A dynamic programming based algorithm for the crew scheduling problem

Computers and Operations Research

Volumn 25, Issue 7-8, 1998, Pages 567-582

  Beasley, J E ^a   Cao, B ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Crew scheduling; Dynamic programming

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; CONSTRAINT THEORY; DYNAMIC PROGRAMMING; HUMAN ENGINEERING; LAGRANGE MULTIPLIERS; PERSONNEL; PERT; PROBLEM SOLVING; RANDOM NUMBER GENERATION; SCHEDULING;

CREW SCHEDULING; LAGRANGEAN-BASED PENALTY METHOD;

WORK-REST SCHEDULES;

EID: 0032118272     PISSN: 03050548     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0305-0548(98)00019-7     Document Type: Article

References (53)

1. Abramson, D., Dang, H. and Krishnamoorthy, M., A comparison of two methods for solving 0-1 integer programs using a general purpose simulated annealing algorithm. Annals of Operations Research, 1996, 63, 129-150.
2. Anbil, R., Barnhart, C., Hatay, L., Johnson, E. L. and Ramakrishnan, V. S., Crew-pairing optimization at American Airlines Decision Technologies. In Optimization in industry: mathematical programming and modeling techniques in practice, eds. T. A. Ciriani and R. C. Leachman. John Wiley, (1993).
3. Anbil, R., Gelman, E., Patty, B. and Tanga, R., Recent advances in crew-pairing optimization at American Airlines. Interfaces, 1991, 21(1), 62-74.
4. Baker, E. K., Bodin, L. D., Finnegan, W. F. and Ponder, R. J., Efficient heuristic solutions to an airline crew scheduling problem. AIIE Transactions, 1979, 11, 79-85.
5. Baker, E. K., Bodin, L. D. and Fisher, M., The development and implementation of a heuristic set covering based system for air crew scheduling. Transportation Policy Decision Making, 1985, 3, 95-110.
6. Baker, E. and Fisher, M., Computational results for very large air crew scheduling problems. OMEGA, 1981, 9, 613-618.
7. Ball, M., Bodin, L. and Dial, R., A matching based heuristic for scheduling mass transit crews and vehicles. Transportation Science, 1983, 17, 4-31.
8. Ball, M. and Roberts, A., A graph partitioning approach to airline crew scheduling. Transportation Science, 1985, 19, 107-126.
9. Beasley, J. E., OR-library: Distributing test problems by electronic mail. Journal of the Operational Research Society, 1990, 41, 1069-1072.
10. Beasley, J. E., Lagrangean relaxation. In Modern heuristic techniques for combinatorial problems, ed. C. R. Reeves, Blackwell Scientific Publications, Oxford, 1993.
11. Beasley, J. E. and Cao, B., A tree search algorithm for the crew scheduling problem. European Journal of Operational Research, 1996, 94, 517-526.
12. Bianco, L., Mingozzi, A., Ricciardelli, S. and Spadoni, M., New exact and heuristic algorithms for the crew scheduling problem. Lecture Notes in Control and Information Sciences, 1990, 143, 446-455.
13. Bodin, L. D. and Golden, B. L., Classification in vehicle routing and scheduling. Networks, 1981, 11, 97-108.
14. Bodin, L., Golden, B., Assad, A. and Ball, M., Routing and scheduling of vehicles and crews - the state of the art. Computers and Operations Research, 1983, 10, 63-211.
15. Cao, B., Algorithms for crew scheduling problems. Ph.D. thesis, Imperial College, London, 1992.
16. Carraresi, P. and Gallo, G., Network models for vehicle and crew scheduling. European Journal of Operational Research, 1984, 16, 139-151.
17. Carraresi, P., Gallo, G. and Rousseau, J.-M., Relaxation approaches to large scale bus driver scheduling problems. Transportation Research, 1982, 16B, 383-397.
18. Chan, T. J. and Yano, C. A., A multiplier adjustment approach for the set partitioning problem. Operations Research, 1992, 40, S40-S47.
19. Cheddad, H., Algorithms for crew scheduling problems. Ph.D. thesis, Imperial College, London, 1987.
20. N. Christofides, Graph theory: An algorithmic approach. Academic Press, London, 1975.
21. Christofides, N., Mingozzi, A. and Toth, P., Exact algorithms for the vehicle routing problem, based on spanning tree and shortest path relaxations. Mathematical Programming, 1981, 20, 255-282.
22. Christofides, N., Mingozzi, A. and Toth, P., State-space relaxation procedures for the computation of bounds to routing problems. Networks, 1981, 11, 145-164.
23. Chu, H. D., Gelman, E. and Johnson, E. L., Solving large scale crew scheduling problems. European Journal of Operational Research, 1997, 97, 260-268.
24. Chu, P. C., A genetic algorithm approach for combinatorial optimisation problems. Ph.D. thesis, Imperial College, London, 1997.
25. Chu, P. C. and Beasley, J. E., Constraint handling in genetic algorithms: the set partitioning problem. Journal of Heuristics, 1998, to appear.
26. Crainic, T. G. and Rousseau, J.-M., The column generation principle and the airline crew scheduling problem. INFOR, 1987, 25, 136-151.
27. Desrochers, M. and Soumis, F., A column generation approach to the urban transit crew scheduling problem. Transportation Science, 1989, 23, 1-13.
28. Falkner, J. C. and Ryan, D. M., A bus crew scheduling system using a set partitioning model. Asia-Pacific Journal of Operational Research, 1987, 4, 39-56.
29. Fischetti, M., Martello, S. and Toth, P., The fixed job schedule problem with spread-time constraints. Operations Research, 1987, 35, 849-858.
30. Fischetti, M., Martello, S. and Toth, P., The fixed job schedule problem with working time constraints. Operations Research, 1989, 37, 395-403.
31. Fisher, M. L., The lagrangian relaxation method for solving integer programming problems. Management Science, 1981, 27, 1-18.
32. Fisher, M. L., An applications oriented guide to Lagrangian relaxation. Interfaces, 1985, 15(2), 10-21.
33. Gershkoff, I., Optimizing flight crew schedules. Interfaces, 1989, 19(4), 29-43.
34. Gertsbakh, I. and Stern, H. I., Minimal resources for fixed and variable job schedules. Operations Research, 1978, 26, 68-85.
35. Graves, G. W., McBride, R. D., Gershkoff, I., Anderson, D. and Mahidhara, D., Flight crew scheduling. Management Science, 1993, 39, 736-745.
36. Gupta, U. I., Lee, D. T. and Leung, J. Y.-T., An optimal solution for the channel-assignment problem. IEEE Transactions on Computers, 1979, C-28, 807-810.
37. Hoffman, K. L. and Padberg, M., Solving airline crew scheduling problems by branch-and-cut. Management Science, 1993, 39, 657-682.
38. Houck, D. J., Picard, J. C., Queyranne, M. and Vemuganti, R. R., The travelling salesman problem as a constrained shortest path problem: Theory and computational experience. Opsearch, 1980, 17, 93-109.
39. Lavoie, S., Minoux, M. and Odier, E., A new approach for crew pairing problems by column generation with an application to air transportation. European Journal of Operational Research, 1988, 35, 45-58.
40. Levine, D., Application of a hybrid genetic algorithm to airline crew scheduling. Computers and Operations Research, 1996, 23, 547-558.
41. Marsten, R. E., Muller, M. R. and Killion, C. L., Crew planning at Flying Tiger: A successful application of integer programming. Management Science, 1979, 25, 1175-1183.
42. Marsten, R. E. and Shepardson, F., Exact solution of crew scheduling problems using the set partitioning model: Recent successful applications. Networks, 1981, 11, 165-177.
43. Martello, S. and Toth, P., A heuristic approach to the bus driver scheduling problem. European Journal of Operational Research, 1986, 24, 106-117.
44. Morgado, E. M. and Martins, J. P., Scheduling and managing crew in the Portuguese railways. Expert Systems with Applications, 1992, 5, 301-321.
45. Paias, A. and Paixao, J., State space relaxation for set covering problems related to bus driver scheduling. European Journal of Operational Research, 1993, 71, 303-316.
46. Rousseau, J.-M., Computer scheduling of public transport 2. North-Holland, Amsterdam, 1985.
47. Rubin, J., A technique for the solution of massive set covering problems with application to airline crew scheduling. Transportation Science, 1973, 7, 34-48.
48. Smith, B. M., IMPACS - a bus crew scheduling system using integer programming. Mathematical Programming, 1988, 42, 181-187.
49. Smith, B. M. and Wren, A., A bus crew scheduling system using a set covering formulation. Transportation Research Part A - General, 1988, 22A, 97-108.
50. de Sousa, J. F., A computer based interactive approach to crew scheduling. European Journal of Operational Research, 1991, 55, 382-393.
51. Wedelin, D., An algorithm for large scale 0-1 integer programming with application to airline crew scheduling. Annals of Operations Research, 1995, 57, 283-301.
52. Wedelin, D., The design of a 0-1 integer optimizer and its application in the Carmen system. European Journal of Operational Research, 1995, 87, 722-730.
53. Wren, A. (ed), Computer scheduling of public transport: urban passenger vehicle and crew scheduling. North-Holland, Amsterdam, 1981.