Advertisement

A New Model for the Mass Transit Crew Scheduling Problem

  • Mohamadreza Banihashemi
  • Ali Haghani
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 505)

Abstract

A new formulation for the “Mass Transit Crew Scheduling” (MTCS) problem is presented. The proposed model is a “task-based” multi-commodity network flow problem in which the variables are defined in conjunction with the tasks and the tasks compatibilities.

Based on the union contracts in the United States the calculations of the task compatibility costs usually cannot be finalized until we establish the workdays and solve the problem. In our approach, we start from an initial model, the relaxed MTCS problem, in which we consider minimum costs for these compatibilities. Then we propose to go through an iterative procedure for establishing the workdays and adjusting the compatibility costs if necessary. This would be accomplished by generating new variables corresponding to the established feasible workdays and a “soft” constraint associated with each new variable.

The relaxed model also lacks the constraints that prevent the construction of the workdays that are illegal based on the union agreements or other rules. For each infeasible workday we could establish a “hard” constraint to be added to the relaxed problem. An exact solution procedure for small instances of this problem could be a constraint and variable generation approach in which the workday variables as well as the soft and the hard constraints would be added to the problem in an iterative procedure.

Keywords

Soft Constraint Hard Constraint Crew Schedule Spread Time Column Generation Approach 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. Banihashemi, M. (1998). Multiple Depot Transit Scheduling Problem Considering Time Restriction Constraints. Ph.D. thesis, Civil Engineering Department, University of Maryland, College Park, USA.Google Scholar
  2. Beasley, J.E. and E.B. Cao (1996). A tree search algorithm for the crew scheduling problem. European Journal of Operational Research 94, 517–526.CrossRefGoogle Scholar
  3. Beasley, J.E. and E.B. Cao (1998). A dynamic programming based algorithm for the crew scheduling problem. Computers & Operations Research 25, 567–582.CrossRefGoogle Scholar
  4. Carraresi, P., M. Nonato, and L. Girardi (1995). Network models, Lagrangean relaxation and subgradients bundle approach in crew scheduling problems. In J.R. Daduna, I. Branco, and J.M.P. Paixão (Eds.), Computer-Aided Transit Scheduling, Lecture Notes in Economics and Mathematical Systems, 430, Springer, Berlin, 188–212.Google Scholar
  5. Clement, R. and A. Wren (1995). Greedy genetic algorithms, optimizing mutations and bus driver scheduling. In J.R. Daduna, I. Branco, and J.M.P. Paixão (Eds.), Computer-Aided Transit Scheduling, Lecture Notes in Economics and Mathematical Systems, 430, Springer, Berlin, 213–235.Google Scholar
  6. Desrochers, M. and F. Soumis (1989). A column generation approach to the urban transit crew scheduling problem. Transportation Science 23, 1–13.CrossRefGoogle Scholar
  7. Fores, S., L. Proll, and A. Wren (1999). An improved ILP system for driver scheduling. In N.H.M. Wilson (Ed.), Computer-Aided Transit Scheduling, Lecture Notes in Economics and Mathematical Systems, 471, Springer, Berlin, 43–61.Google Scholar
  8. Kwan, A.S.K., R.S.K. Kwan, and A. Wren (1999). Driver scheduling using genetic algorithms with embedded combinatorial traits. In N.H.M. Wilson (Ed.), Computer-Aided Transit Scheduling, Lecture Notes in Economics and Mathematical Systems, 471, Springer, Berlin, 81–102.CrossRefGoogle Scholar
  9. Mingozzi, A., M. A. Boschetti, S. Ricciardelli, and L. Bianco (1999). A set partitioning approach to the crew scheduling problem. Operations Research 47, 873–888.CrossRefGoogle Scholar
  10. Mitra, G. and K. Darby-Dowman (1985). CRU-SCHED: A computer based bus crew scheduling system using integer programming. In J.M. Rousseau (Ed.), Computer Scheduling of Public Transport 2, North-Holland, Amsterdam, 223–232.Google Scholar
  11. Paias, A. and J.P. Paixão (1993). State space relaxation for set-covering problems related to bus driver scheduling. European Journal of Operational Research 71, 303–316.CrossRefGoogle Scholar
  12. Paixão, J.P. (1984). Algorithms for Large Scale Set-covering Problems. Ph.D. thesis, Department of Management Science, Imperial College, London.Google Scholar
  13. Paixão, J.P. (1990). Transit crew scheduling on a personal workstation (MS/DOS). In H. Bradley (Ed.), Operational Research90, Pergamon Press, Oxford, 421–432.Google Scholar
  14. Smith, B.M. and A. Wren (1988). A bus crew scheduling system using a set covering formulation. Transportation Research A 22, 97–108.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Mohamadreza Banihashemi
    • 1
  • Ali Haghani
    • 2
  1. 1.A/E Group, Inc., Geometric Design LabTurner-Fairbank Highway Research Center, FHWAMcLeanUSA
  2. 2.Department of Civil and Environmental EngineeringUniversity of Maryland College ParkUSA

Personalised recommendations