M. Gendreau, & B. Gendron (Eds.), Network design with applications to transportation and logistics (pp. 167–185). Springer.
Gendron, B., & Gouveia, L. (2017). Reformulations by discretization for piecewise linear integer multicommodity network flow problems. Transportation Science, 51(2), 629–649.
Hewitt, M. (2019). Enhanced dynamic discretization discovery for the continuous time load plan design problem. Transportation Science, 53(6), 1731–1750.
Hewitt, M., & Lehuédé, F. (2022). The service network scheduling problem. Technical Report, Quinlan School of Business, Loyola University Chicago. https://hal.archives-ouvertes.fr/hal-03598983/.
Hewitt, M., & Lehuédé, F. (2023). New formulations for the scheduled service network design problem. Transportation Research Part B: Methodological, 172, 117–133.
Lai, M., Cai, X., & Hall, N. G. (2022). Cost allocation for less-than-truckload collaboration via shipper consortium. Transportation Science, 56(3), 585–611.
Studio-CPLEX IICO (2022). Users manual-version 22 release 1.0.
Tang, X., Lehuédé, F., Péton, O., & Pan, L. (2019). Network design of a multi-period collaborative distribution system. International Journal of Machine Learning and Cybernetics, 10, 279–290.
Van Rossum, G., & Drake, F. L. (2010). The python language reference. Python Software Foundation Amsterdam.
Vielma, J. P., Ahmed, S., & Nemhauser, G. (2010). Mixed-integer models for nonseparable piecewise-linear optimization: unifying framework and extensions. Operations Research, 58(2), 303–315.
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We would like do dedicate this work to Bernard Gendron for his numerous contributions to the topic and his extreme kindness.
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Hewitt, M., Lehuédé, F. (2024). New Formulations for the Scheduled Service Network Design Problem with Piecewise Linear Costs. In: Crainic, T.G., Gendreau, M., Frangioni, A. (eds) Combinatorial Optimization and Applications. International Series in Operations Research & Management Science, vol 358. Springer, Cham. https://doi.org/10.1007/978-3-031-57603-4_8
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DOI: https://doi.org/10.1007/978-3-031-57603-4_8
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