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Models for Radiation Therapy Patient Scheduling

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11802))

Abstract

In Europe, around half of all patients diagnosed with cancer are treated with radiation therapy. To reduce waiting times, optimizing the use of linear accelerators for treatment is crucial. This paper introduces an Integer Programming (IP) and two Constraint Programming (CP) models for the non-block radiotherapy patient scheduling problem. Patients are scheduled considering priority, pattern, duration, and start day of their treatment. The models include expected future patient arrivals. Treatment time of the day is included in the models as time windows which enable more realistic objectives and constraints. The models are thoroughly evaluated for multiple different scenarios, altering: planning day, machine availability, arrival rates, patient backlog, and the number of time windows in a day. The results demonstrate that the CP models find feasible solutions earlier, while the IP model reaches optimality considerably faster.

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References

  1. Aggoun, A., Beldiceanu, N.: Extending chip in order to solve complex scheduling and placement problems. Math. Comput. Modell. 17(7), 57–73 (1993)

    Article  Google Scholar 

  2. Baatar, D., Boland, N., Brand, S., Stuckey, P.J.: CP and IP approaches to cancer radiotherapy delivery optimization. Constraints 16, 173–194 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Barták, R., Salido, M., Rossi, F.: New trends in constraint satisfaction, planning, and scheduling: a survey. Knowl. Eng. Rev. 25, 249–279 (2010)

    Article  Google Scholar 

  4. Boussemart, F., Hemery, F., Lecoutre, C., Sais, L.: Boosting systematic search by weighting constraints. In: de Mántaras, R.L., Saitta, L. (eds.) Sixteenth European Conference on Artificial Intelligence, pp. 146–150. IOS Press, Valencia (2004)

    Google Scholar 

  5. Burke, E.K., De Causmaecker, P., Berghe, G.V., Van Landeghem, H.: The state of the art of nurse rostering. J. Sched. 7(6), 441–499 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Burke, E.K., Leite-Rocha, P., Petrovic, S.: An integer linear programming model for the radiotherapy treatment scheduling problem. arXiv e-prints arXiv:1103.3391 (2011)

  7. Cayirli, T., Veral, E.: Outpatient scheduling in health care: a review of literature. Prod. Oper. Manage. 12(4), 519–549 (2009)

    Article  Google Scholar 

  8. Chen, Z., King, W., Pearcey, R., Kerba, M., Mackillop, W.J.: The relationship between waiting time for radiotherapy and clinical outcomes: a systematic review of the literature. Radiother. Oncol. 87(1), 3–16 (2008)

    Article  Google Scholar 

  9. Conforti, D., Guerriero, F., Guido, R.: Optimization models for radiotherapy patient scheduling. 4OR 6(3), 263–278 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Conforti, D., Guerriero, F., Guido, R.: Non-block scheduling with priority for radiotherapy treatments. Eur. J. Oper. Res. 201(1), 289–296 (2010)

    Article  MATH  Google Scholar 

  11. Ehrgott, M., Holder, A.: Operations research methods for optimization in radiation oncology. J. Radiat. Oncol. Inform. 6(1), 1–41 (2014)

    Google Scholar 

  12. Fortin, A., Bairati, I., Albert, M., Moore, L., Allard, J., Couture, C.: Effect of treatment delay on outcome of patients with early-stage head-and-neck carcinoma receiving radical radiotherapy. Int. J. Radiat. Oncol. Biol. Phys. 52(4), 929–936 (2002)

    Article  Google Scholar 

  13. Gocgun, Y.: Simulation-based approximate policy iteration for dynamic patient scheduling for radiation therapy. Health Care Manage. Sci. 21(3), 317–325 (2018)

    Article  Google Scholar 

  14. Gomez, D.R., et al.: Time to treatment as a quality metric in lung cancer: staging studies, time to treatment, and patient survival. Radiother. Oncol. 115(2), 257–263 (2015)

    Article  Google Scholar 

  15. Hahn-Goldberg, S., Beck, J.C., Carter, M.W., Trudeau, M., Sousa, P., Beattie, K.: Solving the chemotherapy outpatient scheduling problem with constraint programming. J. Appl. Oper. Res. 6(3), 135–144 (2014)

    Google Scholar 

  16. Halperin, E.C., Wazer, D.E., Brady, L.W., Perez, C.A.: Perez and Brady’s Principles and Practice of Radiation Oncology, 6th edn. Lippincott Williams and Wilkins, Philadelphia (2013)

    Google Scholar 

  17. Jacquemin, Y., Marcon, E., Pommier, P.: A pattern-based approach of radiotherapy scheduling. In: IFAC Proceedings Volumes, vol. 44, pp. 6945–6950 (2011)

    Google Scholar 

  18. Kapamara, T., Sheibani, K., Haas, O.C.L., Reeves, C., Petrovic, D.: A review of scheduling problems in radiotherapy. In: Proceedings of the International Control Systems Engineering Conference on Systems Engineering (ICSE 2006), pp. 201–207 (2006). https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1937-5956.2011.01221.x

  19. Legrain, A., Fortin, M.A., Lahrichi, N., Rousseau, L.M.: Online stochastic optimization of radiotherapy patient scheduling. Health Care Manage. Sci. 18, 110–123 (2015)

    Article  Google Scholar 

  20. Luby, M., Sinclair, A., Zuckerman, D.: Optimal speedup of Las Vegas algorithms. Inform. Process. Lett. 47, 173–180 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  21. May, J.H., Spangler, W.E., Strum, D.P., Vargas, L.G.: The surgical scheduling problem: current research and future opportunities. Prod. Oper. Manage. 20, 392–405 (2011)

    Article  Google Scholar 

  22. O’Rourke, N., Edwards, R.: Lung cancer treatment waiting times and tumour growth. Clin. Oncol. 12(3), 141–144 (2000)

    Article  Google Scholar 

  23. Pesant, G.: A regular language membership constraint for finite sequences of variables. In: Wallace [32], pp. 482–495

    Chapter  MATH  Google Scholar 

  24. Petrovic, D., Castro, E., Petrovic, S., Kapamara, T.: Radiotherapy scheduling. In: Uyar, A., Ozcan, E., Urquhart, N. (eds.) Automated Scheduling and Planning. Studies in Computational Intelligence, vol. 505, pp. 155–189. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39304-4_7

    Chapter  Google Scholar 

  25. Petrovic, S., Leung, W., Song, X., Sundar, S.: Algorithms for radiotherapy treatment booking. In: Qu, R. (ed.) 25th Workshop of the UK Planning and Scheduling Special Interest Group, pp. 105–112, April 2006

    Google Scholar 

  26. Riff, M.C., Cares, J.P., Neveu, B.: RASON: a new approach to the scheduling radiotherapy problem that considers the current waiting times. Expert Syst. Appl. 64, 287–295 (2016)

    Article  Google Scholar 

  27. Sauré, A., Patrick, J., Tyldesley, S., Puterman, M.L.: Dynamic multi-appointment patient scheduling for radiation therapy. Eur. J. Oper. Res. 223(2), 573–584 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  28. Shaw, P.: Using constraint programming and local search methods to solve vehicle routing problems. In: Maher, M., Puget, J.-F. (eds.) CP 1998. LNCS, vol. 1520, pp. 417–431. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-49481-2_30

    Chapter  Google Scholar 

  29. Shaw, P.: A constraint for bin packing. In: Wallace [32], pp. 648–662

    Chapter  Google Scholar 

  30. Van Harten, M.C., Hoebers, F.J., Kross, K.W., Van Werkhoven, E.D., Van Den Brekel, M.W., Van Dijk, B.A.: Determinants of treatment waiting times for head and neck cancer in the netherlands and their relation to survival. Oral Oncol. 51(3), 272–278 (2015)

    Article  Google Scholar 

  31. Vieira, B., Hans, E.W., Van Vliet-Vroegindeweij, C., Van De Kamer, J., VanHarten, W.: Operations research for resource planning and - use in radiotherapy: a literature review. BMC Med. Inform. Decis. Making 16(149) (2016)

    Google Scholar 

  32. Wallace, M. (ed.): CP 2004. LNCS, vol. 3258. Springer, Heidelberg (2004). https://doi.org/10.1007/b100482

    Book  MATH  Google Scholar 

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Acknowledgments

The authors thank Per Enqvist at KTH and Kjell Eriksson at RaySearch Laboratories for a fruitful collaboration. The authors are grateful for insightful discussions about the CP models with Mats Carlsson and Peter J. Stuckey and constructive comments from the anonymous reviewers.

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Correspondence to Sara Frimodig or Christian Schulte .

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Frimodig, S., Schulte, C. (2019). Models for Radiation Therapy Patient Scheduling. In: Schiex, T., de Givry, S. (eds) Principles and Practice of Constraint Programming. CP 2019. Lecture Notes in Computer Science(), vol 11802. Springer, Cham. https://doi.org/10.1007/978-3-030-30048-7_25

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  • DOI: https://doi.org/10.1007/978-3-030-30048-7_25

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-30047-0

  • Online ISBN: 978-3-030-30048-7

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