Abstract
In logistic problems, an Integral Multi-Commodity Network Design Problem on a time-space network is often used to model the problem of routing transportation means and assigning freight units to those means. In Physical Internet and Synchromodal networks an interactive planning approach is preferable, meaning that calculation times of a single planning step should be short. In this paper we provide ways to reduce the size of the problem formulation based on cutting planes, that are effective in reducing the computation time for Integer Linear Programming problem-based solution methods.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Aardal, K., Weismantel, R., Wolsey, L.A.: Non-standard approaches to integer programming. Discrete Appl. Math. 123(1–3), 5–74 (2002)
Andersen, J., Crainic, T.G., Christiansen, M.: Service network design with asset management: Formulations and comparative analyses. Transp. Res. Part C: Emerg. Technol. 17(2), 197–207 (2009)
Balakrishnan, A., Magnanti, T., Wong, R.: A dual-ascent procedure for large-scale uncapacitated network design. Oper. Res. 37(5), 716–740 (1989)
Chouman, M., Crainic, T.: MIP-based Matheuristic for Service Network Design with Design-balanced Requirements. CIRRELT (2012)
Cook, W.J., Cunningham, W.H., Pulleyblank, W.R., Schrijver, A.: Combinatorial Optimization. Wiley Interscience (1998)
Crainic, T.: Service network design in freight transportation. Eur. J. Oper. Res. 122(2), 272–288 (2000)
Crainic, T., Frangioni, A., Gendron, B.: Bundle-based relaxation methods for multicommodity capacitated fixed charge network design. Discrete Appl. Math. 112(1), 73–99 (2001)
Crainic, T., Gendreau, M., Farvolden, J.: A simplex-based tabu search method for capacitated network design. Inf. J. Comput. 12(3), 223–236 (2000)
De Juncker, M.A.M., Huizing, D., del Vecchyo, M.R.O., Phillipson, F., Sangers, A.: Framework of synchromodal transportation problems. ICCL 2017. LNCS, vol. 10572, pp. 383–403. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-68496-3_26
Ghamlouche, I., Crainic, T.G., Gendreau, M.: Path relinking, cycle-based neighbourhoods and capacitated multicommodity network design. Ann. Oper. Res. 131(1–4), 109–133 (2004)
Holmberg, K., Hellstrand, J.: Solving the uncapacitated network design problem by a lagrangean heuristic and branch-and-bound. Oper. Res. 46(2), 247–259 (1998)
Holmberg, K., Yuan, D.: A lagrangian heuristic based branch-and-bound approach for the capacitated network design problem. Oper. Res. 48(3), 461–481 (2000)
Huizing, D.: General methods for synchromodal planning of freight containers and transports. Master’s thesis, TU Delft (2017)
IBM: Cplex optimizer (2017). https://www.ibm.com/analytics/data-science/prescriptive-analytics/cplex-optimizer
IBM: Zero-half cuts (2017). https://www.ibm.com/support/knowledgecenter/SSSA5P_12.5.0/ilog.odms.cplex.help/CPLEX/UsrMan/topics/discr_optim/mip/cuts/38_zerohalf.html
Janic, M.: Modelling the full costs of an intermodal and road freight transport network. Transp. Res. Part D: Transp. Environ. 12(1), 33–44 (2007)
Joborn, M., Crainic, T.G., Gendreau, M., Holmberg, K., Lundgren, J.T.: Economies of scale in empty freight car distribution in scheduled railways. Transp. Sci. 38(2), 121–134 (2004)
Letchford, A.N., Lodi, A.: Strengthening Chvátal-Gomory cuts and Gomory fractional cuts. Oper. Res. Lett. 30(2), 74–82 (2002)
Li, X., Wei, K., Aneja, Y., Tian, P.: Design-balanced capacitated multicommodity network design with heterogeneous assets. Omega 67, 145–159 (2017)
Magnanti, T.L., Wong, R.T.: Network design and transportation planning: Models and algorithms. Transp. Sci. 18(1), 1–55 (1984)
Magnanti, T.L., Mirchandani, P., Vachani, R.: Modeling and solving the two-facility capacitated network loading problem. Oper. Res. 43(1), 142–157 (1995)
Marchand, H., Martin, A., Weismantel, R., Wolsey, L.: Cutting planes in integer and mixed integer programming. Discrete Appl. Math. 123(1–3), 397–446 (2002)
Pedersen, M., Crainic, T., Madsen, O.: Models and tabu search metaheuristics for service network design with asset-balance requirements. Transp. Sci. 43(2), 158–177 (2009)
Sharypova, K.: Optimization of Hinterland Intermodal Container Transportation. Ph.D. thesis, Eindhoven University of Technology (2014)
Vu, D.M., Crainic, T.G., Toulouse, M., Hewitt, M.: Service network design with resource constraints. Transp. Sci. 50(4), 1380–1393 (2014)
Acknowledgement
This work has been carried out within the project ‘Complexity Methods for Predictive Synchromodality’ (Comet-PS), supported by NWO (the Netherlands Organisation for Scientific Research), TKI-Dinalog (Top Consortium Knowledge and Innovation) and the Early Research Program ‘Grip on Complexity’ of TNO (The Netherlands Organisation for Applied Scientific Research).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Kalicharan, K., Phillipson, F., Sangers, A. (2020). Cutting Planes for Solving Logistic Flow Problems. In: Lalla-Ruiz, E., Mes, M., Voß, S. (eds) Computational Logistics. ICCL 2020. Lecture Notes in Computer Science(), vol 12433. Springer, Cham. https://doi.org/10.1007/978-3-030-59747-4_37
Download citation
DOI: https://doi.org/10.1007/978-3-030-59747-4_37
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-59746-7
Online ISBN: 978-3-030-59747-4
eBook Packages: Computer ScienceComputer Science (R0)