Abstract
Nowadays most cancer patients are treated by radiotherapy. The treatment duration of patients will grow longer over time because of the half-life decaying effect of the radioactive source, which can be regarded as a continuous non-linear deteriorating effect. How to sequence the treatment of the patients before the radioactivity is reduced to the lowest available intensity is an important and complex problem. Meanwhile, the treatment sequence of cancer patients should not only be based on the waiting time but also on the severity of their illness. Therefore, the dual factors which reflect the severity of patients’ illness as well as waiting time should be considered. The dual factors are denoted as the treatment value of patients in this paper and we determine patients in the waiting list to be selected, assigned and sorted for treatment, so as to maximize the overall treatment value of all patients. We also consider the setup time for each time of treatment, which cannot be ignored in reality. The original problem model is difficult to solve directly, so we reformulate the original problem to a set covering problem and it is solved by a column generation approach we develop. The master problem of selecting plans for treatment blocks and subproblems of generating plans are solved by GUROBI and dynamic programming, respectively. Numerical experiments are conducted to demonstrate the efficiency of the proposed column generation approach.
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References
Bard JF, Purnomo HW (2005) Preference scheduling for nurses using column generation. Eur J Oper Res 164(2):510–534. https://doi.org/10.1016/j.ejor.2003.06.046
Conforti D, Guerriero F, Guido R (2010) Non-block scheduling with priority for radiotherapy treatments. Eur J Oper Res 201(1):289–296. https://doi.org/10.1016/j.ejor.2009.02.016
Gerber D (2008) Recent advances in radiation therapy radiation principles and modalities. Am Fam Phys 71(4):1034–1041
Gocgun Y (2018) Simulation-based approximate policy iteration for dynamic patient scheduling for radiation therapy. Health Care Manage Sci 21(3):317–325. https://doi.org/10.1007/s10729-016-9388-9
Conforti D, Guerriero F, Guido R (2008) Optimization models for radiotherapy patient scheduling. 4OR 6:263–278. https://doi.org/10.1007/s10288-007-0050-8
Jacquemin Y, Marcon E, Pommier P (2010) Towards an improved resolution of radiotherapy scheduling, 2010 IEEE Workshop on Health Care Management (WHCM), Venice, 2010, pp. 1–6. https://doi.org/10.1109/WHCM.2010.5441263
Kong M, Liu X, Pei J, Zhou Z, Pardalos PM (2019) Parallel-batching scheduling of deteriorating jobs with non-identical sizes and rejection on a single machine. Optim Lett. https://doi.org/10.1007/s11590-019-01389-x
Lamiri, M., Augusto, V., & Xie, X. (2008). Patients scheduling in a hospital operating theatre. 4th IEEE Conference on Automation Science and Engineering, CASE 2008, 627–632. https://doi.org/https://doi.org/10.1109/COASE.2008.4626529
Lazarev AA, Werner F (2009) A graphical realization of the dynamic programming method for solving N P-hard combinatorial problems. Comput Math Appl 58(4):619–631. https://doi.org/10.1016/j.camwa.2009.06.008
Legrain A, Fortin MA, Lahrichi N, Rousseau LM (2015) Online stochastic optimization of radiotherapy patient scheduling. Health Care Manage Sci 18(2):110–123. https://doi.org/10.1007/s10729-014-9270-6
Liu X, Lu S, Pei J, Pardalos PM (2018) A hybrid VNS-HS algorithm for a supply chain scheduling problem with deteriorating jobs. Int J Prod Res 56(17):5758–5775. https://doi.org/10.1080/00207543.2017.1418986
Lu S, Liu X, Pei J, Thai T, M., & M. Pardalos, P. (2018) A hybrid ABC-TS algorithm for the unrelated parallel-batching machines scheduling problem with deteriorating jobs and maintenance activity. Appl Soft Comput J 66:168–182. https://doi.org/10.1016/j.asoc.2018.02.018
Pei J, Pardalos PM, Liu X, Fan W, Yang S (2015) Serial batching scheduling of deteriorating jobs in a two-stage supply chain to minimize the makespan. Eur J Oper Res 244(1):13–25. https://doi.org/10.1016/j.ejor.2014.11.034
Pei J, Liu X, Liao B, Pardalos PM, Kong M (2018) Single-machine scheduling with learning effect and resource-dependent processing times in the serial-batching production. Appl Math Model 58:245–253. https://doi.org/10.1016/j.apm.2017.07.028
Pei J, Cheng B, Liu X, Pardalos PM, Kong M (2019a) Single-machine and parallel-machine serial-batching scheduling problems with position-based learning effect and linear setup time. Ann Oper Res 272(1–2):217–241. https://doi.org/10.1007/s10479-017-2481-8
Pei J, Liu X, Fan W, Pardalos PM, Lu S (2019b) A hybrid BA-VNS algorithm for coordinated serial-batching scheduling with deteriorating jobs, financial budget and resource constraint in multiple manufacturers. Omega (United Kingdom) 82:55–69. https://doi.org/10.1016/j.omega.2017.12.003
Petrovic, S., & Leite-Rocha, P. (2008). Constructive and GRASP approaches to radiotherapy treatment scheduling. Proceedings-Advances in electrical and electronics engineering-IAENG special edition of the world congress on engineering and computer science 2008, WCECS 2008, 192–200. https://doi.org/https://doi.org/10.1109/WCECS.2008.31
Petrovic D, Morshed M, Petrovic S (2011a) Expert systems with applications multi-objective genetic algorithms for scheduling of radiotherapy treatments for categorised cancer patients. Expert Syst Appl 38(6):6994–7002. https://doi.org/10.1016/j.eswa.2010.12.015
Petrovic D, Morshed M, Petrovic S (2011b) Multi-objective genetic algorithms for scheduling of radiotherapy treatments for categorised cancer patients. Expert Syst Appl 38(6):6994–7002. https://doi.org/10.1016/j.eswa.2010.12.015
Range TM, Lusby RM, Larsen J (2014) A column generation approach for solving the patient admission scheduling problem. Eur J Oper Res 235(1):252–264. https://doi.org/10.1016/j.ejor.2013.10.050
Riff MC, Cares JP, Neveu B (2016) RASON: A new approach to the scheduling radiotherapy problem that considers the current waiting times. Expert Syst Appl 64:287–295. https://doi.org/10.1016/j.eswa.2016.07.045
Sauré A, Patrick J, Tyldesley S, Puterman ML (2012) Dynamic multi-appointment patient scheduling for radiation therapy. Eur J Oper Res 223(2):573–584. https://doi.org/10.1016/j.ejor.2012.06.046
Shao K, Fan W, Yang Z, Yang S, Pardalos PM (2020) Patient scheduling with deteriorating treatment duration and maintenance activity. Soft Comput. https://doi.org/10.1007/s00500-020-05156-4
Vogl P, Braune R, Doerner KF (2019) Scheduling recurring radiotherapy appointments in an ion beam facility: Considering optional activities and time window constraints. J Sched 22(2):137–154. https://doi.org/10.1007/s10951-018-0574-0
Wang Y, Tang J, Fung RYK (2014) A column-generation-based heuristic algorithm for solving operating theater planning problem under stochastic demand and surgery cancellation risk. Int J Prod Econ 158:28–36. https://doi.org/10.1016/j.ijpe.2014.07.015
Wang H, Huang M, Wang J (2018a) An effective metaheuristic algorithm for flowshop scheduling with deteriorating jobs. J Intell Manuf 1990:1–10. https://doi.org/10.1007/s10845-018-1425-8
Wang T, Baldacci R, Lim A, Hu Q (2018b) A branch-and-price algorithm for scheduling of deteriorating jobs and flexible periodic maintenance on a single machine. Eur J Oper Res 271(3):826–838. https://doi.org/10.1016/j.ejor.2018.05.050
Wang Y, Zhang G, Zhang L, Tang J, Mu H (2018c) A column-generation based approach for integrating surgeon and surgery scheduling. IEEE Access 6:41578–41589. https://doi.org/10.1109/ACCESS.2018.2854839
Xia C, Zuo T, Yang Z, He J, Zheng R, Zhang S, Zeng H (2017) Cancer incidence and mortality in China in 2013: an analysis based on urbanization level. Chin J Cancer Res 29(1):1–10
van Sambeek JRC, Joustra PE, Das SF et al (2011) Reducing MRI access times by tackling the appointment-scheduling strategy. BMJ Quality & Safety 20:1075–1080
Acknowledgments
This work is supported by the National Natural Science Foundation of China (Nos. 72071057, 71922009, 71871080 and 71690235) and Innovative Research Groups of the National Natural Science Foundation of China (71521001).
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Shao, K., Fan, W., Yang, Z. et al. A column generation approach for patient scheduling with setup time and deteriorating treatment duration. Oper Res Int J 22, 2555–2586 (2022). https://doi.org/10.1007/s12351-021-00620-x
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DOI: https://doi.org/10.1007/s12351-021-00620-x