Skip to main content
Log in

The task assignment problem for unrestricted movement between workstation groups

  • Published:
Journal of Scheduling Aims and scope Submit manuscript

Abstract

The purpose of this paper is to investigate the problem of assigning tasks to workers during their daily shifts. For a homogeneous workforce, a given set of workstation groups, and a corresponding demand for labor, the objective is to develop a disaggregated schedule for each worker that minimizes the weighted sum of transitions between workstation groups. In the formulation of the problem, each day is divided into 48 1/2-hour time periods and a multi-commodity network is constructed in which each worker corresponds to a unique commodity and each node represents a workstation group-time period combination. Lunch breaks and idle time are also included in the model.

Initial attempts to solve large instances with a commercial code indicated a need for a more practical approach. This led to the development of a reduced network representation in which idle periods are treated implicitly, and a sequential methodology in which the week is decomposed into 7 daily problems and each solved in turn. To gain more computational efficiency, a tabu search procedure was also developed.

All procedures were tested using data obtained from a U.S. Postal Service mail processing and distribution center. Depending on the labor category, anywhere from 3 to 28 workstation groups and up to 311 full-time and part-time workers had to be scheduled together. The results were mixed. While small problems could be solved to near-optimality with the integer programming approaches, tabu search was the best alternative for the very large instances. However, the excessive number of swaps needed to gain marginal improvements, undermined its effectiveness.Combining the two provided a good balance in most cases.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Aronson, J. E., “The Multi-Period Assignment Problem: A Multi Commodity Network Flow Model and Specialized Branch and Bound Algorithm,” European Journal Of Operational Research, 23, 367–381, (1986).

    Article  Google Scholar 

  • Aykin, T., “Optimal Shift Scheduling with Multiple Break Windows,” Management Science, 42(4), 591–602, (1996).

    Google Scholar 

  • Bard, J.F., “Selecting the Appropriate Input Data Set When Configuring a Permanent Workforce,” Computers & Industrial Engineering, 47(4), 371–389, (2004).

    Article  Google Scholar 

  • Bard, J.F., C. Binici, and A.H. deSilva, “Staff Scheduling at the United States Postal Service,” Computers & Operations Research, 30(5), 745–771, (2003).

    Article  Google Scholar 

  • Bechtold, S. E and L.W. Jacobs, “Implicit Modeling of Flexible Break Assignments in Optimal Shift Scheduling,” Management Science, 36(11), 1339–1351, (1990).

    Google Scholar 

  • Berman, O., R.C. Larson, and E. Pinker, “Scheduling Workforce and Workflow in a High Volume Factory,” Management Science, 43(2), 158–172, (1997).

    Google Scholar 

  • Brusco, M. J and L. W. Jacobs, “Personal Tour Scheduling When Starting Time Restrictions are Present,” Management Science, 44(4), 534–547, (1998).

    Google Scholar 

  • Burke, E. K., P. D. Causmaecker, G. Vanden Berghe and H. Van Landeghem, “The State of the Art of Nurse Rostering,” Journal of Scheduling, 7(6), 441–499, (2004).

    Article  Google Scholar 

  • Burns, R. N, and M. W. Carter, “Work Force Size and Single Shift Schedules with Variable Demands,” Management Science, 31(5), 599–607, (1985).

    Google Scholar 

  • Campbell, G. M. and M. Diaby, “Development and Evaluation of an Assignment Heuristic for Allocating Cross-Trained Workers,” European Journal of Operational Research, 138(1), 9–20, (2002).

    Article  Google Scholar 

  • Cheang, B., H. Li, A. Lim, and B. Rodrigues, “Nurse Rostering Problems—A Bibliographic Survey,” European Journal of Operational Research, 151, 447–460, (2003).

    Article  Google Scholar 

  • Ernst, A.T., H. Jiang, M. Krishnamoorthy, and D. Sier, “Staff Scheduling and Rostering: A Review of Applications, Methods and Models,” European Journal of Operational Research, 153(1), 3–17, (2004).

    Article  Google Scholar 

  • Dawid, H., J. Konig, and C. Strauss, “An Enhanced Rostering Model for Airline Crews,” Computers & Operations Research, 28, 671–688, (2001).

    Article  Google Scholar 

  • Franz, L.S and J.L. Miller, “Scheduling Medical Residents to Rotations: Solving the Large-Scale Multi-Period Staff Assignment Problem,” Operations Research, 41(2), 269–279, (1993).

    Google Scholar 

  • Garey, M.R and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman: New York, NY, 1979.

    Google Scholar 

  • Glover, F. and M. Laguna, Tabu Search, Kluwer Academic Publishers: Boston, MA, 1997.

    Google Scholar 

  • Hall, R.W. and D. Lotspeich, “Optimized Lane Assignment on an Automated Highway,” Transportation Research, Part C: Emerging Technology, 4(4), 211–229, (1996).

    Article  Google Scholar 

  • Jarrah, A.I.Z., J.F. Bard, and A.H. deSilva, “Solving Large-scale Tour Scheduling Problems,” Management Science, 40(9), 1124–1145, (1994).

    Google Scholar 

  • Lewis, L.H., A. Srinivasan and E. Subramanian, “Staffing and Allocation of Workers in an Administrative Office,” Management Science, 44(4), 548–570, (1998).

    Article  Google Scholar 

  • Malhotra, M.K., L.P. Ritzman, W.C. Benton, and G.K. Leong, “A Model for Scheduling Postal Distribution Employees,” European Journal of Operational Research, 58, 374–385, (1992).

    Article  Google Scholar 

  • Mukherjee, A.K. and K.C. Gilbert, “Lagrangian Heuristics for Instructor Scheduling in Executive Development Programmes,” Journal of Operations Research Society, 48(4), 373–382, (1997).

    Article  Google Scholar 

  • Nanda, R. and J. Browne, Introduction to Employee Scheduling, Van Nostrand Reinhold: New York, NY, 1992.

    Google Scholar 

  • Sherali, H.D. and J. C. Smith, “Improving Discrete Model Representations via Symmetry Considerations,” Management Science, 47(10), 1396–1407, (2001).

    Article  Google Scholar 

  • Showalter, M.J., L.J. Krajewski, and L.P. Ritzman, “Manpower Allocation in US Postal Facilities: A Heuristic Approach,” Computers & Operations Research, 4(4), 257–269, (1977).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Jonathan F. Bard.

Additional information

This work was supported in part by the National Science Foundation under grant # DMI-0218701.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bard, J.F., Wan, L. The task assignment problem for unrestricted movement between workstation groups. J Sched 9, 315–341 (2006). https://doi.org/10.1007/s10951-006-7038-7

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10951-006-7038-7

Keywords

Navigation