Keywords
Crew assignment
Ergonomics
Frimat Coefficient
Goal Programming
How to Cite
Abstract
Objective: This paper proposes a crew assignment model which considers an approach for balancing human fatigue. Based on a case study for scheduling cash-in-transit (CIT) routes, we suggest a workload assignment by considering a balanced effort according to each route requirement. Materials and Method: The worker effort was measured through heart rate measures and the Frimat Coefficient (FC). A mathematical model of goal programming is designed to minimize the variation between the effort made by each worker. The model developed presents results for a case study and instances designed to evaluate different problem sizes. Results: The case study results yield a low variability for the Crew Leaders and the Crew Members in the differences between the obtained FC and the goal. In the case of Drivers, higher variability in these values is evidenced. The computational performance for solving the problem demonstrates that the model can reach optimal solutions in reasonable times, for instances of 12 routes in 18 consecutive days or lower. Similarly, it showed extensive computational times, for example 25 routes in 12 consecutive days or longer. Conclusion: This study integrated human factors/ergonomics techniques with Operational Research techniques to jointly solve the problem of scheduling crews to CIT routes
[1] J. Heil, K. Hoffmann, and U. Buscher, “Railway crew scheduling: Models, methods and applications,” Eur J Oper Res, vol. 283, no. 2, pp. 405–425, Jun. 2020, doi: 10.1016/J.EJOR.2019.06.016.
[2] J. Zhou, X. Xu, J. Long, and J. Ding, “Integrated optimization approach to metro crew scheduling and rostering,” Transp Res Part C Emerg Technol, vol. 123, p. 102975, Feb. 2021, doi: 10.1016/J.TRC.2021.102975.
[3] M. Lucci, D. Severín, and P. Zabala, “A metaheuristic for crew scheduling in a pickup-and-delivery problem with time windows,” International Transactions in Operational Research, vol. 30, no. 2, pp. 970–1001, Mar. 2023, doi: https://doi.org/10.1111/itor.13096.
[4] H. Snijders and R. L. Saldanha, “Decision support for scheduling security crews at Netherlands Railways,” Public Transport, vol. 9, no. 1, pp. 193–215, 2017, doi: 10.1007/s12469-016-0142-y.
[5] M. S. Rasmussen, T. Justesen, A. Dohn, and J. Larsen, “The Home Care Crew Scheduling Problem: Preference-based visit clustering and temporal dependencies,” Eur J Oper Res, vol. 219, no. 3, pp. 598–610, Jun. 2012, doi: 10.1016/J.EJOR.2011.10.048.
[6] A. M. Horvat, B. Dudic, B. Radovanov, B. Melovic, O. Sedlak, and M. Davidekova, “Binary Programming Model for Rostering Ambulance Crew-Relevance for the Management and Business,” Mathematics, vol. 9, no. 1, 2021, doi: 10.3390/math9010064.
[7] A. Caprara, P. Toth, D. Vigo, and M. Fischetti, “Modeling and Solving the Crew Rostering Problem,” Oper Res, vol. 46, no. 6, pp. 820–830, Apr. 1998, [Online]. Available: http://www.jstor.org/stable/222936
[8] S. Ramos, F. Serranheira, and A. Sousa-Uva, “Perceived occupational hazards among cash-in-transit guards.,” Rev Bras Med Trab, vol. 16, no. 3, pp. 327–335, 2018, doi: 10.5327/Z1679443520180264.
[9] S. Mancini, M. Gansterer, and R. F. Hartl, “The collaborative consistent vehicle routing problem with workload balance,” Eur J Oper Res, 2021, doi: https://doi.org/10.1016/j.ejor.2020.12.064.
[10] L. Talarico, K. Sörensen, and J. Springael, “Metaheuristics for the risk-constrained cash-in-transit vehicle routing problem,” Eur J Oper Res, vol. 244, no. 2, pp. 457–470, 2015, doi: https://doi.org/10.1016/j.ejor.2015.01.040.
[11] A. Goel and T. Vidal, “Hours of Service Regulations in Road Freight Transport: An Optimization-Based International Assessment,” Transportation Science, vol. 48, no. 3, pp. 391–412, Apr. 2014, [Online]. Available: http://www.jstor.org/stable/43666693
[12] L. Talarico, K. Sörensen, and J. Springael, “A biobjective decision model to increase security and reduce travel costs in the cash-in-transit sector.,” Int. Trans. Oper. Res., vol. 24, no. 1–2, pp. 59–76, 2017, doi: 10.1111/itor.12214.
[13] S. F. Ghannadpour and F. Zandiyeh, “A new game-theoretical multi-objective evolutionary approach for cash-in-transit vehicle routing problem with time windows (A Real life Case),” Appl Soft Comput, vol. 93, p. 106378, 2020, doi: https://doi.org/10.1016/j.asoc.2020.106378.
[14] Z. E. Bowden and C. T. Ragsdale, “The truck driver scheduling problem with fatigue monitoring,” Decis Support Syst, vol. 110, pp. 20–31, 2018, doi: https://doi.org/10.1016/j.dss.2018.03.002.
[15] A. Kasirzadeh, M. Saddoune, and F. Soumis, “Airline crew scheduling: models, algorithms, and data sets,” EURO Journal on Transportation and Logistics, vol. 6, no. 2, pp. 111–137, 2017, doi: 10.1007/s13676-015-0080-x.
[16] A. T. Ernst, H. Jiang, M. Krishnamoorthy, B. Owens, and D. Sier, “An Annotated Bibliography of Personnel Scheduling and Rostering,” Ann Oper Res, vol. 127, no. 1, pp. 21–144, 2004, doi: 10.1023/B:ANOR.0000019087.46656.e2.
[17] A. Goel, C. Archetti, and M. Savelsbergh, “Truck driver scheduling in Australia,” Comput Oper Res, vol. 39, no. 5, pp. 1122–1132, 2012, doi: https://doi.org/10.1016/j.cor.2011.05.021.
[18] N. Clavijo-Buritica, M. Abushaega, A. Gonzalez, P. Amorim, and A. Polo, “Resilience-based Analysis of Road Closures in Colombia,” in Engineering Analytics, 1st Edition., L. Rabelo, E. Gutierrez-Franco, A. Sarmiento, and C. Mejía-Argueta, Eds., CRC Press, 2021, pp. 19–40.
[19] M. Wen, E. Krapper, J. Larsen, and T. K. Stidsen, “A Multilevel Variable Neighborhood Search Heuristic for a Practical Vehicle Routing and Driver Scheduling Problem,” Netw., vol. 58, no. 4, pp. 311–322, 2011, doi: 10.1002/net.20470.
[20] C. Archetti and M. Savelsbergh, “The Trip Scheduling Problem,” Transportation Science, vol. 43, no. 4, pp. 417–431, Apr. 2009, [Online]. Available: http://www.jstor.org/stable/25769466
[21] M. Drexl, J. Rieck, T. Sigl, and B. Press, “Simultaneous Vehicle and Crew Routing and Scheduling for Partial- and Full-Load Long-Distance Road Transport,” Business Research, vol. 6, no. 2, pp. 242–264, 2013, doi: 10.1007/BF03342751.
[22] A. Goel and S. Irnich, “An Exact Method for Vehicle Routing and Truck Driver Scheduling Problems,” Transportation Science, vol. 51, no. 2, pp. 737–754, 2017, doi: 10.1287/trsc.2016.0678.
[23] C. Ciancio, D. Laganà, R. Musmanno, and F. Santoro, “An integrated algorithm for shift scheduling problems for local public transport companies,” Omega (Westport), vol. 75, pp. 139–153, 2018, doi: https://doi.org/10.1016/j.omega.2017.02.007.
[24] H. Tikani, M. Setak, and E. Demir, “A risk-constrained time-dependent cash-in-transit routing problem in multigraph under uncertainty,” Eur J Oper Res, vol. 293, no. 2, pp. 703–730, 2021, doi: https://doi.org/10.1016/j.ejor.2020.12.020.
[25] L. A. Saavedra-Robinson and L. A. Quintana J, “Carga física y consumo de oxígeno en conductores de vehículos de carga y de pasajeros,” Arch Prev Riesgos Labor, vol. 9, no. 3, pp. 109–113, 2006, [Online]. Available: https://archivosdeprevencion.eu/index.php/aprl/numeros2019
[26] A. Frimat, P., Amphoux, M., Chamoux, “Interprétation et mesure de la fréquence cardiaque,” Revue de Medicine du Travail, vol. 15, no. 4, pp. 147–165, 1988.
[27] K. Peng and Y. Shen, “A variable iterated greedy algorithm based on grey relational analysis for crew scheduling,” Scientia Iranica, vol. 25, no. 2, pp. 831–840, 2018, doi: 10.24200/sci.2017.4434.
[28] R. Hanafi and E. Kozan, “A hybrid constructive heuristic and simulated annealing for railway crew scheduling,” Comput Ind Eng, vol. 70, no. 1, pp. 11–19, Apr. 2014, doi: 10.1016/J.CIE.2014.01.002.
[29] A. Tahir, G. Desaulniers, and I. El Hallaoui, “Integral column generation for the set partitioning problem,” EURO Journal on Transportation and Logistics, vol. 8, no. 5, pp. 713–744, Dec. 2019, doi: 10.1007/S13676-019-00145-6.
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