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The break scheduling problem: complexity results and practical algorithms

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Abstract

Break scheduling problems arise in working areas where breaks are indispensable, e.g., in air traffic control, supervision, or assembly lines. We regard such a problem from the area of supervision personnel. The objective is to find a break assignment for an existing shiftplan such that various constraints reflecting legal demands or ergonomic criteria are satisfied and such that staffing requirement violations are minimised. We prove the NP-completeness of this problem when all possible break patterns for each shift are given explicitly as part of the input. To solve our problem we propose two variations of a memetic algorithm. We define genetic operators, a local search based on three neighbourhoods, and a penalty system that helps to avoid local optima. Parameters influencing the algorithms are experimentally evaluated and assessed with statistical methods. We compare our algorithms, each with the best parameter setting according to the evaluation, with the state-of-the-art algorithm on a set of 30 real-life and randomly generated instances that are publicly available. One of our algorithms returns improved results on 28 out of the 30 benchmark instances. To the best of our knowledge, our improved results for the real-life instances constitute new upper bounds for this problem

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References

  1. Aykin T (1996) Optimal shift scheduling with multiple break windows. Manag Sci 42:591–603

    Article  MATH  Google Scholar 

  2. Aykin T (2000) A comparative evaluation of modelling approaches to the labour shift scheduling problem. Eur J Oper Res 125:381–397

    Article  MATH  Google Scholar 

  3. Bechtold S, Jacobs L (1990) Implicit modelling of flexible break assignments in optimal shift scheduling. Manag Sci 36(11):1339–1351

    Article  Google Scholar 

  4. Beer A, Gaertner J, Musliu N, Schafhauser W, Slany W (2008) An iterated local search algorithm for a real-life break scheduling problem. In: Proceedings of Matheuristics 2008, 2nd international workshop on model based Metaheuristics, Bertinoro

  5. Beerm A, Gaertner J, Musliu N, Schafhauser W, Slany W (2008) Scheduling breaks in shift plans for call centers. In: Proceedings of the 7th international conference on the practice and theory of automated timetabling, Montreal

  6. Beer A, Gärtner J, Musliu N, Schafhauser W, Slany W (2010) An AI-based break-scheduling system for supervisory personnel. IEEE Intell Syst 25(2):60–73

    Article  Google Scholar 

  7. Burke EK, Cowling PI, Causmaecker PD, Berghe GV (2001) A memetic approach to the nurse rostering problem. Appl Intell 15(3):199–214

    Google Scholar 

  8. Côté M-C, Gendron B, Quimper C-G, Rousseau L-M (2011) Formal languages for integer programming modeling of shift scheduling problems. Constraints 16(1):55–76

    Article  Google Scholar 

  9. Côté M-C, Gendron B, Rousseau L-M (2011) Grammar-based integer programming models for multiactivity shift scheduling. Manag Sci 57(1):151–163

    Article  MATH  Google Scholar 

  10. Cotta C, Fernández AJ (2007) Memetic algorithms in planning, scheduling, and timetabling. Evolutionary scheduling. Springer, Berlin

    Google Scholar 

  11. Dantzig GB (1954) A comment on Eddie’s traffic delays at toll booths. Oper Res 2:339–341

    MathSciNet  Google Scholar 

  12. Dechter R, Meiri I, Pearl J (1991) Temporal constraint networks. Artif Intell 49:61–95

    Article  MATH  MathSciNet  Google Scholar 

  13. Di Gaspero L, Gärtner J, Kortsarz G, Musliu N, Schaerf A, Slany W (2007) The minimum shift design problem. Ann Oper Res 155:79–105

    Article  MATH  MathSciNet  Google Scholar 

  14. Garey M, Johnson D (1979) Computers and intractability: a guide to the theory of NP-completeness. W.H. Freeman, New York

    MATH  Google Scholar 

  15. Gärtner J, Musliu N, Slany W (2004) A heuristic based system for generation of shifts with breaks. In: Proceedings of the 24th SGAI international conference on innovative techniques and applications of artificial intelligence, Cambridge

  16. Gaspero LD, Gärtner J, Musliu N, Schaerf A, Schafhauser W, Slany W (2010) A hybrid LS-CP solver for the shifts and breaks design problem. In: Proceedings of the 7th international workshop on hybrid metaheuristics. Springer, Berlin/Heidelberg, pp 46–61

  17. Glover F, Laguna M (1999) Tabu search. Handbook of combinatorial optimization, 3rd edn. Kluwer Academic Publishers, London

    Google Scholar 

  18. Goldberg DE, Deb K (1990) A comparative analysis of selection schemes used in genetic algorithms. In: Foundations of genetic algorithms (FOGA). Morgan Kaufmann, San Franciso, pp 69–93

  19. Montgomery D (2005) Design and analysis of experiments. Wiley, New York

    MATH  Google Scholar 

  20. Moscato P (1989) On evolution, search, optimization, gas and martial arts: towards memetic algorithms. In: Technical report of Caltech concurrent computer programming report, vol 826. California Institute of Technology, Pasadena

  21. Musliu N, Schaerf A, Slany W (2004) Local search for shift design. Eur J Oper Res 153(1):51–64

    Article  MATH  MathSciNet  Google Scholar 

  22. Musliu N, Schafhauser W, Widl M (2009) A memetic algorithm for a break scheduling problem. In: 8th Metaheuristic international conference, Hamburg

  23. Papadimitriou CH, Steiglitz K (1982) Combinatorial optimization: algorithms and complexity. Prentice Hall, London

  24. Quimper C-G, Rousseau L-M (2010) A large neighbourhood search approach to the multi-activity shift scheduling problem. J Heuristics 16(3):373–391

    Google Scholar 

  25. Rekik M, Cordeau J, Soumis F (2010) Implicit shift scheduling with multiple breaks and work stretch duration restrictions. J Sched 13:49–75

    Google Scholar 

  26. Schafhauser W (2010) TEMPLE—a domain specific language for modeling and solving real-life staff scheduling problems. PhD thesis, Vienna University of Technology, Wien

  27. Softnet (2008) http://www.dbai.tuwien.ac.at/proj/SoftNet/Supervision/Benchmarks/.Accessed 14 March 2014

  28. Tellier P, White G (2006) Generating personnel schedules in an industrial setting using a tabu search algorithm. In: Burke EK, Rudova H (eds) The 5th international conference on the practice and theory of automated timetabling, pp 293–302

  29. Thompson G (1995) Improved implicit modeling of the labor shift scheduling problem. Manag Sci 41(4):595–607

    Article  MATH  Google Scholar 

  30. Widl M (2010) Memetic algorithms for break scheduling. Master’s thesis, Vienna University of Technology, Vienna http://www.kr.tuwien.ac.at/staff/widl/publications/Masterthesis.pdf. Accessed 14 March 2014

  31. Widl M, Musliu N (2010) An improved memetic algorithm for break scheduling. In: Hybrid Metaheuristics, vol 6373 of LNCS, pp 133–147

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Acknowledgments

This work was supported by the Austrian Science Fund (FWF) under grants P24814-N23 and S11409-N23, and by the Vienna Science and Technology Fund (WWTF) under grant ICT10-018.

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Authors and Affiliations

  1. Knowledge-based Systems Group, Vienna University of Technology, Favoritenstrasse 9, 1040 , Vienna, Austria

    Magdalena Widl

  2. Databases and Artificial Intelligence Group, Vienna University of Technology, Favoritenstrasse 9, 1040, Vienna, Austria

    Nysret Musliu

Authors
  1. Magdalena Widl
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  2. Nysret Musliu
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Correspondence to Magdalena Widl.

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Widl, M., Musliu, N. The break scheduling problem: complexity results and practical algorithms. Memetic Comp. 6, 97–112 (2014). https://doi.org/10.1007/s12293-014-0131-0

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  • DOI: https://doi.org/10.1007/s12293-014-0131-0

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