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.
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References
Bredström, D., Rönnqvist, M.: Combined vehicle routing and scheduling with temporal precedence and synchronization constraints. Eur. J. Oper. Res. 191(1), 19–31 (2008)
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)
Angelis, V.D.: Planning home assistance for AIDS patients in the City of Rome, Italy. Interfaces 28, 75–83 (1998)
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)
Benders, J.: Partitioning procedures for solving mixed-variables programming problems. Numer. Math. 4(1), 238–252 (1962)
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)
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)
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
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)
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)
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)
Dantzig, G.B., Ramser, J.H.: The truck dispatching problem. Manage. Sci. (pre-1986) 6(1), 80–91 (1959)
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)
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)
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
Goldberg, D.E.: Genetic Algorithms. Pearson Education (2006). ISBN: 9788177588293
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)
Husbands, P.: Genetic algorithms for scheduling. Intell. Simul. Behav. (AISB) Q. 89, 38–45 (1994)
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)
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)
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)
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)
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)
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)
Mesghouni, K., Hammadi, S.: Evolutionary algorithms for job shop scheduling. Int. J. Appl. Math. Comput. Sci. 2004, 91–103 (2004)
Perl, J., Daskin, M.S.: A warehouse location-routing problem. Transp. Res. Part B Methodol. 19(5), 381–396 (1985)
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
Potvin, J.Y.: Evolutionary algorithms for vehicle routing. Technical report 48, CIRRELT (2007)
Ralphs, T.K., Galati, M.V.: Decomposition Methods for Integer Programming. Wiley Encyclopedia of Operations Research and Management Science. Wiley, New York (2010)
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)
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)
Trautsamwieser, A., Hirsch, P.: Optimization of daily scheduling for home health care services. J. Appl. Oper. Res. 3, 124–136 (2011)
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)
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)
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Special thanks to the Development and Promotion for Science and Technology talents project (DPST, Thailand) who providing partial financial support.
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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
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