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The multicommodity network flow problem: state of the art classification, applications, and solution methods

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  • Khodakaram Salimifard

    (Persian Gulf University)

  • Sara Bigharaz

    (Università degli Studi di Torino)

Abstract

Over the past decades, the Multicommodity Network Flow (MCNF) problem has grown popular in the academic literature and a growing number of researchers are interested in this field. It is a powerful operational research approach to tackle and solve many complicated problems, especially in transportation and telecommunication contexts. Yet, few literature reviews have made an effort to classify the existing articles accordingly. In this article, we present a taxonomic review of the MCNF literature published between 2000 and 2019. Based on an adapted version of an existing comprehensive taxonomy, we have classified 263 articles into two main categories of applications and solution methods. We have also analyzed the research interests in the MCNF literature. This classification is the first to categorize the articles into this level of detail. Results show that there are topics, which need to be addressed in future researches.

Suggested Citation

  • Khodakaram Salimifard & Sara Bigharaz, 2022. "The multicommodity network flow problem: state of the art classification, applications, and solution methods," Operational Research, Springer, vol. 22(1), pages 1-47, March.
    • Handle: RePEc:spr:operea:v:22:y:2022:i:1:d:10.1007_s12351-020-00564-8
    DOI: 10.1007/s12351-020-00564-8
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    as
    1. K. Truemper & Y. Soun, 1979. "Minimal Forbidden Subgraphs of Unimodular Multicommodity Networks," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 379-389, November.
    2. Anantaram Balakrishnan & Gang Li & Prakash Mirchandani, 2017. "Optimal Network Design with End-to-End Service Requirements," Operations Research, INFORMS, vol. 65(3), pages 729-750, June.
    3. Jeff L. Kennington, 1978. "A Survey of Linear Cost Multicommodity Network Flows," Operations Research, INFORMS, vol. 26(2), pages 209-236, April.
    4. Gouveia, Luis, 1996. "Multicommodity flow models for spanning trees with hop constraints," European Journal of Operational Research, Elsevier, vol. 95(1), pages 178-190, November.
    5. Paraskevopoulos, Dimitris C. & Gürel, Sinan & Bektaş, Tolga, 2016. "The congested multicommodity network design problem," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 85(C), pages 166-187.
    6. Richard D. McBride, 1998. "Advances in Solving the Multicommodity-Flow Problem," Interfaces, INFORMS, vol. 28(2), pages 32-41, April.
    7. Y. P. Aneja & K. P. K. Nair, 1982. "Multicommodity Network Flows with Probabilistic Losses," Management Science, INFORMS, vol. 28(9), pages 1080-1086, September.
    8. Levitin, G. & Gertsbakh, I. & Shpungin, Y., 2013. "Evaluating the damage associated with intentional supply deprivation in multi-commodity network," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 11-17.
    9. Mesquita, Marta & Moz, Margarida & Paias, Ana & Pato, Margarida, 2015. "A decompose-and-fix heuristic based on multi-commodity flow models for driver rostering with days-off pattern," European Journal of Operational Research, Elsevier, vol. 245(2), pages 423-437.
    10. Gamst, M. & Petersen, B., 2012. "Comparing branch-and-price algorithms for the Multi-Commodity k-splittable Maximum Flow Problem," European Journal of Operational Research, Elsevier, vol. 217(2), pages 278-286.
    11. Pengfei Zhang & Neng Fan, 2017. "Analysis of budget for interdiction on multicommodity network flows," Journal of Global Optimization, Springer, vol. 67(3), pages 495-525, March.
    12. Ouorou, A. & Mahey, P., 2000. "A minimum mean cycle cancelling method for nonlinear multicommodity flow problems," European Journal of Operational Research, Elsevier, vol. 121(3), pages 532-548, March.
    13. Powell, Warren B. & Carvalho, Tassio A., 1997. "Dynamic control of multicommodity fleet management problems," European Journal of Operational Research, Elsevier, vol. 98(3), pages 522-541, May.
    14. Sedeno-Noda, A. & Gonzalez-Martin, C. & Gutierrez, J., 2005. "The biobjective undirected two-commodity minimum cost flow problem," European Journal of Operational Research, Elsevier, vol. 164(1), pages 89-103, July.
    15. Burak Ayar & Hande Yaman, 2012. "An intermodal multicommodity routing problem with scheduled services," Computational Optimization and Applications, Springer, vol. 53(1), pages 131-153, September.
    16. Michał Pióro & Yoann Fouquet & Dritan Nace & Michael Poss, 2016. "Optimizing Flow Thinning Protection in Multicommodity Networks with Variable Link Capacity," Operations Research, INFORMS, vol. 64(2), pages 273-289, April.
    17. Margarida Moz & Margarida Pato, 2004. "Solving the Problem of Rerostering Nurse Schedules with Hard Constraints: New Multicommodity Flow Models," Annals of Operations Research, Springer, vol. 128(1), pages 179-197, April.
    18. Kaj Holmberg & Di Yuan, 2003. "A Multicommodity Network-Flow Problem with Side Constraints on Paths Solved by Column Generation," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 42-57, February.
    19. L. R. Ford, Jr. & D. R. Fulkerson, 1958. "A Suggested Computation for Maximal Multi-Commodity Network Flows," Management Science, INFORMS, vol. 5(1), pages 97-101, October.
    20. Antoine Gautier & Frieda Granot, 1995. "Forest Management: A Multicommodity Flow Formulation and Sensitivity Analysis," Management Science, INFORMS, vol. 41(10), pages 1654-1668, October.
    21. Hadjiat, Malika & Maurras, Jean-Francois & Vaxes, Yann, 2000. "A primal partitioning approach for single and non-simultaneous multicommodity flow problems," European Journal of Operational Research, Elsevier, vol. 123(2), pages 382-393, June.
    22. Ilfat Ghamlouche & Teodor Crainic & Michel Gendreau, 2004. "Path Relinking, Cycle-Based Neighbourhoods and Capacitated Multicommodity Network Design," Annals of Operations Research, Springer, vol. 131(1), pages 109-133, October.
    23. Hamoud S. Bin Obaid & Theodore B. Trafalis, 2020. "An approximation to max min fairness in multi commodity networks," Computational Management Science, Springer, vol. 17(1), pages 65-77, January.
    24. Aimé Kamgaing Kuiteing & Patrice Marcotte & Gilles Savard, 2018. "Pricing and revenue maximization over a multicommodity transportation network: the nonlinear demand case," Computational Optimization and Applications, Springer, vol. 71(3), pages 641-671, December.
    25. F. Babonneau & O. du Merle & J.-P. Vial, 2006. "Solving Large-Scale Linear Multicommodity Flow Problems with an Active Set Strategy and Proximal-ACCPM," Operations Research, INFORMS, vol. 54(1), pages 184-197, February.
    26. Oğuz, Murat & Bektaş, Tolga & Bennell, Julia A., 2018. "Multicommodity flows and Benders decomposition for restricted continuous location problems," European Journal of Operational Research, Elsevier, vol. 266(3), pages 851-863.
    27. Ghasemi, Peiman & Khalili-Damghani, Kaveh & Hafezalkotob, Ashkan & Raissi, Sadigh, 2019. "Uncertain multi-objective multi-commodity multi-period multi-vehicle location-allocation model for earthquake evacuation planning," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 105-132.
    28. Yogesh K. Agarwal, 2002. "Design of Capacitated Multicommodity Networks with Multiple Facilities," Operations Research, INFORMS, vol. 50(2), pages 333-344, April.
    29. Jin, Wen-Long, 2012. "A kinematic wave theory of multi-commodity network traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1000-1022.
    30. Farahani, Reza Zanjirani & Miandoabchi, Elnaz & Szeto, W.Y. & Rashidi, Hannaneh, 2013. "A review of urban transportation network design problems," European Journal of Operational Research, Elsevier, vol. 229(2), pages 281-302.
    31. Balma, Ali & Salem, Safa Ben & Mrad, Mehdi & Ladhari, Talel, 2018. "Strong multi-commodity flow formulations for the asymmetric traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 271(1), pages 72-79.
    32. Naoto Katayama, 2019. "A combined fast greedy heuristic for the capacitated multicommodity network design problem," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 70(11), pages 1983-1996, November.
    33. Morabito, Reinaldo & de Souza, Mauricio C. & Vazquez, Mariana, 2014. "Approximate decomposition methods for the analysis of multicommodity flow routing in generalized queuing networks," European Journal of Operational Research, Elsevier, vol. 232(3), pages 618-629.
    34. A. M. Geoffrion & G. W. Graves, 1974. "Multicommodity Distribution System Design by Benders Decomposition," Management Science, INFORMS, vol. 20(5), pages 822-844, January.
    35. Holmberg, Kaj & Joborn, Martin & Melin, Kennet, 2008. "Lagrangian based heuristics for the multicommodity network flow problem with fixed costs on paths," European Journal of Operational Research, Elsevier, vol. 188(1), pages 101-108, July.
    36. Cynthia Barnhart & Christopher A. Hane & Pamela H. Vance, 2000. "Using Branch-and-Price-and-Cut to Solve Origin-Destination Integer Multicommodity Flow Problems," Operations Research, INFORMS, vol. 48(2), pages 318-326, April.
    37. Gamst, Mette & Neergaard Jensen, Peter & Pisinger, David & Plum, Christian, 2010. "Two- and three-index formulations of the minimum cost multicommodity k-splittable flow problem," European Journal of Operational Research, Elsevier, vol. 202(1), pages 82-89, April.
    38. Jordi Castro, 2003. "Solving Difficult Multicommodity Problems with a Specialized Interior-Point Algorithm," Annals of Operations Research, Springer, vol. 124(1), pages 35-48, November.
    39. Al-Khayyal, Faiz & Hwang, Seung-June, 2007. "Inventory constrained maritime routing and scheduling for multi-commodity liquid bulk, Part I: Applications and model," European Journal of Operational Research, Elsevier, vol. 176(1), pages 106-130, January.
    40. Sankaran, Jayaram K., 1995. "Column generation applied to linear programs in course registration," European Journal of Operational Research, Elsevier, vol. 87(2), pages 328-342, December.
    41. Natashia Boland & Thomas Kalinowski & Fabian Rigterink, 2016. "New multi-commodity flow formulations for the pooling problem," Journal of Global Optimization, Springer, vol. 66(4), pages 669-710, December.
    42. Mohammadi, Mehrdad & Jula, Payman & Tavakkoli-Moghaddam, Reza, 2017. "Design of a reliable multi-modal multi-commodity model for hazardous materials transportation under uncertainty," European Journal of Operational Research, Elsevier, vol. 257(3), pages 792-809.
    43. T. C. Hu, 1963. "Multi-Commodity Network Flows," Operations Research, INFORMS, vol. 11(3), pages 344-360, June.
    44. Jeff Kennington & Mohamed Shalaby, 1977. "An Effective Subgradient Procedure for Minimal Cost Multicommodity Flow Problems," Management Science, INFORMS, vol. 23(9), pages 994-1004, May.
    45. Belanger, Nicolas & Desaulniers, Guy & Soumis, Francois & Desrosiers, Jacques, 2006. "Periodic airline fleet assignment with time windows, spacing constraints, and time dependent revenues," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1754-1766, December.
    46. P. Chardaire & A. Lisser, 2002. "Simplex and Interior Point Specialized Algorithms for Solving Nonoriented Multicommodity Flow Problems," Operations Research, INFORMS, vol. 50(2), pages 260-276, April.
    47. Karsten, Christian Vad & Pisinger, David & Ropke, Stefan & Brouer, Berit Dangaard, 2015. "The time constrained multi-commodity network flow problem and its application to liner shipping network design," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 76(C), pages 122-138.
    48. Alumur, Sibel A. & Nickel, Stefan & Saldanha-da-Gama, Francisco & Verter, Vedat, 2012. "Multi-period reverse logistics network design," European Journal of Operational Research, Elsevier, vol. 220(1), pages 67-78.
    49. Letchford, Adam N. & Salazar-González, Juan-José, 2016. "Stronger multi-commodity flow formulations of the (capacitated) sequential ordering problem," European Journal of Operational Research, Elsevier, vol. 251(1), pages 74-84.
    50. Abbas Azadi Moghaddam Arani & Fariborz Jolai & Mohammad Mahdi Nasiri, 2019. "A multi-commodity network flow model for railway capacity optimization in case of line blockage," International Journal of Rail Transportation, Taylor & Francis Journals, vol. 7(4), pages 297-320, October.
    51. Lin, Yi-Kuei, 2006. "A simple algorithm to generate all (d,B)-MCs of a multicommodity stochastic-flow network," Reliability Engineering and System Safety, Elsevier, vol. 91(8), pages 923-929.
    52. Letchford, Adam N. & Salazar-González, Juan-José, 2015. "Stronger multi-commodity flow formulations of the Capacitated Vehicle Routing Problem," European Journal of Operational Research, Elsevier, vol. 244(3), pages 730-738.
    53. Y. L. Chen & Y. H. Chin, 1992. "Multicommodity Network Flows with Safety Considerations," Operations Research, INFORMS, vol. 40(1-supplem), pages 48-55, February.
    54. Khouja, Moutaz & Michalewicz, Zgibniew & Wilmot, Michael, 1998. "The use of genetic algorithms to solve the economic lot size scheduling problem," European Journal of Operational Research, Elsevier, vol. 110(3), pages 509-524, November.
    55. Erera, Alan L. & Morales, Juan C. & Savelsbergh, Martin, 2005. "Global intermodal tank container management for the chemical industry," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 41(6), pages 551-566, November.
    56. Margarida Moz & Margarida Pato, 2003. "An Integer Multicommodity Flow Model Applied to the Rerostering of Nurse Schedules," Annals of Operations Research, Springer, vol. 119(1), pages 285-301, March.
    57. Rina R. Schneur & James B. Orlin, 1998. "A Scaling Algorithm for Multicommodity Flow Problems," Operations Research, INFORMS, vol. 46(2), pages 231-246, April.
    58. Young-Soo Myung & Hu-Gon Kim & Dong-Wan Tcha, 1997. "Optimal Load Balancing on Sonet Bidirectional Rings," Operations Research, INFORMS, vol. 45(1), pages 148-152, February.
    59. Dorneles, Árton P. & de Araújo, Olinto C.B. & Buriol, Luciana S., 2017. "A column generation approach to high school timetabling modeled as a multicommodity flow problem," European Journal of Operational Research, Elsevier, vol. 256(3), pages 685-695.
    60. George B. Dantzig & Philip Wolfe, 1960. "Decomposition Principle for Linear Programs," Operations Research, INFORMS, vol. 8(1), pages 101-111, February.
    61. Julie A. Ward, 1999. "Minimum-Aggregate-Concave-Cost Multicommodity Flows in Strong-Series-Parallel Networks," Mathematics of Operations Research, INFORMS, vol. 24(1), pages 106-129, February.
    62. Wright, Matthew A. & Gomes, Gabriel & Horowitz, Roberto & Kurzhanskiy, Alex A., 2017. "On node models for high-dimensional road networks," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 212-234.
    63. A. Ouorou & P. Mahey & J.-Ph. Vial, 2000. "A Survey of Algorithms for Convex Multicommodity Flow Problems," Management Science, INFORMS, vol. 46(1), pages 126-147, January.
    64. Yeh, Wei-Chang, 2008. "A simple minimal path method for estimating the weighted multi-commodity multistate unreliable networks reliability," Reliability Engineering and System Safety, Elsevier, vol. 93(1), pages 125-136.
    65. Foulds, L. R., 1981. "A multi-commodity flow network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 15(4), pages 273-283, August.
    66. Paola Cappanera & Giorgio Gallo, 2004. "A Multicommodity Flow Approach to the Crew Rostering Problem," Operations Research, INFORMS, vol. 52(4), pages 583-596, August.
    67. Masri, H. & Krichen, S. & Guitouni, A., 2015. "A multi-start variable neighborhood search for solving the single path multicommodity flow problem," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 132-142.
    68. Paola Cappanera & Antonio Frangioni, 2003. "Symmetric and Asymmetric Parallelization of a Cost-Decomposition Algorithm for Multicommodity Flow Problems," INFORMS Journal on Computing, INFORMS, vol. 15(4), pages 369-384, November.
    69. Alysson Costa & Jean-François Cordeau & Bernard Gendron, 2009. "Benders, metric and cutset inequalities for multicommodity capacitated network design," Computational Optimization and Applications, Springer, vol. 42(3), pages 371-392, April.
    70. J. A. Tomlin, 1966. "Minimum-Cost Multicommodity Network Flows," Operations Research, INFORMS, vol. 14(1), pages 45-51, February.
    71. M. H. Alavidoost & Mosahar Tarimoradi & M. H. Fazel Zarandi, 2018. "Bi-objective mixed-integer nonlinear programming for multi-commodity tri-echelon supply chain networks," Journal of Intelligent Manufacturing, Springer, vol. 29(4), pages 809-826, April.
    72. Michel Minoux, 2001. "Discrete Cost Multicommodity Network Optimization Problems and Exact Solution Methods," Annals of Operations Research, Springer, vol. 106(1), pages 19-46, September.
    73. Castro, J. & Nabona, N., 1996. "An implementation of linear and nonlinear multicommodity network flows," European Journal of Operational Research, Elsevier, vol. 92(1), pages 37-53, July.
    74. Daniel Wagner & Günther R. Raidl & Ulrich Pferschy & Petra Mutzel & Peter Bachhiesl, 2007. "A Multi-Commodity Flow Approach for the Design of the Last Mile in Real-World Fiber Optic Networks," Operations Research Proceedings, in: Karl-Heinz Waldmann & Ulrike M. Stocker (ed.), Operations Research Proceedings 2006, pages 197-202, Springer.
    75. R. Baldacci & E. Hadjiconstantinou & A. Mingozzi, 2004. "An Exact Algorithm for the Capacitated Vehicle Routing Problem Based on a Two-Commodity Network Flow Formulation," Operations Research, INFORMS, vol. 52(5), pages 723-738, October.
    76. Ozgur Kabadurmus & Alice E. Smith, 2016. "Multi-commodity k-splittable survivable network design problems with relays," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 62(1), pages 123-133, May.
    77. G. Caimi & F. Chudak & M. Fuchsberger & M. Laumanns & R. Zenklusen, 2011. "A New Resource-Constrained Multicommodity Flow Model for Conflict-Free Train Routing and Scheduling," Transportation Science, INFORMS, vol. 45(2), pages 212-227, May.
    78. Fortz, Bernard & Gouveia, Luís & Joyce-Moniz, Martim, 2017. "Models for the piecewise linear unsplittable multicommodity flow problems," European Journal of Operational Research, Elsevier, vol. 261(1), pages 30-42.
    79. Huseyin Topaloglu & Warren B. Powell, 2006. "Dynamic-Programming Approximations for Stochastic Time-Staged Integer Multicommodity-Flow Problems," INFORMS Journal on Computing, INFORMS, vol. 18(1), pages 31-42, February.
    80. Mohammed Alfaki & Dag Haugland, 2013. "A multi-commodity flow formulation for the generalized pooling problem," Journal of Global Optimization, Springer, vol. 56(3), pages 917-937, July.
    81. John W. Mamer & Richard D. McBride, 2000. "A Decomposition-Based Pricing Procedure for Large-Scale Linear Programs: An Application to the Linear Multicommodity Flow Problem," Management Science, INFORMS, vol. 46(5), pages 693-709, May.
    82. Haghani, Ali & Oh, Sei-Chang, 1996. "Formulation and solution of a multi-commodity, multi-modal network flow model for disaster relief operations," Transportation Research Part A: Policy and Practice, Elsevier, vol. 30(3), pages 231-250, May.
    83. Lisa Fleischer & Jay Sethuraman, 2005. "Efficient Algorithms for Separated Continuous Linear Programs: The Multicommodity Flow Problem with Holding Costs and Extensions," Mathematics of Operations Research, INFORMS, vol. 30(4), pages 916-938, November.
    84. Luce Brotcorne & Martine Labbé & Patrice Marcotte & Gilles Savard, 2001. "A Bilevel Model for Toll Optimization on a Multicommodity Transportation Network," Transportation Science, INFORMS, vol. 35(4), pages 345-358, November.
    85. Cortés, Pablo & Muñuzuri, Jesús & Guadix, José & Onieva, Luis, 2013. "Optimal algorithm for the demand routing problem in multicommodity flow distribution networks with diversification constraints and concave costs," International Journal of Production Economics, Elsevier, vol. 146(1), pages 313-324.
    86. Moradi, Siamak & Raith, Andrea & Ehrgott, Matthias, 2015. "A bi-objective column generation algorithm for the multi-commodity minimum cost flow problem," European Journal of Operational Research, Elsevier, vol. 244(2), pages 369-378.
    87. Psaraftis, Harilaos N., 2011. "A multi-commodity, capacitated pickup and delivery problem: The single and two-vehicle cases," European Journal of Operational Research, Elsevier, vol. 215(3), pages 572-580, December.
    88. Ilfat Ghamlouche & Teodor Gabriel Crainic & Michel Gendreau, 2003. "Cycle-Based Neighbourhoods for Fixed-Charge Capacitated Multicommodity Network Design," Operations Research, INFORMS, vol. 51(4), pages 655-667, August.
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