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

  • Wasakorn Laesanklang
  • Rodrigo Lankaites Pinheiro
  • Haneen Algethami
  • Dario Landa-Silva
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 577)


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.


Workforce scheduling Routing problem Mixed integer programming Problem decomposition Genetic algorithm 



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


  1. 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)CrossRefzbMATHGoogle Scholar
  2. 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)CrossRefGoogle Scholar
  3. 3.
    Angelis, V.D.: Planning home assistance for AIDS patients in the City of Rome, Italy. Interfaces 28, 75–83 (1998)CrossRefGoogle Scholar
  4. 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)CrossRefGoogle Scholar
  5. 5.
    Benders, J.: Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4(1), 238–252 (1962)CrossRefMathSciNetzbMATHGoogle Scholar
  6. 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)CrossRefzbMATHGoogle Scholar
  7. 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. 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 2007Google Scholar
  9. 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. 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. 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)CrossRefzbMATHGoogle Scholar
  12. 12.
    Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manage. Sci. (pre-1986) 6(1), 80–91 (1959)CrossRefMathSciNetzbMATHGoogle Scholar
  13. 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)CrossRefMathSciNetzbMATHGoogle Scholar
  14. 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)CrossRefGoogle Scholar
  15. 15.
    Feillet, D.: A tutorial on column generation and branch-and-price for vehicle routing problems. 4OR 8(4), 407–424 (2010). CrossRefMathSciNetzbMATHGoogle Scholar
  16. 16.
    Goldberg, D.E.: Genetic Algorithms. Pearson Education (2006). ISBN: 9788177588293Google Scholar
  17. 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. 18.
    Husbands, P.: Genetic algorithms for scheduling. Intell. Simul. Behav. (AISB) Q. 89, 38–45 (1994)Google Scholar
  19. 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)CrossRefGoogle Scholar
  20. 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. 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. 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)CrossRefGoogle Scholar
  23. 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)CrossRefGoogle Scholar
  24. 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)CrossRefMathSciNetGoogle Scholar
  25. 25.
    Mesghouni, K., Hammadi, S.: Evolutionary algorithms for job shop scheduling. Int. J. Appl. Math. Comput. Sci. 2004, 91–103 (2004)MathSciNetGoogle Scholar
  26. 26.
    Perl, J., Daskin, M.S.: A warehouse location-routing problem. Transp. Res. Part B Methodol. 19(5), 381–396 (1985)CrossRefGoogle Scholar
  27. 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 2012Google Scholar
  28. 28.
    Potvin, J.Y.: Evolutionary algorithms for vehicle routing. Technical report 48, CIRRELT (2007)Google Scholar
  29. 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. 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)CrossRefzbMATHGoogle Scholar
  31. 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)CrossRefzbMATHGoogle Scholar
  32. 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. 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)CrossRefMathSciNetzbMATHGoogle Scholar
  34. 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

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Wasakorn Laesanklang
    • 1
  • Rodrigo Lankaites Pinheiro
    • 1
  • Haneen Algethami
    • 1
  • Dario Landa-Silva
    • 1
  1. 1.ASAP Research Group, School of Computer ScienceThe University of NottinghamNottinghamUK

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