Journal of Combinatorial Optimization

, Volume 37, Issue 1, pp 62–82 | Cite as

MRI appointment scheduling with uncertain examination time

  • Huaxin Qiu
  • Dujuan Wang
  • Yanzhang Wang
  • Yunqiang YinEmail author


This paper addresses the appointment scheduling problem for a single diagnostic facility—the magnetic resonance imaging equipment, which provides several services to the appointed patients. The examinations have random service durations given by a joint discrete probability distribution. We consider two performance criteria: (1) the expected cost incurred from the equipment idle time and the examination overtime representing the operating costs of the hospital; and (2) the expected cost incurred from the patient waiting time reflecting the customer satisfaction. The overall goal is to identify the examination sequence and the scheduled start times for the appointed patients so as to minimize simultaneously the aforementioned criteria by determining all the Pareto-optimal schedules. The problem is first formulated as a two-stage stochastic integer programming model and it is shown to be NP-hard in the strong sense even for the case with only two scenarios. An improved multi-objective evolutionary algorithm is then proposed in the MOEA/D framework, where the uncertainty is simulated by constructing a number of different scenarios. To replace the time-consuming simulations during the process of evaluating the rescheduling cost, we integrate the algorithm with a support vector regression surrogate model which efficiently improves the robustness of the baseline schedule and the quality of the solution. Finally, using the real medical data, we assess the feasibility and effectiveness of the proposed model by comparing with the classical NSGA-II and the MOEA/D algorithm, and extract some appropriate management inspirations to medical staffs for decision-making references.


Appointment scheduling Duration uncertainty Multi-objective evolutionary algorithm Support vector regression 



We gratefully thank the anonymous referees for their helpful comments on the earlier versions of our paper. This research was supported by the National Natural Science Foundation of China (Grant Nos. 71501024, 71533001, 71672019, 71271039).


  1. Astaraky D, Patrick J (2015) A simulation based approximate dynamic programming approach to multi-class, multi-resource surgical scheduling. Eur J Oper Res 245(1):309–319MathSciNetCrossRefzbMATHGoogle Scholar
  2. Bai M, Storer RH, Tonkay GL (2017) A sample gradient-based algorithm for a multiple-or and pacu surgery scheduling problem. IISE Trans 49(4):367–380Google Scholar
  3. Batun S, Denton B, Huschka TR, Schaefer AJ (2011) Operating room pooling and parallel surgery processing under uncertainty. Informs J Comput 23(2):220–237Google Scholar
  4. Cayirli T, Veral E (2010) Outpatient scheduling in health care: a review of literature. Prod Oper Manag 12(4):519–549CrossRefGoogle Scholar
  5. Chen RR, Robinson LW (2015) Sequencing and scheduling appointments with potential call in patients. Prod Oper Manag 23(9):1522–1538CrossRefGoogle Scholar
  6. Cheng R, Jin Y (2015) A competitive swarm optimizer for large scale optimization. IEEE Trans Cybern 45(2):191CrossRefGoogle Scholar
  7. Demeulemeester E, Belien J, Cardoen B, Samudra M (2010) Operating room planning and scheduling. Eur J Oper Res 201(3):921–932CrossRefzbMATHGoogle Scholar
  8. Denton B, Gupta D (2003) A sequential bounding approach for optimal appointment scheduling. IIE Trans 3(11):1003–1016Google Scholar
  9. Denton B, Viapiano J, Vogl A (2007) Optimization of surgery sequencing and scheduling decisions under uncertainty. Health Care Manag Sci 10(1):13CrossRefGoogle Scholar
  10. Gupta D, Denton B (2008) Appointment scheduling in health care: challenges and opportunities. IIE Trans 40(9):800–819CrossRefGoogle Scholar
  11. Gartner D, Kolisch R (2014) Scheduling the hospital-wide flow of elective patients. Eur J Oper Res 223(3):689–699Google Scholar
  12. Gunes ED, Yaman H, Cekyay B, Verter V (2014) Matching patient and physician preferences in designing a primary care facility network. J Oper Res Soc 65(4):483–496CrossRefGoogle Scholar
  13. Hulshof PJH, Kortbeek N, Boucherie RJ, Hans EW, Bakker PJM (2012) Taxonomic classification of planning decisions in health care: a structured review of the state of the art in OR/MS. Health Syst 1(2):129–175CrossRefGoogle Scholar
  14. Liu HL, Gu F, Zhang Q (2014) Decomposition of a multiobjective optimization problem into a number of simple multiobjective subproblems. IEEE Trans Evol Comput 18(3):450–455CrossRefGoogle Scholar
  15. Ma X, Tao Z, Wang Y, Yu H, Wang Y (2015) Long short-term memory neural network for traffic speed prediction using remote microwave sensor data. Transp Res Part C Emerg Technol 54:187–197CrossRefGoogle Scholar
  16. Mancilla C, Storer R (2012) A sample average approximation approach to stochastic appointment sequencing and scheduling. IIE Trans 44(8):655–670CrossRefGoogle Scholar
  17. Martinez SZ, Coello CAC (2014) A multi-objective evolutionary algorithm based on decomposition for constrained multi-objective optimization. In: IEEE transactions on evolutionary computation, pp 429–436Google Scholar
  18. May JH, Spangler WE, Strum DP, Vargas LG (2011) The surgical scheduling problem: current research and future opportunities. Prod Oper Manag 20(3):392–405CrossRefGoogle Scholar
  19. Newell MA, Jannink JL (2014) Genomic selection in plant breeding. Adv Agron 1145(2):117Google Scholar
  20. Peng Y (2013) Applying simulation and genetic algorithm for patient appointment scheduling optimization. Dissertations and theses—Gradworks, 2(2)Google Scholar
  21. Rubio-Largo A, Zhang Q, Vega-Rodrguez MA (2014) A multiobjective evolutionary algorithm based on decomposition with normal boundary intersection for traffic grooming in optical networks. Inf Sci 289(1):91–116MathSciNetCrossRefzbMATHGoogle Scholar
  22. Samudra M, Riet CV, Demeulemeester E, Cardoen B, Vansteenkiste N, Rademakers FE (2016) Scheduling operating rooms: achievements, challenges and pitfalls. J Sched 19(5):1–33MathSciNetCrossRefzbMATHGoogle Scholar
  23. Saremi A, Jula P, Elmekkawy T, Wang GG (2013) Appointment scheduling of outpatient surgical services in a multistage operating room department. Int J Prod Econ 141(2):646–658CrossRefGoogle Scholar
  24. Saremi A, Jula P, Elmekkawy T, Wang GG (2015) Bi-criteria appointment scheduling of patients with heterogeneous service sequences. Expert Syst Appl 42(8):4029–4041CrossRefGoogle Scholar
  25. Shen XN, Yao X (2015) Mathematical modeling and multi-objective evolutionary algorithms applied to dynamic flexible job shop scheduling problems. Inf Sci 298:198–224MathSciNetCrossRefGoogle Scholar
  26. Smola AJ, Scholkopf B (2004) A tutorial on support vector regression. Stat Comput 14(3):199–222MathSciNetCrossRefGoogle Scholar
  27. Sun C, Jin Y, Cheng R, Ding J, Zeng J (2017) Surrogate-assisted cooperative swarm optimization of high-dimensional expensive problems. IEEE Trans Evol Comput PP(99):1–1Google Scholar
  28. Wang DJ, Liu F, Wang YZ, Jin Y (2015a) A knowledge-based evolutionary proactive scheduling approach in the presence of machine breakdown and deterioration effect. Knowl Based Syst 90(C):70–80CrossRefGoogle Scholar
  29. Wang DJ, Liu F, Yin Y, Wang J, Wang Y (2015b) Prioritized surgery scheduling in face of surgeon tiredness and fixed off-duty period. J Combin Optim 30(4):967–981MathSciNetCrossRefzbMATHGoogle Scholar
  30. Xu H, Lu Z, Cheng TC (2014) Iterated local search for single-machine scheduling with sequence-dependent setup times to minimize total weighted tardiness. J Sched 17(3):271–287MathSciNetCrossRefzbMATHGoogle Scholar
  31. Yang Y, Shen B, Gao W, Liu Y, Zhong L (2015) A surgical scheduling method considering surgeons’ preferences. J Combin Optim 30(4):1–11MathSciNetCrossRefzbMATHGoogle Scholar
  32. Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731CrossRefGoogle Scholar
  33. Zhang Z, Xie X (2015) Simulation-based optimization for surgery appointment scheduling of multiple operating rooms. IIE Trans 47(9):998–1012CrossRefGoogle Scholar
  34. Zhang X, Zhou Y, Zhang Q, Lee VC, Li M (2016) Problem specific MOEA/D for barrier coverage with wireless sensors. IEEE Trans Cybern PP(99):1–12Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  1. 1.School of Management Science and EngineeringDalian University of TechnologyDalianPeople’s Republic of China
  2. 2.Data Science Research CenterKunming University of Science and TechnologyKunmingPeople’s Republic of China

Personalised recommendations