Skip to main content
Article thumbnail
Location of Repository

Bus crew scheduling using mathematical programming

By Barbara Mary Smith


This thesis describes a bus crew scheduling system, IMPACS, which has been demonstrated to be successful for a wide variety of scheduling conditions, and is at present in regular use by three British bus companies including the largest, London Buses Ltd.\ud \ud The background to the bus crew scheduling problem 1S described and the existing literature on methods for solution is reviewed.\ud \ud In IMPACS, the crew scheduling problem is formulated as an integer linear programme using a formulation which is an extension of set covering; a very large set of possible duties is generated, from which the duties forming the schedule are selected in such a way as to minimise the total cost. The variables of the set covering problem correspond to the duties generated and the constraints to the pieces of work in the bus schedule.\ud \ud For realistic schedules, it is impossible to generate all legal duties, and there are often too many pieces of work to allow each one to give rise to a constraint. IMPACS contains several heuristic methods which reduce the set covering problem to a manageable size, while still allowing good quality schedules to be compiled.\ud \ud Techniques for speeding up the solution of the set covering problem have been investigated, and in particular a branching strategy which exploits features of the crew scheduling problem has been developed.\ud \u

Publisher: School of Computing (Leeds)
Year: 1986
OAI identifier:

Suggested articles


  1. (1985). A cC?mmuter r,,:il crew assignment/work rules model.
  2. (1981). A computer based crew scheduling syst~m using a mathematical programming approach.
  3. (1981). A computer based crew scheduling system using a mathematical programming approach and e:cperience of its use.
  4. (1979). A linear programming approach to crew ~cheduling.
  5. (1983). A matching based heuristic for scheduling mass transit vehicles and crews.
  6. (1966). A mathematical model for optimizing the assignment of man and machine in public transit "run-cutting".
  7. (1978). A new algorithm for very large crew pairing problems.
  8. A perspective on automated bus operator sCJ::eduling: o:,:e years' experience in Portland, Oregon.
  9. (1977). A practicable steepest-edge simplex algorithm.
  10. A tec.hni9-ue for the solution of massive set coverin ~~~~~~T9s73~ lth appllcatIons to airline crew scheduling.
  11. (1975). An examination of the run-cutting and scheduling (RUCUS) system - a case analysi~. Presen~ed at the Workshop on Automated Techniques for SchedulIng of VehIcle O~erators for Urban Public Transportation Services,
  12. (1981). An integer programming approach to ~~~~~~glI~g. tIhn_HColml pudtepr Sc:he~uling of Public Transport,
  13. (1975). An integer programming approach to the vehIcle schedullng problem. Opl Res.
  14. and Hal1ma A B A .. approach to scheduling the d . d n. .. problem decomposltion Computer Scheduling of P r~r-ersTan crews of mass transit systems.
  15. (1975). Automated formation of staff schedules and duty ro~ters. Pres.ented at the Workshop on Automated Techniques for ~chedul~ng of VehIcle Operators for Urban Public Transportation ServIces,
  16. (1985). Complementary approaches to crew scheduhng.
  17. (1981). Computational results for very large air crew scheduling problems.
  18. (1981). Computerized vehicle and driver scheduling for the Ham~urger Hochbahn Aktiengesellschaft.
  19. (1981). Crew scheduling by computer: A test on the possibility of designing duties for a certain bus line.
  20. (1985). CRU-SCHED - A computer based bus crew scheduling system using integer programming.
  21. (1981). Efficient heuristic algorithms for the weighted set covering problem.
  22. (1979). Efficient heuristic solutions to an airline crew scheduling problem.
  23. (1985). Enhancements to the HASTUS crew scheduling algorithm.
  24. (1985). Enhancements to the RUCUS2 crew schedullng system.
  25. (1981). Exact solution of crew scheduling problems using the set partitioning model: Recent successful applications.
  26. (1981). Experimentation with a computerized system for scheduling mass transit vehicles and crews.
  27. Fortran subroutines for handling sparse linear programming Bases.
  28. (1985). HASTUS - An interactive system for buses and crew scheduling.
  29. (1981). Hastus I: A mathematical programming approach to the bus driver scheduling problem.
  30. (1985). II: A review of system capabilities.
  31. (1985). IMPACS - A hybrid interactive approach to computerIzed crew scheduling.
  32. (1972). Integer Programming.
  33. (1977). Mathematical and heuristic approaches to road transport scheduling.
  34. (1975). Overview of the RUCUS package driver run cutting program - RUNS. Presented at the Workshop on Automated Techniques for Scheduling of Vehicle Operators for Urban Public Transportation Services,
  35. (1975). Pivot selection methods of the Devex LP code.
  36. (1975). Preparing duty rosters by computer. Presented at the Workshop on Automated Techniques for Scheduling of Vehicle Operators for Urban Public Transportation Services,
  37. Relaxation approaches to large scale bus driver scheduling problems.
  38. (1984). Report on Queens Road Saturday duties for GMT,
  39. (1985). Results and experience of calibrating HASTUS-MACRO for work rule cost estimation at the Southern California Rapid Transit District, 10s Angeles.
  40. (1983). Routing and scheduling of v( ehlc~es . and crews: The state of the art.
  41. run cutting in N;rth Am . s. i'
  42. (1975). Scheduling by computer - A report on a pilot study undertaken for London Transport. Report ULORU-15,
  43. (1980). Set covering algorithms using cutting planes. heurlshcs and subgradient optimization: a computational study.
  44. (1971). Set covering and involutory bases.
  45. (1946). t ,) JS'~' TI imeta?le and duty schedule compilation (Road passenger ranspor . ir saac Pitman
  46. (1972). The advancement of computerized assignment of transit operators to vehicles through heuristic programming techniques.
  47. The airline crew scheduhng problem: A survey.
  48. (1977). The efficient solution of large-scale integer programming problems.
  49. (1966). The scheduling of buses and crews by computer. Paper presented to the Public Transport Association annual conference,
  50. The use c:f di~ital co.mputers in th.e economic scheduling for both man and machIne In publIc transportation.
  51. (1984). Towards the fully computerised schedules office. Presented at the 15th Annual Seminar on Public Transport Operations Research,
  52. (1981). Two approaches to computer crew scheduling.
  53. (1985). Two complementary bus scheduling programs.
  54. (1980). ZIP - a zero-one integer prog~amming package for scheduling.

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.