Abstract
We consider a workforce scheduling problem which consists of determining optimal working shifts for cleaning personnel at a rail station. Trains arrive and depart according to a specified schedule and require a given amount of cleaning time from the personnel before their departure from the station. Working shifts must specify a sequence of trains to be cleaned by a worker together with corresponding cleaning times and are subject to contract regulations which impose both a minimum and a maximum duration of the shift. We model the problem as a mixed-integer program with a pseudo-polynomial number of variables and propose an exponentially sized reformulation obtained through Dantzig–Wolfe reformulation. The reformulation is strengthened by valid inequalities and used to compute lower bounds on the optimal cost. A heuristic algorithm based on column generation and variable fixing is then proposed and computationally evaluated on both a set of instances derived from real data and a larger set of randomly generated ones. The reported computational results show that the algorithm provides solutions very close to the optimal ones within 1 h of computing time.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Albers, S. (2010). Energy-efficient algorithms. Communications of the ACM, 53(5), 86–96.
Albers, S., Antoniadis, A., & Greiner, G. (2015). On multi-processor speed scaling with migration. Journal of Computer and System Sciences, 81(7), 1194–1209.
Arkin, E. M., Hassin, R., & Levin, A. (2006). Approximations for minimum and min–max vehicle routing problems. Journal of Algorithms, 59, 1–18.
Castillo-Salazar, A. J., Landa-Silva, D., & Qu, R. (2014). Workforce scheduling and routing problems: literature survey and computational study. Annals of Operations Research, 239(1), 39–67.
Chen, B., Potts, C. N., & Woeginger, G. J. (1998). A review of machine scheduling: Complexity, algorithms and approximabilit. In D.-Z. Du & P. M. Pardalos (Eds.), Handbook of combinatorial optimization (pp. 21–169). Norwell: Klower Academic Publisher.
Cirne, W., & Desai, N. (Eds.) (2015). Job scheduling strategies for parallel processing, volume 8828 of Lecture Notes in Computer Science. Springer International Publishing.
Correa, J., Marchetti-Spaccamela, A., Matuschke, J., Stougie, L., Svensson, O., Verdugo, V., et al. (2015). Strong lp formulations for scheduling splittable jobson unrelated machines. Mathematical Programming, B, 154, 305–328.
Dantzig, G. B., & Wolfe, P. (1960). Decomposition principle for linear programs. Operations Research, 8, 101–111.
Desaulniers, G. (2010). Branch-and-price-and-cut for the split-delivery vehicle routing problem with time windows. Operations Research, 58, 179–192.
Feitelson, D. G., & Rudolph, L. (1995). Parallel job scheduling: Issues and approaches. In D. G. Feitelson & L. Rudolph (Eds.), Job scheduling strategies for parallel processing, Lecture Notes in Computer Science, (pp. 1–18). Berlin Heidelberg: Springer.
Lim, A., Rodrigues, B., & Song, L. (2004). Manpower allocation with time windows. Journal of the Operational Research Society, 55, 1178–1186.
Nemhauser, G. L., & Wolsey, L. A. (1988). Integer and combinatorial optimization. New York: Wiley-Interscience.
Pinedo, M. L. (2012). Scheduling. Berlin: Springer-Verlag.
Potts, C. N., & Strusevich, V. A. (2009). Fifty years of scheduling: A survey of milestones. Journal of the Operational Research Society, 60, 541–568.
Roberti, R., Bartolini, E., & Mingozzi, A. (2015). The fixed charge transportation problem: An exact algorithm based on a new integer programming formulation. Management Science, 61, 1275–1291.
Serafini, P. (1996). Scheduling jobs on severalmachines with the job splitting property. Operations Research, 44, 617–628.
Shioura, K., Shakhlevich, N.V., & Strusevich, V.A. (2015). Energy saving computational models with speed scaling via submodular optimization. In Proceedings of Third International Conference on Green Computing, Technology and Innovation, ICGCTI2015, pp. 7–18, Wilmington, New Castle, DE 19801, USA. The Society of Digital Information and Wireless Communications.
Tikar, A., Jaybhaye, S. M., & Pathak, G. R. (2014). A survey on task scheduling for parallel workloads in the cloud computing system. International Journal of Innovative Research in Science, Engineering and Technology, 3, 16879–16885.
Tilk, C., & Irnich, S. (2014). Dynamic programming for the minimum tour duration problem. Technical report, Chair of Logistics Management, Johannes Gutenberg University.
Xing, W., & Zhang, J. (2000). Parallel machine scheduling with splitting jobs. Discrete Applied Mathematics, 103, 259–269.
Acknowledgements
We are indebted to two anonymous referees for detailed comments that improved the presentation of this paper. Manuel Iori acknowledges partial financial support by Capes (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior) under Grant PVE no. A007/2013.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Bartolini, E., Dell’Amico, M. & Iori, M. Scheduling cleaning activities on trains by minimizing idle times. J Sched 20, 493–506 (2017). https://doi.org/10.1007/s10951-017-0517-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10951-017-0517-1