Skip to main content
Log in

Mixed Integer Programming to Schedule a Single-Shift Workforce under Annualized Hours

  • Published:
Annals of Operations Research Aims and scope Submit manuscript

Abstract

Nowadays flexibility is a strategic concept for firms. Indeed workload has to follow, as close as possible, the development of demand throughout the year. However, firms cannot engage and dismiss employees according to production requirements. Thus, workforce scheduling becomes a delicate task. In this paper, four mixed integer programming models are developed to solve the workforce schedule problem for a single-shift. The annualized hour scenario is considered with respect to a set of Swiss legal constrains. Furthermore, the minimal required workforce is guaranteed and it is assumed that each employee is able to perform each task within the team. All employees are full-time workers.

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

  • Azmat, C. and M. Widmer. (2004). “Single Shift Planning and Scheduling under Annualized Hours: A Simple Three Step Approach.” European Journal of Operational Research, Special Issue on Timetabling and Rostering 153(1), 148–175.

    Google Scholar 

  • Baker, K. (1976). “Workforce Allocation in Cyclical Scheduling Problems: A Survey.” Operational Research Quarterly 27, 115–167.

    Google Scholar 

  • Beaumont, N. (1997). “ Scheduling Staff Using Mixed Integer Programming.” European Journal of Operational Research 98, 473–484.

    Google Scholar 

  • Betchhol, S., M. Brusco, and M. Showalter. (1991). “A Comparative Evaluation of Labour Tour Scheduling Methods.” Decision Sciences 19, 353–373.

    Google Scholar 

  • Billionnet, A. (1999). “Integer Programming to Schedule a Hierarchical Workforce with Variable Demands.” European Journal of Operational Research 114, 105–114.

    Google Scholar 

  • Burns, R.N. and R. Namimhan. (1994). “10-Hours Multiple Shift Scheduling.” Working paper 94-36, Queen's School of Business.

  • Burns, R.N. and R. Narasimhan. (1995). “8-Hours Multiple Shift Scheduling of Hierarchical Workforce.” Working paper 95-02, Queen's School of Business.

  • Burns, R.N., R. Narasimhan, and L.D. Smith. (1995). “An Algorithm for Scheduling a Single-Category Workforce on Four-Day Work Weeks.” Working paper 95-11, Queen's School of Business.

  • Cezik, T., O. Günlük, and H. Luss. (2001). “An Integer Programming Model for the Weekly Tour Scheduling Problem.” Naval Research Logistics 48, 607–624.

    Google Scholar 

  • Chiffelle, X. (1995). La production au plus juste. Editions Universitaires Fribourg Suisse.

  • Corominas, A., A. Lusa, and R. Pastor. (2002). “Using MILP to Plan Annualized Working Hours.” Journal of Operational Research Society 53, 1101–1108.

    Google Scholar 

  • Dantzig, G. (1954). “A Comment on Edie's Traffic Delays at Toll Booths.” Operational Research 2, 339–341.

    Google Scholar 

  • De Coster, M. (1999). Sociologie du travail et gestion de resources humaines. De Boeck Université, Belgique.

    Google Scholar 

  • Emmons, H. and R.N. Burns. (1991). “Off-Day Scheduling with Hierarchical Worker Categories.” Operations Research 39(3), 484–495.

    Google Scholar 

  • Hung, R. (1991a). “Single-Shift Workforce Scheduling under a Compressed Workweek.” OMEGA 19(5), 494–497.

    Google Scholar 

  • Hung, R. (1991b). “A Cyclical Schedule of 10-Hour, Four-Day Workweeks.” Nursing Management 22(9), 30–33.

    Google Scholar 

  • Hung, R. (1993). “A Three-Day Workweek Multiple-Shift Scheduling Model.” Journal of the Operational Research Society 44(2), 141–146.

    Google Scholar 

  • Hung, R. (1994a). “Multiple-Shift Workforce Scheduling under the 3-4 Compressed Workweek with Different Weekday and Weekend Labor Requirements.” Management Science 40(2), 280–284.

    Google Scholar 

  • Hung, R. (1994b). “Managing Compressed Workweeks: A Comparison of 4-Day and 3-4 Workweeks.” International Journal of Technology Management 9(2), 261–266.

    Google Scholar 

  • Hung, R. (1994c). “A Multiple-ShiftWorkforce Scheduling Model under the 4-Day Workweek withWeekday and Weekend Labour Demands.” Journal of the Operational Research Society 45(9), 1088–1092.

    Google Scholar 

  • Hung, R. (1994d). “Single-Shift Off-Day Scheduling of a HierarchicalWorkforce with Variable Demands.” European Journal of Operational Research 78(1), 49–57.

    Google Scholar 

  • Hung, R. (1995). “Compressed Work Schedules in a Police Force: A Survey of Applications.” Optimum 26(2), 32–36.

    Google Scholar 

  • Hung, R. (1996). “An Annotated Bibliography of Compressed Workweeks.” International Journal of Manpower 17(6/7), 43–53.

    Google Scholar 

  • Hung, R. (1999a). “Scheduling aWorkforce under Annualized Hours.” International Journal of Production Research 37(11), 2419–2427.

    Google Scholar 

  • Hung, R. (1999b). “A Multiple-Shift Workforce Scheduling Model under Annualized Hours.” Naval Research Logistics 46, 726–736.

    Google Scholar 

  • Hung, R. and H. Emmons. (1993). “Multiple-ShiftWorkforce Scheduling under the 3-4 CompressedWorkweek with a Hierarchical Workforce.” IIE Transactions 25(5), 82–89.

    Google Scholar 

  • ILOG. (2004). www.ilog.com <http://www.ilog.com>

  • Jarrah, A., J. Bard, and A. de Silva. (1994). “Solving Large-Scale Tour Scheduling Problems.” Management Science 40, 1125–1144.

    Google Scholar 

  • Namimhan, R. (1995). “An Algorithm for Single Shift Scheduling of Hierarchical Workforce.” Working paper 95-04, Queen's School of Business.

  • Namimhan, R. (2000). “An Algorithm for Multiple Shift Scheduling of Hierarchical Workforce on Four Days or Three Days Workweeks.” INFOR 38(1), 14–32.

    Google Scholar 

  • Namimhan, R. and R.N. Burns. (1994). “10-Hours Single Shift Scheduling of Hierarchical Workforce.” Working paper 94-37, Queen's School of Business.

  • Runolfsson, A. and M. Goldschmid. (1997). Les nouvelles organisations du travail. Chaire de pédagogie et didactique, Ecole polytechnique fédérale de Lausanne, Lausanne.

    Google Scholar 

  • Stewart, B.D., D.B. Webster, S. Ahmad, and J.O. Matson. (1994). “Mathematical Models for Solving a Flexible Workforce.” International Journal of Production Economics 36, 243–254.

    Google Scholar 

  • Stredwick, J. (2000). An Introduction to Human Resource Management. Butterworth Heinemann, UK.

    Google Scholar 

  • VIRTUAL-OPTIMA. (2004). www.virtual-optima.com

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Azmat, C.S., Hürlimann, T. & Widmer, M. Mixed Integer Programming to Schedule a Single-Shift Workforce under Annualized Hours. Annals of Operations Research 128, 199–215 (2004). https://doi.org/10.1023/B:ANOR.0000019105.54898.a4

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:ANOR.0000019105.54898.a4

Navigation