IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v46y2000i12p1630-1641.html
   My bibliography  Save this article

Optimal Models for Meal-Break and Start-Time Flexibility in Continuous Tour Scheduling

Author

Listed:
  • Michael J. Brusco

    (Information and Management Sciences Department, College of Business, Florida State University, Tallahassee, Florida 32306-1110)

  • Larry W. Jacobs

    (Operations Management and Information Systems Department, Northern Illinois University, DeKalb, Illinois 60115-2854)

Abstract

This paper presents a compact integer-programming model for large-scale continuous tour scheduling problems that incorporate meal-break window, start-time band, and start-time interval policies. For practical scheduling environments, generalized set-covering formulations (GSCFs) of such problems often contain hundreds of millions of integer decision variables, usually precluding identification of optimal solutions. As an alternative, we present an implicit integer-programming model that frequently has fewer than 1,500 variables and can be formulated and solved using PC-based hardware and software platforms. An empirical study using labor-requirement distributions for customer service representatives at a Motorola, Inc. call center was used to demonstrate the importance of having a model that can evaluate tradeoffs among the various scheduling policies.

Suggested Citation

  • Michael J. Brusco & Larry W. Jacobs, 2000. "Optimal Models for Meal-Break and Start-Time Flexibility in Continuous Tour Scheduling," Management Science, INFORMS, vol. 46(12), pages 1630-1641, December.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:12:p:1630-1641
    DOI: 10.1287/mnsc.46.12.1630.12074
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.46.12.1630.12074
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.46.12.1630.12074?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. John J. Bartholdi & James B. Orlin & H. Donald Ratliff, 1980. "Cyclic Scheduling via Integer Programs with Circular Ones," Operations Research, INFORMS, vol. 28(5), pages 1074-1085, October.
    2. R. N. Burns & M. W. Carter, 1985. "Work Force Size and Single Shift Schedules with Variable Demands," Management Science, INFORMS, vol. 31(5), pages 599-607, May.
    3. Michael J. Brusco & Larry W. Jacobs & Robert J. Bongiorno & Duane V. Lyons & Baoxing Tang, 1995. "Improving Personnel Scheduling at Airline Stations," Operations Research, INFORMS, vol. 43(5), pages 741-751, October.
    4. Philip E. Taylor & Stephen J. Huxley, 1989. "A Break from Tradition for the San Francisco Police: Patrol Officer Scheduling Using an Optimization-Based Decision Support System," Interfaces, INFORMS, vol. 19(1), pages 4-24, February.
    5. Adel Gaballa & Wayne Pearce, 1979. "Telephone Sales Manpower Planning at Qantas," Interfaces, INFORMS, vol. 9(3), pages 1-9, May.
    6. Pamela H. Vance & Cynthia Barnhart & Ellis L. Johnson & George L. Nemhauser, 1997. "Airline Crew Scheduling: A New Formulation and Decomposition Algorithm," Operations Research, INFORMS, vol. 45(2), pages 188-200, April.
    7. Oded Berman & Richard C. Larson & Edieal Pinker, 1997. "Scheduling Workforce and Workflow in a High Volume Factory," Management Science, INFORMS, vol. 43(2), pages 158-172, February.
    8. Jackie Hueter & William Swart, 1998. "An Integrated Labor-Management System for Taco Bell," Interfaces, INFORMS, vol. 28(1), pages 75-91, February.
    9. Ahmad I. Z. Jarrah & Jonathan F. Bard & Anura H. deSilva, 1994. "Solving Large-Scale Tour Scheduling Problems," Management Science, INFORMS, vol. 40(9), pages 1124-1144, September.
    10. Glenn W. Graves & Richard D. McBride & Ira Gershkoff & Diane Anderson & Deepa Mahidhara, 1993. "Flight Crew Scheduling," Management Science, INFORMS, vol. 39(6), pages 736-745, June.
    11. Karla L. Hoffman & Manfred Padberg, 1993. "Solving Airline Crew Scheduling Problems by Branch-and-Cut," Management Science, INFORMS, vol. 39(6), pages 657-682, June.
    12. Beaumont, Nicholas, 1997. "Scheduling staff using mixed integer programming," European Journal of Operational Research, Elsevier, vol. 98(3), pages 473-484, May.
    13. Michael J. Brusco & Larry W. Jacobs, 1998. "Personnel Tour Scheduling When Starting-Time Restrictions Are Present," Management Science, INFORMS, vol. 44(4), pages 534-547, April.
    14. James G. Morris & Michael J. Showalter, 1983. "Simple Approaches to Shift, Days-Off and Tour Scheduling Problems," Management Science, INFORMS, vol. 29(8), pages 942-950, August.
    15. Gary M. Thompson, 1997. "Assigning Telephone Operators to Shifts at New Brunswick Telephone Company," Interfaces, INFORMS, vol. 27(4), pages 1-11, August.
    16. Sol Schindler & Ted Semmel, 1993. "Station Staffing at Pan American World Airways," Interfaces, INFORMS, vol. 23(3), pages 91-98, June.
    17. Larry W. Jacobs & Michael J. Brusco, 1996. "Overlapping Start-Time Bands in Implicit Tour Scheduling," Management Science, INFORMS, vol. 42(9), pages 1247-1259, September.
    18. Paul R. Day & David M. Ryan, 1997. "Flight Attendant Rostering for Short-Haul Airline Operations," Operations Research, INFORMS, vol. 45(5), pages 649-661, October.
    19. Robert R. Love & James M. Hoey, 1990. "Management Science Improves Fast-Food Operations," Interfaces, INFORMS, vol. 20(2), pages 21-29, April.
    20. Ira Gershkoff, 1989. "Optimizing Flight Crew Schedules," Interfaces, INFORMS, vol. 19(4), pages 29-43, August.
    21. Gary M. Thompson, 1995. "Improved Implicit Optimal Modeling of the Labor Shift Scheduling Problem," Management Science, INFORMS, vol. 41(4), pages 595-607, April.
    22. Stephen E. Bechtold & Larry W. Jacobs, 1990. "Implicit Modeling of Flexible Break Assignments in Optimal Shift Scheduling," Management Science, INFORMS, vol. 36(11), pages 1339-1351, November.
    23. Bruce H. Andrews & Henry L. Parsons, 1989. "L. L. Bean Chooses a Telephone Agent Scheduling System," Interfaces, INFORMS, vol. 19(6), pages 1-9, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Arpan Rijal & Marco Bijvank & Asvin Goel & René de Koster, 2021. "Workforce Scheduling with Order-Picking Assignments in Distribution Facilities," Transportation Science, INFORMS, vol. 55(3), pages 725-746, May.
    2. Noah Gans & Ger Koole & Avishai Mandelbaum, 2003. "Telephone Call Centers: Tutorial, Review, and Research Prospects," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 79-141, September.
    3. Jens O. Brunner & Jonathan F. Bard & Jan M. Köhler, 2013. "Bounded flexibility in days‐on and days‐off scheduling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(8), pages 678-701, December.
    4. Hua Ni & Hernán Abeledo, 2007. "A branch-and-price approach for large-scale employee tour scheduling problems," Annals of Operations Research, Springer, vol. 155(1), pages 167-176, November.
    5. Idris Addou & François Soumis, 2007. "Bechtold-Jacobs generalized model for shift scheduling with extraordinary overlap," Annals of Operations Research, Springer, vol. 155(1), pages 177-205, November.
    6. Mark W. Isken & Osman T. Aydas, 2022. "A tactical multi-week implicit tour scheduling model with applications in healthcare," Health Care Management Science, Springer, vol. 25(4), pages 551-573, December.
    7. Banu Sungur & Cemal Özgüven & Yasemin Kariper, 2017. "Shift scheduling with break windows, ideal break periods, and ideal waiting times," Flexible Services and Manufacturing Journal, Springer, vol. 29(2), pages 203-222, June.
    8. Ferdinand Kiermaier & Markus Frey & Jonathan F. Bard, 2020. "The flexible break assignment problem for large tour scheduling problems with an application to airport ground handlers," Journal of Scheduling, Springer, vol. 23(2), pages 177-209, April.
    9. Robbins, Thomas R. & Harrison, Terry P., 2010. "A stochastic programming model for scheduling call centers with global Service Level Agreements," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1608-1619, December.
    10. Wan, Xiang & Sanders, Nadia R., 2017. "The negative impact of product variety: Forecast bias, inventory levels, and the role of vertical integration," International Journal of Production Economics, Elsevier, vol. 186(C), pages 123-131.
    11. Thompson, Gary M. & Pullman, Madeleine E., 2007. "Scheduling workforce relief breaks in advance versus in real-time," European Journal of Operational Research, Elsevier, vol. 181(1), pages 139-155, August.
    12. Chu, Sydney C.K., 2007. "Generating, scheduling and rostering of shift crew-duties: Applications at the Hong Kong International Airport," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1764-1778, March.
    13. María I. Restrepo & Bernard Gendron & Louis-Martin Rousseau, 2016. "Branch-and-Price for Personalized Multiactivity Tour Scheduling," INFORMS Journal on Computing, INFORMS, vol. 28(2), pages 334-350, May.
    14. Restrepo, María I. & Lozano, Leonardo & Medaglia, Andrés L., 2012. "Constrained network-based column generation for the multi-activity shift scheduling problem," International Journal of Production Economics, Elsevier, vol. 140(1), pages 466-472.
    15. Oyku Ahipasaoglu & Nesim Erkip & Oya Ekin Karasan, 2019. "The venue management problem: setting staffing levels, shifts and shift schedules at concession stands," Journal of Scheduling, Springer, vol. 22(1), pages 69-83, February.
    16. Hur, Daesik & Mabert, Vincent A. & Bretthauer, K.M.Kurt M., 2004. "Real-time schedule adjustment decisions: a case study," Omega, Elsevier, vol. 32(5), pages 333-344, October.
    17. Glass, Celia A. & Knight, Roger A., 2010. "The nurse rostering problem: A critical appraisal of the problem structure," European Journal of Operational Research, Elsevier, vol. 202(2), pages 379-389, April.
    18. Sanders, Nada R. & Graman, Gregory A., 2009. "Quantifying costs of forecast errors: A case study of the warehouse environment," Omega, Elsevier, vol. 37(1), pages 116-125, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michael J. Brusco & Larry W. Jacobs, 1998. "Personnel Tour Scheduling When Starting-Time Restrictions Are Present," Management Science, INFORMS, vol. 44(4), pages 534-547, April.
    2. Brusco, Michael J. & Jacobs, Larry W., 2001. "Starting-time decisions in labor tour scheduling: An experimental analysis and case study," European Journal of Operational Research, Elsevier, vol. 131(3), pages 459-475, June.
    3. Aykin, Turgut, 2000. "A comparative evaluation of modeling approaches to the labor shift scheduling problem," European Journal of Operational Research, Elsevier, vol. 125(2), pages 381-397, September.
    4. Peters, Emmanuel & de Matta, Renato & Boe, Warren, 2007. "Short-term work scheduling with job assignment flexibility for a multi-fleet transport system," European Journal of Operational Research, Elsevier, vol. 180(1), pages 82-98, July.
    5. Gary M. Thompson, 1997. "Labor staffing and scheduling models for controlling service levels," Naval Research Logistics (NRL), John Wiley & Sons, vol. 44(8), pages 719-740, December.
    6. M J Brusco & T R Johns, 2011. "An integrated approach to shift-starting time selection and tour-schedule construction," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(7), pages 1357-1364, July.
    7. Hua Ni & Hernán Abeledo, 2007. "A branch-and-price approach for large-scale employee tour scheduling problems," Annals of Operations Research, Springer, vol. 155(1), pages 167-176, November.
    8. Jonathan Bard & David Morton & Yong Wang, 2007. "Workforce planning at USPS mail processing and distribution centers using stochastic optimization," Annals of Operations Research, Springer, vol. 155(1), pages 51-78, November.
    9. Brusco, Michael J. & Johns, Tony R., 1996. "A sequential integer programming method for discontinuous labor tour scheduling," European Journal of Operational Research, Elsevier, vol. 95(3), pages 537-548, December.
    10. Giovanni Felici & Claudio Gentile, 2004. "A Polyhedral Approach for the Staff Rostering Problem," Management Science, INFORMS, vol. 50(3), pages 381-393, March.
    11. Mark W. Isken & Osman T. Aydas, 2022. "A tactical multi-week implicit tour scheduling model with applications in healthcare," Health Care Management Science, Springer, vol. 25(4), pages 551-573, December.
    12. Ernst, A. T. & Jiang, H. & Krishnamoorthy, M. & Sier, D., 2004. "Staff scheduling and rostering: A review of applications, methods and models," European Journal of Operational Research, Elsevier, vol. 153(1), pages 3-27, February.
    13. Oyku Ahipasaoglu & Nesim Erkip & Oya Ekin Karasan, 2019. "The venue management problem: setting staffing levels, shifts and shift schedules at concession stands," Journal of Scheduling, Springer, vol. 22(1), pages 69-83, February.
    14. Idris Addou & François Soumis, 2007. "Bechtold-Jacobs generalized model for shift scheduling with extraordinary overlap," Annals of Operations Research, Springer, vol. 155(1), pages 177-205, November.
    15. L Wan & J F Bard, 2007. "Weekly staff scheduling with workstation group restrictions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(8), pages 1030-1046, August.
    16. Easton, Fred F. & Mansour, Nashat, 1999. "A distributed genetic algorithm for deterministic and stochastic labor scheduling problems," European Journal of Operational Research, Elsevier, vol. 118(3), pages 505-523, November.
    17. Maenhout, Broos & Vanhoucke, Mario, 2010. "A hybrid scatter search heuristic for personalized crew rostering in the airline industry," European Journal of Operational Research, Elsevier, vol. 206(1), pages 155-167, October.
    18. Sriram, Chellappan & Haghani, Ali, 2003. "An optimization model for aircraft maintenance scheduling and re-assignment," Transportation Research Part A: Policy and Practice, Elsevier, vol. 37(1), pages 29-48, January.
    19. Haase, Knut, 1999. "Retail business staff scheduling under complex labor relations," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 511, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    20. Cynthia Barnhart & Amy Cohn, 2004. "Airline Schedule Planning: Accomplishments and Opportunities," Manufacturing & Service Operations Management, INFORMS, vol. 6(1), pages 3-22, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:inm:ormnsc:v:46:y:2000:i:12:p:1630-1641. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.