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Divide-and-price: a decomposition algorithm for solving large railway crew scheduling problems. (English) Zbl 1244.90120
Summary: The railway crew scheduling problem consists of generating crew duties to operate trains at minimal cost, while meeting all work regulations and operational requirements. Typically, a railway operation uses tens of thousands of train movements (trips) and requires thousands of crew members to be assigned to these trips. Despite the large size of the problem, crew schedules need to be generated in short time, because large parts of the train schedule are not finalized until few days before operation. We present a column generation based decomposition algorithm which achieves high-quality solutions at reasonable runtimes. Our divide-and-price algorithm decomposes the problem into overlapping regions which are optimized in parallel. A trip belonging to several regions is initially assigned to one region (“divide”). The corresponding dual information from optimization is then used as a bonus to offer the trip to other regions (“price”). Pricing and assignment of trips are dynamically updated in the course of the optimization. Tests of our algorithm on large-scale problem instances of a major European freight railway carrier yielded promising results.

90B70Theory of organizations, manpower planning
90C06Large-scale problems (mathematical programming)
90C27Combinatorial optimization
90B35Scheduling theory, deterministic
Full Text: DOI
[1] Abbink, E., van’t Wout, J., Huisman, D., 2007. Solving large scale crew scheduling problems by using iterative partitioning. In: Proceedings of the Seventh Workshop on Algorithmic Approaches for Transportation Modeling, Optimization and Systems, Vol. 7, pp. 96 -- 106.
[2] Alefragis, P.; Sanders, P.; Takkula, T.; Wedelin, D.: Parallel integer optimization for crew scheduling, Annals of operations research 99, 141-166 (2000) · Zbl 0990.90074 · doi:10.1023/A:1019293017474
[3] Barnhart, C.; Cohn, A. M.; Johnson, E. L.; Klabjan, D.; Nemhauser, G. L.; Vance, P. H.: Airline crew scheduling, Handbook of transportation science, 517-560 (2003)
[4] Barnhart, C.; Hatay, L.; Johnson, E. L.: Deadhead selection for the long-haul crew pairing problem, Operations research 43, 491-499 (1995) · Zbl 0840.90098 · doi:10.1287/opre.43.3.491
[5] Barnhart, C., Johnson, E. L., Anbil, R., Hatay, L., 1994. A column generation technique for the long-haul crew assignment problem. In: Ciriano, T., Leachman, R. (Eds.), Optimization in Industry, John Wiley & Sons, New York, Vol. II, pp. 7 -- 24. · Zbl 0862.90077
[6] Barnhart, C.; Johnson, E. L.; Nemhauser, G. L.; Savelsbergh, M. W. P.; Vance, P. H.: Branch-and-price: column generation for solving huge integer programs, Operations research 46, 316-329 (1998) · Zbl 0979.90092 · doi:10.1287/opre.46.3.316
[7] Ben Amor, H. M.; Desrosiers, J.; Frangioni, A.: On the choice of explicit stabilizing terms in column generation, Discrete applied mathematics 157, 1167-1184 (2009) · Zbl 1169.90395 · doi:10.1016/j.dam.2008.06.021
[8] Borndörfer, R., Grötschel, M., Löbel, A. 2001. Scheduling duties by adaptive column generation. Technical Report 01 -- 02 Konrad-Zuse Zentrum für Informationstechnik, Berlin.
[9] Bramel, J.; Simchi-Levi, D.: On the effectiveness of set covering formulations for the vehicle routing problem with time windows, Operations research 45, 295-301 (1997) · Zbl 0890.90054 · doi:10.1287/opre.45.2.295
[10] Caprara, A.; Fischetti, M.; Toth, P.: A heuristic method for the set covering problem, Operations research 47, 730-743 (1999) · Zbl 0976.90086 · doi:10.1287/opre.47.5.730
[11] Caprara, A.; Fischetti, M.; Toth, P.; Vigo, D.; Luigi, P.: Algorithms for railway crew management, Mathematical programming 79, 125-141 (1997) · Zbl 0887.90056 · doi:10.1007/BF02614314
[12] Caprara, A.; Kroon, L.; Monaci, M.; Peeters, M.; Toth, P.: Passenger railway optimization, Handbooks in operations research and management science, 129-187 (2007)
[13] Desaulniers, G.; Desrosiers, J.; Dumas, Y.; Marc, S.; Rioux, B.; Solomon, M. M.; Soumis, F.: Crew pairing at air France, European journal of operational research 97, 245-259 (1997) · Zbl 0944.90040 · doi:10.1016/S0377-2217(96)00195-6
[14] Desaulniers, G.; Desrosiers, J.; Lasry, A.; Solomon, M. M.: Crew pairing for a regional carrier, Lecture notes in economics and mathematical systems 471, 19-41 (1999) · Zbl 0935.90005
[15] Desrochers, M.; Soumis, F.: A generalized permanent labelling algorithm for the shortest path problem with time windows, Infor 26, 191-212 (1988) · Zbl 0652.90097
[16] Desrosiers, J.; Dumas, Y.; Solomon, M. M.; Soumis, F.: Time constraint routing and scheduling, Handbooks in operations research and management science, 35-139 (1995) · Zbl 0861.90052
[17] Desrosiers, J.; Lübbecke, M. E.: A primer in column generation, Column generation 3, 1-32 (2005) · Zbl 1246.90093
[18] Dumerle, O.; Villeneuve, D.; Desrosiers, J.; Hansen, P.: Stabilized column generation, Discrete mathematics 194, 229-237 (1999) · Zbl 0949.90063 · doi:10.1016/S0012-365X(98)00213-1
[19] Elhallaoui, I.; Desaulniers, G.; Metrane, A.; Soumis, F.: Bi-dynamic constraint aggregation and subproblem reduction, Computers & operations research 35, 1713-1724 (2008) · Zbl 1211.90118 · doi:10.1016/j.cor.2006.10.007
[20] Elhallaoui, I.; Metrane, A.; Soumis, F.; Desaulniers, G.: Multi-phase dynamic constraint aggregation for set partitioning type problems, Mathematical programming 123, 345-370 (2010) · Zbl 1189.90099 · doi:10.1007/s10107-008-0254-5
[21] Elhallaoui, I.; Villeneuve, D.; Soumis, F.; Desaulniers, G.: Dynamic aggregation of set-partitioning constraints in column generation, Operations research 53, 632-645 (2005) · Zbl 1165.90604 · doi:10.1287/opre.1050.0222
[22] Ernst, A. T.; Jiang, H.; Krishnamoorthy, M.; Sier, D.: Staff scheduling and rostering: A review of applications, methods and models, European journal of operational research 153, 3-27 (2004) · Zbl 1053.90034 · doi:10.1016/S0377-2217(03)00095-X
[23] Freling, R.; Lentink, R. M.; Wagelmans, A. P. M.: A decision support system for crew planning in passenger transportation using a flexible branch-and-price algorithm, Annals of operations research 127, 203-222 (2004) · Zbl 1087.90036 · doi:10.1023/B:ANOR.0000019090.39650.32
[24] Gamache, M.; Soumis, F.; Marquis, G.; Desrosiers, J.: A column generation approach for large-scale aircrew rostering problems, Operations research 47, 247-263 (1999) · Zbl 1041.90513 · doi:10.1287/opre.47.2.247
[25] Gopalakrishnan, B.; Johnson, E. L.: Airline crew scheduling: state-of-the-art, Annals of operations research 140, 305-337 (2005) · Zbl 1091.90019 · doi:10.1007/s10479-005-3975-3
[26] Huisman, D.; Wagelmans, A.: A solution approach for dynamic vehicle and crew scheduling, European journal of operational research 172, 453-471 (2006) · Zbl 1120.90020 · doi:10.1016/j.ejor.2004.10.009
[27] Irnich, S.; Desaulniers, G.: Shortest path problems with resource constraints, Column generation, 33-65 (2005) · Zbl 1130.90315
[28] Jütte, S.; Albers, M.; Thonemann, U. W.; Haase, K.: Optimizing railway crew scheduling at DB schenker, Interfaces 41, 109-122 (2011)
[29] Karp, R.M. 2010. Reducibility among combinatorial problems. In: Jünger, M., Liebling, T.M., Naddef, D., Nemhauser, G.L., Pulleyblank, W.R., Reinelt, G., Rinaldi, G., Wolsey, L.A. (Eds.), 50 Years of Integer Programming 1958 -- 2008, Berlin, Heidelberg, Springer, pp. 219 -- 241.
[30] Kwan, R. S. K.; Kwan, A.: Effective search space control for large and/or complex driver scheduling problems, Annals of operations research 155, 417-435 (2007) · Zbl 1145.90388 · doi:10.1007/s10479-007-0203-3
[31] Lan, G.; Depuy, G.; Whitehouse, G.: An effective and simple heuristic for the set covering problem, European journal of operational research 176, 1387-1403 (2007) · Zbl 1102.90048 · doi:10.1016/j.ejor.2005.09.028
[32] Lübbecke, M. E.: Dual variable based fathoming in dynamic programs for column generation, European journal of operational research 162, 122-125 (2005) · Zbl 1132.90376 · doi:10.1016/j.ejor.2003.05.006
[33] Lübbecke, M. E.; Desrosiers, J.: Selected topics in column generation, Operations research 53, 1007-1023 (2005) · Zbl 1165.90578 · doi:10.1287/opre.1050.0234
[34] Saddoune, M.; Desaulniers, G.; Elhallaoui, I.; Soumis, F.: Integrated airline crew scheduling: A bi-dynamic constraint aggregation method using neighborhoods, European journal of operational research 212, 445-454 (2011) · Zbl 1237.90127
[35] Topaloglu, H.; Powell, W. B.: A distributed decision-making structure for dynamic resource allocation using nonlinear functional approximations, Operations research 53, 281-297 (2005) · Zbl 1165.90549 · doi:10.1287/opre.1040.0166
[36] Vanderbeck, F.: On dantzig -- Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm, Operations research 48, 111-128 (2000) · Zbl 1106.90360 · doi:10.1287/opre.
[37] Wedelin, D.: An algorithm for large scale 0 -- 1 integer programming with application to airline crew scheduling, Annals of operations research 57, 283-301 (1995) · Zbl 0831.90087 · doi:10.1007/BF02099703