This paper addresses a task assignment problem encountered by check-in counter personnel at airports. The problem consists of assigning multiskilled agents to a sequence of tasks in check-in counters. Because each task’s ending time is fixed to comply with the flight schedule, its processing time depends on the arrival of the assigned agents. We propose a mixed-integer program and a branch-and-price algorithm to solve this problem. We exploit the problem structure to efficiently formulate the pricing problems and improve computation time. Using real-world data from a German ground-handling agency, we conduct numerical studies to evaluate the performance of the proposed solutions.
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Barnhart, C., Johnson, E. L., Nemhauser, G. L., Savelsbergh, M. W., & Vance, P. H. (1998). Branch-and-price: Column generation for solving huge integer programs. Operations Research, 46(3), 316–329.
Bode, C., & Irnich, S. (2014). The shortest-path problem with resource constraints with (k,2)-loop elimination and its application to the capacitated arc-routing problem. European Journal of Operational Research, 238(2), 415–426.
Campbell, G. M. (1999). Cross-utilization of workers whose capabilities differ. Management Science, 45(5), 722–732.
Campbell, G. M., & Diaby, M. (2002). Development and evaluation of an assignment heuristic for allocating cross-trained workers. European Journal of Operational Research, 138(1), 9–20.
Caseau, Y., & Koppstein, P. (1992). A cooperative-architecture expert system for solving large time/travel assignment problems. In Database and expert systems applications (pp. 197–202). Vienna: Springer.
Choi, E., & Tcha, D.-W. (2007). A column generation approach to the heterogeneous fleet vehicle routing problem. Computers and Operations Research, 34(7), 2080–2095.
Cordeau, J.-F., Desaulniers, G., Desrosiers, J., Solomon, M. M., & Soumis, F. (2001). The VRP with time windows. In P. Toth & D. Vigo (Eds.), The vehicle routing problem (pp. 157–193). Philadelphia: Society for Industrial and Applied Mathematics.
Cordeau, J.-F., Laporte, G., Pasin, F., & Ropke, S. (2010). Scheduling technicians and tasks in a telecommunications company. Journal of Scheduling, 13(4), 393–409.
Corominas, A., Olivella, J., & Pastor, R. (2010). A model for the assignment of a set of tasks when work performance depends on experience of all tasks involved. International Journal of Production Economics, 126(2), 335–340.
Corominas, A., Pastor, R., & Rodríguez, E. (2006). Rotational allocation of tasks to multifunctional workers in a service industry. International Journal of Production Economics, 103(1), 3–9.
Dantzig, G. (1954). A comment on edie’s “Traffic Delays at Toll Booths”. Journal of the Operations Research Society of America, 2(3), 339–341.
Desrochers, M., Desrosiers, J., & Solomon, M. M. (1992). A new optimization algorithm for the vehicle routing problem with time windows. Operations Research, 40(2), 342–354.
Dohn, A., Kolind, E., & Clausen, J. (2009). The manpower allocation problem with time windows and job-teaming constraints: A branch-and-price approach. Computers and Operations Research, 36(4), 1145–1157.
Dror, M. (1994). Note on the complexity of the shortest path models for column generation in VRPTW. Operations Research, 42(5), 977–978.
Edison, E., & Shima, T. (2011). Integrated task assignment and path optimization for cooperating uninhabited aerial vehicles using genetic algorithms. Computers and Operations Research, 38(1), 340–356.
Eveborn, P., Flisberg, P., & Rönnqvist, M. (2006). LAPS CARE—an operational system for staff planning of home care. European Journal of Operational Research, 171(3), 962–976.
Feillet, D., Dejax, P., Gendreau, M., & Gueguen, C. (2004). An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems. Networks, 44(3), 216–229.
Ferland, J. A., & Michelon, P. (1988). The vehicle scheduling problem with multiple vehicle types. Journal of the Operational Research Society, 39(6), 577–583.
Gleave, S. D. (2010). Possible revision of Directive 96/67/EC on access to the groundhandling market at Community airports. London.
Irnich, S., Desaulniers, G., & Solomon, M. M. (2005). Shortest path problems with resource constraints. Column Generation, 6730, 33–65.
Jiang, J., Ng, K. M., Poh, K. L., & Teo, K. M. (2014). Vehicle routing problem with a heterogeneous fleet and time windows. Expert Systems with Applications, 41(8), 3748–3760.
Kovacs, A. A., Parragh, S. N., Doerner, K. F., & Hartl, R. F. (2012). Adaptive large neighborhood search for service technician routing and scheduling problems. Journal of Scheduling, 15(5), 579–600.
Krishnamoorthy, M., Ernst, A. T., & Baatar, D. (2012). Algorithms for large scale shift minimisation personnel task scheduling problems. European Journal of Operational Research, 219(1), 34–48.
Li, Y., Lim, A., & Rodrigues, B. (2005). Manpower allocation with time windows and job-teaming constraints. Naval Research Logistics (NRL), 52(4), 302–311.
Liang, T. T., & Buclatin, B. B. (1988). Improving the utilization of training resources through optimal personnel assignment in the U.S. Navy. European Journal of Operational Research, 33(2), 183–190.
Liberatore, F., Righini, G., & Salani, M. (2010). A column generation algorithm for the vehicle routing problem with soft time windows. 4OR, 9(1), 49–82.
Lieder, A., Moeke, D., Koole, G., & Stolletz, R. (2015). Task scheduling in long-term care facilities: A client-centered approach. Operations Research for Health Care, 6, 11–17.
Liu, C., Yang, N., Li, W., Lian, J., Evans, S., & Yin, Y. (2013). Training and assignment of multi-skilled workers for implementing seru production systems. The International Journal of Advanced Manufacturing Technology, 69(5–8), 937–959.
Loucks, J. S., & Jacobs, F. R. (1991). Tour scheduling and task assignment of a heterogeneous work force: A heuristic approach. Decision Sciences, 22(4), 719–738.
Lübbecke, M. E., & Desrosiers, J. (2005). Selected topics in column generation. Operations Research, 53(6), 1007–1023.
Miller, J. L., & Franz, L. S. (1996). A binary-rounding heuristic for multi-period variable-task-duration assignment problems. Computers and Operations Research, 23(8), 819–828.
Olivella, J., Corominas, A., & Pastor, R. (2013). Task assignment considering cross-training goals and due dates. International Journal of Production Research, 51(3), 952–962.
Pessoa, A., Uchoa, E., & Poggi de Aragão, M. (2009). A robust branch-cut-and-price algorithm for the heterogeneous fleet vehicle routing problem. Networks, 54(4), 167–177.
Smet, P., Wauters, T., Mihaylov, M., & Berghe, G. V. (2014). The shift minimisation personnel task scheduling problem: A new hybrid approach and computational insights. Omega, 46, 64–73.
Solomon, M. M. (1987). Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research, 35(2), 254–265.
Solomon, M. M., & Desrosiers, J. (1988). Survey paper—time window constrained routing and scheduling problems. Transportation Science, 22(1), 1–13.
Stolletz, R. (2010). Operational workforce planning for check-in counters at airports. Transportation Research Part E: Logistics and Transportation Review, 46(3), 414–425.
Stolletz, R., & Zamorano, E. (2014). A rolling planning horizon heuristic for scheduling agents with different qualifications. Transportation Research Part E: Logistics and Transportation Review, 68, 39–52.
Tsang, E., & Voudouris, C. (1997). Fast local search and guided local search and their application to British Telecom’s workforce scheduling problem. Operations Research Letters, 20(3), 119–127.
Yang, R. (1996). Solving a workforce management problem with constraint programming. In The 2nd international conference on the practical application of constraint technology (pp. 373–387). The Practical Application Company Ltd.
Zamorano, E., & Stolletz, R. (2017). Branch-and-price approaches for the multiperiod technician routing and scheduling problem. European Journal of Operational Research, 257(1), 55–68.
This research was supported by the Erich-Becker-Stiftung, a foundation of Fraport AG. The authors are grateful to the anonymous referees for helpful and constructive suggestions.
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Zamorano, E., Becker, A. & Stolletz, R. Task assignment with start time-dependent processing times for personnel at check-in counters. J Sched 21, 93–109 (2018). https://doi.org/10.1007/s10951-017-0523-3