Skip to main content
Book cover

International Conference on Operations Research and Enterprise Systems

ICORES 2015: Operations Research and Enterprise Systems pp 191–211Cite as

Extended Decomposition for Mixed Integer Programming to Solve a Workforce Scheduling and Routing Problem

Part of the Communications in Computer and Information Science book series (CCIS,volume 577)

Abstract

We propose an approach based on mixed integer programming (MIP) with decomposition to solve a workforce scheduling and routing problem, in which a set of workers should be assigned to tasks that are distributed across different geographical locations. We present a mixed integer programming model that incorporates important real-world features of the problem such as defined geographical regions and flexibility in the workers’ availability. We decompose the problem based on geographical areas. The quality of the overall solution is affected by the ordering in which the sub-problems are tackled. Hence, we investigate different ordering strategies to solve the sub-problems. We also use a procedure to have additional workforce from neighbouring regions and this helps to improve results in some instances. We also developed a genetic algorithm to compare the results produced by the decomposition methods. Our experimental results show that although the decomposition method does not always outperform the genetic algorithm, it finds high quality solutions in practical computational times using an exact optimization method.

Keywords

  • Workforce scheduling
  • Routing problem
  • Mixed integer programming
  • Problem decomposition
  • Genetic algorithm

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-319-27680-9_12
  • Chapter length: 21 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   54.99
Price excludes VAT (USA)
  • ISBN: 978-3-319-27680-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   69.99
Price excludes VAT (USA)
Learn about institutional subscriptions
Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

References

  1. Bredström, D., Rönnqvist, M.: Combined vehicle routing and scheduling with temporal precedence and synchronization constraints. Eur. J. Oper. Res. 191(1), 19–31 (2008)

    CrossRef  MATH  Google Scholar 

  2. Akjiratikarl, C., Yenradee, P., Drake, P.R.: PSO-based algorithm for home care worker scheduling in the UK. Comput. Ind. Eng. 53(4), 559–583 (2007)

    CrossRef  Google Scholar 

  3. Angelis, V.D.: Planning home assistance for AIDS patients in the City of Rome, Italy. Interfaces 28, 75–83 (1998)

    CrossRef  Google Scholar 

  4. Barrera, D., Nubia, V., Ciro-Alberto, A.: A network-based approach to the multi-activity combined timetabling and crew scheduling problem: workforce scheduling for public health policy implementation. Comput. Ind. Eng. 63(4), 802–812 (2012)

    CrossRef  Google Scholar 

  5. Benders, J.: Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4(1), 238–252 (1962)

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Bertels, S., Torsten, F.: A hybrid setup for a hybrid scenario: combining heuristics for the home health care problem. Comput. Oper. Res. 33(10), 2866–2890 (2006)

    CrossRef  MATH  Google Scholar 

  7. Borsani, V., Andrea, M., Giacomo, B., Francesco, S.: A home care scheduling model for human resources. In: 2006 International Conference on Service Systems and Service Management pp. 449–454 (2006)

    Google Scholar 

  8. Bredstrom, D., Ronnqvist, M.: A branch and price algorithm for the combined vehicle routing and scheduling problem with synchronization constraints. NHH Department of Finance & Management Science Discussion Paper No. 2007/7, February 2007

    Google Scholar 

  9. Castillo-Salazar, J., Landa-Silva, D., Qu, R.: Workforce scheduling and routing problems: literature survey and computational study. Ann. Oper. Res. 78, 1–29 (2014)

    Google Scholar 

  10. Castro-Gutierrez, J., Landa-Silva, D., Moreno, P.J.: Nature of real-world multi-objective vehicle routing with evolutionary algorithms. In: 2011 IEEE International Conference onSystems, Man, and Cybernetics (SMC), pp. 257–264 (2011)

    Google Scholar 

  11. Cordeau, J.F., Stojkovic, G., Soumis, F., Desrosiers, J.: Benders decomposition for simultaneous aircraft routing and crew scheduling. Transp. Sci. 35(4), 375–388 (2001)

    CrossRef  MATH  Google Scholar 

  12. Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manage. Sci. (pre-1986) 6(1), 80–91 (1959)

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Dohn, A., Esben, K., Jens, C.: The manpower allocation problem with time windows and job-teaming constraints: a branch-and-price approach. Comput. Oper. Res. 36(4), 1145–1157 (2009)

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Eveborn, P., Ronnqvist, M., Einarsdottir, H., Eklund, M., Liden, K., Almroth, M.: Operations research improves quality and efficiency in home care. Interfaces 39(1), 18–34 (2009)

    CrossRef  Google Scholar 

  15. Feillet, D.: A tutorial on column generation and branch-and-price for vehicle routing problems. 4OR 8(4), 407–424 (2010). http://dx.doi.org/10.1007/s10288-010-0130-z

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Goldberg, D.E.: Genetic Algorithms. Pearson Education (2006). ISBN: 9788177588293

    Google Scholar 

  17. Hart, E., Sim, K., Urquhart, N.: A real-world employee scheduling and routing application. In: Proceedings of the 2014 Conference Companion on Genetic and Evolutionary Computation Companion, GECCO Comp 2014, pp. 1239–1242. ACM, New York (2014)

    Google Scholar 

  18. Husbands, P.: Genetic algorithms for scheduling. Intell. Simul. Behav. (AISB) Q. 89, 38–45 (1994)

    Google Scholar 

  19. Jeon, G., Leep, H.R., Shim, J.Y.: A vehicle routing problem solved by using a hybrid genetic algorithm. Comput. Ind. Eng. 53(4), 680–692 (2007)

    CrossRef  Google Scholar 

  20. Kergosien, Y., Lente, C., Billaut, J.C.: Home health care problem, an extended multiple travelling salesman problem. In: Proceedings of the 4th Multidisciplinary International Scheduling Conference: Theory and Applications (MISTA 2009), Dublin, Ireland, pp. 85–92 (2009)

    Google Scholar 

  21. Landa-Silva, D., Wang, Y., Donovan, P., Kendall, G., Way, S.: Hybrid heuristic for multi-carrier transportation plans. In: The 9th Metaheuristics International Conference (MIC 2011), pp. 221–229 (2011)

    Google Scholar 

  22. Liu, R., Xie, X., Garaix, T.: Hybridization of tabu search with feasible and infeasible local searches for periodic home health care logistics. Omega 47, 17–32 (2014)

    CrossRef  Google Scholar 

  23. Mankowska, D., Meisel, F., Bierwirth, C.: The home health care routing and scheduling problem with interdependent services. Health Care Manage. Sci. 17(1), 15–30 (2014)

    CrossRef  Google Scholar 

  24. Mercier, A., Cordeau, J.F., Soumis, F.: A computational study of Benders decomposition for the integrated aircraft routing and crew scheduling problem. Comput. Oper. Res. 32(6), 1451–1476 (2005)

    CrossRef  MathSciNet  Google Scholar 

  25. Mesghouni, K., Hammadi, S.: Evolutionary algorithms for job shop scheduling. Int. J. Appl. Math. Comput. Sci. 2004, 91–103 (2004)

    MathSciNet  Google Scholar 

  26. Perl, J., Daskin, M.S.: A warehouse location-routing problem. Transp. Res. Part B Methodol. 19(5), 381–396 (1985)

    CrossRef  Google Scholar 

  27. Pillac, V., Gueret, C., Medaglia, A.: On the dynamic technician routing and scheduling problem. In: Proceedings of the 5th International Workshop on Freight Transportation and Logistics (ODYSSEUS 2012), Mikonos, Greece, p. 194, May 2012

    Google Scholar 

  28. Potvin, J.Y.: Evolutionary algorithms for vehicle routing. Technical report 48, CIRRELT (2007)

    Google Scholar 

  29. Ralphs, T.K., Galati, M.V.: Decomposition Methods for Integer Programming. Wiley Encyclopedia of Operations Research and Management Science. Wiley, New York (2010)

    Google Scholar 

  30. Rasmussen, M.S., Justesen, T., Dohn, A., Larsen, J.: The home care crew scheduling problem: preference-based visit clustering and temporal dependencies. Eur. J. Oper. Res. 219(3), 598–610 (2012)

    CrossRef  MATH  Google Scholar 

  31. Reimann, M., Doerner, K., Hartl, R.F.: D-Ants: savings based ants divide and conquer the vehicle routing problem. Comput. Oper. Res. 31(4), 563–591 (2004)

    CrossRef  MATH  Google Scholar 

  32. Trautsamwieser, A., Hirsch, P.: Optimization of daily scheduling for home health care services. J. Appl. Oper. Res. 3, 124–136 (2011)

    Google Scholar 

  33. Vanderbeck, F.: On Dantzig-Wolfe decomposition in integer programming and ways to perform branching in a branch-and-price algorithm. Oper. Res. 48(1), 111 (2000)

    CrossRef  MathSciNet  MATH  Google Scholar 

  34. Vanderbeck, F., Wolsey, L.: Reformulation and decomposition of integer programs. In: Junger, M., et al. (eds.) 50 Years of Integer Programming 1958–2008, pp. 431–502. Springer, Heidelberg (2010)

    Google Scholar 

Download references

Acknowledgements

Special thanks to the Development and Promotion for Science and Technology talents project (DPST, Thailand) who providing partial financial support.

Author information

Authors and Affiliations

  1. ASAP Research Group, School of Computer Science, The University of Nottingham, Jubilee Campus, Wollaton Road, Nottingham, NG8 1BB, UK

    Wasakorn Laesanklang, Rodrigo Lankaites Pinheiro, Haneen Algethami & Dario Landa-Silva

Authors
  1. Wasakorn Laesanklang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rodrigo Lankaites Pinheiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Haneen Algethami
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Dario Landa-Silva
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wasakorn Laesanklang .

Editor information

Editors and Affiliations

  1. EPFL SB-DO, Lausanne, Switzerland

    Dominique de Werra

  2. MAS of INFORMS, Madison, Alabama, USA

    Greg H. Parlier

  3. Complutense University, Madrid, Spain

    Begoña Vitoriano

Rights and permissions

Reprints and Permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Laesanklang, W., Pinheiro, R.L., Algethami, H., Landa-Silva, D. (2015). Extended Decomposition for Mixed Integer Programming to Solve a Workforce Scheduling and Routing Problem. In: de Werra, D., Parlier, G., Vitoriano, B. (eds) Operations Research and Enterprise Systems. ICORES 2015. Communications in Computer and Information Science, vol 577. Springer, Cham. https://doi.org/10.1007/978-3-319-27680-9_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-27680-9_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27679-3

  • Online ISBN: 978-3-319-27680-9

  • eBook Packages: Computer ScienceComputer Science (R0)