Journal of the Korean Operations Research and Management Science Society (한국경영과학회지)

The Korean Operations Research and Management Science Society (한국경영과학회)
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An Integer Programming Approach to the Subway Daily Crew Scheduling Problem

지하철 일간승무계획문제의 정수계획해법

  • 변종익 (한국과학기술원 산업공학과) ;
  • 이경식 (한국과학기술원 산업공학과) ;
  • 박성수 (한국과학기술원 산업공학과) ;
  • 강성열 (홍익대학교 경영정보학과)
  • Published : 2002.12.01
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Abstract

This paper considers subway crew scheduling problem. Crew scheduling is concerned with finding a minimum number of assignments of crews to a given timetable satisfying various restrictions. Traditionally, crew scheduling problem has been formulated as a set covering or set partitioning problem possessing exponentially many variables, but even the LP relaxation of the problem is hard to solve due to the exponential number of variables. In this paper. we propose two basic techniques that solve the subway crew scheduling problem in a reasonable time, though the optimality of the solution is not guaranteed. We develop an algorithm that solves the column-generation problem in polynomial time. In addition, the integrality of the solution is accomplished by variable-fixing technique. Computational result for a real instance is reported.

Keywords

References

  1. IBM systems J. v.31 A global optimization approach to crew scheduling Anbil, R.;E.R. Tanga;E.L. Johnson
  2. Network flows : Theory, Algorithms, and Applications Ahuja, R.K.;T.L. Magnanti;J.B. Orlin
  3. Transportation Science v.17 A matching based heuristic for scheduling mass transit crews and vehicles Ball, M.;L. Bodin;R. Dial https://doi.org/10.1287/trsc.17.1.4
  4. Transportations Science v.19 A graph partitioning approach to airline crew scheduling Ball, M.;A. Roberts https://doi.org/10.1287/trsc.19.2.107
  5. Operations Research v.46 Branch-and-Price : Column gengeration for solving huge integer programs Barnhart, C.;E.L. Johnson;G.L. Nemhauser;M.W.P. Savelsbergh;P.H. Vance https://doi.org/10.1287/opre.46.3.316
  6. European Journal of Operational Research v.94 A tree search algorithm for the crew scheduling problem Beasley, J.E.;B. Cao https://doi.org/10.1016/0377-2217(95)00093-3
  7. European Journal of Operational Research v.58 A heuristic procedure for the crew rostering problem Bianco, L.;M. Bielli;A, Mingozzi;S. Ricciardelli;M. Spadoin https://doi.org/10.1016/0377-2217(92)90213-S
  8. Mathemational Programming v.79 Algorithms for railway crew managements Caprara, A.;M. Fischetti; P. Toth;D. Vigo
  9. INFOR v.25 The column generation principle and the airline crew scheduling problem Crainic, T.G.;J.M. Rousseau
  10. Transportation Science v.23 A column generation approcah to the urban transit crew scheduling problem Desrochers, M.;F. Soumis https://doi.org/10.1287/trsc.23.1.1
  11. Asia-Pacific Journal of Operational Research v.4 A bus crew scheduling system using a set partitioning model Falkner, J.C.;D.M. Ryan
  12. Interfaces v.5 Optimizing flight crew schedules Gershkoff, I.
  13. Management Science v.39 Solving airline crew scheduling problem by branch-and-cut Hoffman, K.;M. Padberg https://doi.org/10.1287/mnsc.39.6.657
  14. European Journal of Operational Research v.35 A new approach for crew pairing problems by column gengeration with an application to air transportation Lavoie, S.;M. Minoux;E. Odier https://doi.org/10.1016/0377-2217(88)90377-3
  15. Networks v.11 Exact solution of crew scheduling problems using the set partitioning model : recent successful applications Marsten, F.;Shepardson https://doi.org/10.1002/net.3230110208
  16. European Journal of Operational Research v.24 A heruristic approach to the bus driver scheduling problem Martello, S.;P. Toth https://doi.org/10.1016/0377-2217(86)90016-0
  17. Computers & Operations Research v.23 A binary-rounding heuristic for multi-period variable-task-duration assignment problems Miller, J.L.;Franz, L.S. https://doi.org/10.1016/0305-0548(95)00073-9
  18. Operations Research v.47 A set partitioning approcah to the crew scheduling problem Mingozzi, A.;M.A. Boschetti;S. Ricciardelli;L. Bianco https://doi.org/10.1287/opre.47.6.873
  19. European Journal of Operational Research v.71 State space relaxation for set covering problems related tobus driver schedule Paias, A.;J. Paixao https://doi.org/10.1016/0377-2217(93)90056-S
  20. European Journal of Operational Research v.39 A structural lagrangean relaxation for two-duty period bus driver scheduling problems Paixao, J.;M. Pato https://doi.org/10.1016/0377-2217(89)90194-X
  21. Management Science v.42 An interger programing approach to the bandwidth packing problem Park, K.;S. Kang;S. Park https://doi.org/10.1287/mnsc.42.9.1277
  22. Operations Research v.45 A Branch-and-Price algorithm for the generalized assignment problem Savelsbergh, M. https://doi.org/10.1287/opre.45.6.831
  23. Operations Research v.45 Airline crew scheduling : A new formulation and decomposition algorithm Vance, P.H.;C. Branhart;E.L. Johnson;G.L. Nemhauser https://doi.org/10.1287/opre.45.2.188