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Cyclic and non-cyclic crew rostering problems in public bus transit

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Abstract

The crew rostering problem arises in public transport bus companies, and addresses the task of assigning a given set of anonymous duties and some other activities, such as standbys and days off, to drivers or groups of drivers, without violating any complex labor union rules. In addition, the preferences of drivers are considered during the assignment. The plan generated for each driver/group of drivers is called a roster. Optimal rosters are characterized by maximum satisfaction of drivers and minimal operational costs. To generate a personalized roster for each driver/group of drivers, the problem is formulated as a multi-commodity network flow problem in this paper. In each network layer, a roster is generated for each driver or driver group. The network model is very flexible and can accommodate a variety of constraints. In addition, with a minor modification, the network can formulate the cyclic and non-cyclic crew rostering problems. To the best of our knowledge, this is the first publication which solves both problems with one model. The main goal of this paper is to develop a mixed-integer mathematical optimization network model for both problems with sequential and integrated approaches and to solve this model using commercial solvers. Both problems are usually solved with the sequential approach. Therefore, another contribution of this paper is comparing the sequential approach with the integrated one. Our experiments on real-world instances show that the integrated approach outperforms the sequential one in terms of solution quality.

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References

  • Bianco L, Bielli M, Mingozzi A, Ricciardelli S, Spadoni M (1992) A heuristic procedure for the crew rostering problem. Eur J Oper Res 58:272–283

    Article  Google Scholar 

  • Burke EK, Landa Silva JD (2005) The design of memetic algorithms for scheduling and timetabling problems, In: Krasnogor N, Hart WE, Smith JE (eds) Recent advances in memetic algorithms, studies in fuzziness and soft computing, vol 166. Springer, pp 289–312

  • Cappanera P, Gallo G (2004) A multicommodity flow approach to the crew rostering problem. Opera Res 52(4):583–596

    Article  Google Scholar 

  • Carraresi P, Gallo G (1984) A multilevel bottleneck assignment approach to the bus driver’s rostering problem. Eur J Oper Res 16(2):163–173

    Article  Google Scholar 

  • Catanas F, Paixão J (1995) A new approach for the crew rostering problem. In: Proceedings of Daduna, J, Branco I, Paixão J (eds) Computer-aided transit scheduling of lecture notes in economics and mathematical systems, vol 430. Springer, pp 267–277

  • Day PR, Ryan DM (1997) Flight attendant rostering for short-haul airline operations. Oper Res 45(5):649–661

    Article  Google Scholar 

  • De Pont G (2006) Personalized crew rostering at Netherlands railways, Master’s thesis, University of Tilburg (2006)

  • Dorigo M, Blum C (2005) Ant colony optimization theory: a survey. Theor Comput Sci 344(2):243–278

    Article  Google Scholar 

  • Emden-Weinert T, Kotas HG, Speer U (2000) Dissy-a driver scheduling system for public transport. Technical report, VSS GmbH and Bremer Strassenbahn AG Bremen, Germany

  • Ferreira J, Guimaraes R (1995) A travelling salesman model for the sequencing of duties in bus crew rotas. J Oper Res Soc 46(4):415–426

    Article  Google Scholar 

  • Freling R (1997) Models and techniques for integrating vehicle and crew scheduling, PhD thesis, Erasmus University of Rotterdam (1997)

  • Gurobi Optimization (2013) Gurobi Optimizer 5.5. Gurobi: http://www.gurobi.com/

  • Hanne T, Dornberger R, Frey L (2009) Multiobjective and preference-based decision support for rail crew rostering. In: Proceedings of 11th conference on congress on evolutionary computation, IEEE, pp 990–996 (2009)

  • Hartog A, Huisman D, Abbink EJW, Kroon LG (2009) Decision support for crew rostering at NS. Public Transp 1(2):121–133

    Article  Google Scholar 

  • IBM Corporation (2013) IBM ILOG CPLEX Optimizer 12.5. IBM: http://www-01.ibm.com/software/integration/optimization/cplex-optimizer/

  • Jachnik J (1981) Attendance and rostering systems, In: Wren A (ed) Computer scheduling of public transport, Elsevier pp 337–344

  • Kohl N, Karisch S (2004) Airline crew rostering: problem types, modeling, and optimization. Ann Oper Res 127:223–257

    Article  Google Scholar 

  • Kyngäs J, Nurmi K (2011) Days-off scheduling for a bus transportation company. Int J Innov Comput Appl 2(1):42–59

    Article  Google Scholar 

  • Lezaun M, Pérez G, de la Maza ES (2006) Crew rostering problem in a public tranport company. J Oper Res Soc 57:1173–1179

    Article  Google Scholar 

  • Lezaun M, Pérez G, de la Maza ES (2007) Rostering in a rail passenger carrier. J Sched 10(4–5):245–254

    Article  Google Scholar 

  • Lučić P, Teodorovic T (2007) Metaheuristics approach to the aircrew rostering problem. Ann Oper Res 155:311–338

    Article  Google Scholar 

  • Mesquita M, Moz M, Paias A, Paixão J, Pato M, Respício A (2011) A new model for the integrated vehicle-crew-rostering problem and a computational study on rosters. J Sched 14(3):319–334

    Article  Google Scholar 

  • Moz M, Pato MV (2007) A genetic algorithm approach to a nurse rerostering problem. Comput Oper Res 34(3):667–691

    Article  Google Scholar 

  • Moz M, Respicio A, Pato MV (2007) Bi-objective evolutionary heuristics for bus drivers rostering. University of Lisbon, Centro de Investigacao Operacional

    Google Scholar 

  • Nemhauser GL, Wolsey LA (1998) Integer and combinatorial optimization, vol 18, Wiley, New York

  • Nurmi K, Kyngäs J (2011) Driver rostering for a Finnish bus Transportation Company. Satakunta University of Applied Sciences, Finland

    Google Scholar 

  • Pedrosa D, Constantino M (2001) Days-off scheduling in public transport companies. In: Voss S, Daduna J (eds) Computer-aided scheduling of public transport. Lecture notes in economics and mathematical systems, vol 505. Springer, Heidelberg, pp 215–232

    Chapter  Google Scholar 

  • Prakash J, Sinha SB, Sahay SS (1984) Bus transportation crews planning by goal programming. Socio-Econ Plan Sci 18(3):207–210

    Article  Google Scholar 

  • Respício A, Moz M, Pato MV (2007) A memetic algorithm for a bi-objective bus driver rostering problem. University of Lisbon, Centro de Investigacao Operacional

    Google Scholar 

  • Sodhi MS, Norris S (2004) A fexible, fast, and optimal modeling approach applied to crew rostering at London underground. Ann Oper Res 127:259–281

    Article  Google Scholar 

  • Townsend W (1986) An application of the assignment model to bus crew rostering. J Math Manag 1:45–52

    Google Scholar 

  • Townsend W (1988) An approach to bus-crew roster design in London regional transport. J Oper Res Soc 6:543–550

    Article  Google Scholar 

  • Xie L, Naumann M, Suhl L (2012) A stochastic model for rota scheduling in public bus transport. In: Proceedings of 2nd stochastic modeling techniques and data analysis international conference, pp 785–792

  • Xie L, Kliewer N, Suhl L (2012) Integrated driver rostering problem in public bus transit. Procedia-Soc Behav Sci 54:656–665

    Article  Google Scholar 

  • Zuse Institute Berlin, (2013) MIPLIB 2010, ZIB: http://miplib.zib.de/miplib2010.php. Accessed on 07 Jan 2013

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Authors and Affiliations

  1. University of Paderborn, Paderborn, Germany

    Lin Xie & Leena Suhl

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  1. Lin Xie
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  2. Leena Suhl
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Correspondence to Lin Xie.

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Xie, L., Suhl, L. Cyclic and non-cyclic crew rostering problems in public bus transit. OR Spectrum 37, 99–136 (2015). https://doi.org/10.1007/s00291-014-0364-9

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