Multi-objective admission planning problem: a two-stage stochastic approach

  • Ana BatistaEmail author
  • Jorge Vera
  • David Pozo


Effective admission planning can improve inpatient throughput and waiting times, resulting in better quality of service. The uncertainty in the patient arrival and the availability of resources makes the patient’s allocation difficult to manage. Thus, in the admission process hospitals aim to accomplish targets of resource utilization and to lower the cost of service. Both objectives are related and in conflict. In this paper, we present a bi-objective stochastic optimization model to study the trade-off between the resource utilization and the cost of service, taking into account demand and capacity uncertainties. Real data from the surgery and medical areas of a Chilean public hospital are used to illustrate the approach. The results show that the solutions of our approach outperform the actual practice in the Chilean hospital.


Admission planning Bi-objective Stochastic Uncertainty Bed capacity planning Resource allocation 



This research was supported by CONICYT under Grant 6635/2014 and FONDEF project CA13I10319. Author J. Vera would like to acknowledge the support of Iniciativa Milenio grant ICM/FIC RC130003. The authors would like to thank the collaboration of the managers of the Chilean Hospital used in this research as they provide data and insights used to solve the problem presented in this paper.


  1. 1.
    Adan I, Bekkers J, Dellaert N, Jeunet J, Vissers J (2011) Improving operational effectiveness of tactical master plans for emergency and elective patients under stochastic demand and capacitated resources. Eur J Oper Res 213(1):290–308CrossRefGoogle Scholar
  2. 2.
    Adan I, Bekkers J, Dellaert N, Vissers J, Yu X (2009) Patient mix optimisation and stochastic resource requirements: a case study in cardiothoracic surgery planning. Health Care Management Science 12(2):129CrossRefGoogle Scholar
  3. 3.
    Alvarez PP, Vera JR (2014) Application of robust optimization to the sawmill planning problem. Ann Oper Res 219(1):457–475CrossRefGoogle Scholar
  4. 4.
    Bekker R, Koeleman PM (2011) Scheduling admissions and reducing variability in bed demand. Health Care Management Science 14(3):237CrossRefGoogle Scholar
  5. 5.
    Birge JR, Louveaux F (2011) Introduction to stochastic programming. Springer Science & Business Media, BerlinCrossRefGoogle Scholar
  6. 6.
    Conejo AJ, Carrión M, Morales JM, et al. (2010) Decision making under uncertainty in electricity markets, vol 1. Springer, BerlinCrossRefGoogle Scholar
  7. 7.
    Deb K (2014) Multi-objective optimization. Search methodologies. Springer, New York, pp 403–49Google Scholar
  8. 8.
    Dobson G, Lee H-H, Pinker E (2010) A model of icu bumping. Operations Research 58(6):1564–1576CrossRefGoogle Scholar
  9. 9.
    Durán G., Rey PA, Wolff P (2017) Solving the operating room scheduling problem with prioritized lists of patients. Ann Oper Res 258(2):395–414CrossRefGoogle Scholar
  10. 10.
    Gallivan S, Utley M, Treasure T, Valencia O (2002) Booked inpatient admissions and hospital capacity: mathematical modelling study. Bmj 324(7332):280–282CrossRefGoogle Scholar
  11. 11.
    Gemmel P, Van Dierdonck R (1999) Admission scheduling in acute care hospitals: does the practice fit with the theory? International Journal of Operations & Production Management 19(9):863–878CrossRefGoogle Scholar
  12. 12.
    Green LV (2002) How many hospital beds? Inquiry: the Journal of Health Care Organization, Provision, and Financing 39(4):400–412CrossRefGoogle Scholar
  13. 13.
    Green LV (2005) Capacity planning and management in hospitals. In: Operations research and health care. Springer. pp 15–41Google Scholar
  14. 14.
    Guerriero F, Guido R (2011) Operational research in the management of the operating theatre: a survey. Health Care Management Science 14(1):89–114CrossRefGoogle Scholar
  15. 15.
    Helm JE, AhmadBeygi S, Van Oyen MP (2011) Design and analysis of hospital admission control for operational effectiveness. Prod Oper Manag 20(3):359–374CrossRefGoogle Scholar
  16. 16.
    Hulshof PJ, Boucherie RJ, Hans EW, Hurink JL (2013) Tactical resource allocation and elective patient admission planning in care processes. Health Care Management Science 16(2):152–166CrossRefGoogle Scholar
  17. 17.
    Hulshof PJ, Mes MR, Boucherie RJ, Hans EW (2016) Patient admission planning using approximate dynamic programming. Flex Serv Manuf J 28(1–2):30–61CrossRefGoogle Scholar
  18. 18.
    Kortbeek N, Braaksma A, Burger CA, Bakker PJ, Boucherie RJ (2015) Flexible nurse staffing based on hourly bed census predictions. Int J Prod Econ 161:167–180CrossRefGoogle Scholar
  19. 19.
    Kusters RJ, Groot PM (1996) Modelling resource availability in general hospitals design and implementation of a decision support model. Eur J Oper Res 88(3):428–445CrossRefGoogle Scholar
  20. 20.
    Lamiri M, Xie X, Dolgui A, Grimaud F (2008) A stochastic model for operating room planning with elective and emergency demand for surgery. Eur J Oper Res 185(3):1026–1037CrossRefGoogle Scholar
  21. 21.
    Min D, Yih Y (2010) An elective surgery scheduling problem considering patient priority. Comput Oper Res 37(6):1091–1099CrossRefGoogle Scholar
  22. 22.
    Mullen PM (2003) Prioritising waiting lists: how and why? Eur J Oper Res 150(1):32–45CrossRefGoogle Scholar
  23. 23.
    Peters-Groot P (1993) Decision support for admission planning under multiple resource constraints. PhD thesis. Technische Universiteit EindhovenGoogle Scholar
  24. 24.
    Pozo D, Sauma EE, Contreras J (2013) A three-level static milp model for generation and transmission expansion planning. IEEE Transactions on Power Systems 28(1):202–210CrossRefGoogle Scholar
  25. 25.
    Samudra M, Van Riet C, Demeulemeester E, Cardoen B, Vansteenkiste N, Rademakers FE (2016) Scheduling operating rooms: achievements, challenges and pitfalls. J Sched 19(5): 493–525CrossRefGoogle Scholar
  26. 26.
    Tamiz M, Mirrazavi S, Jones D (1999) Extensions of pareto efficiency analysis to integer goal programming. Omega 27(2): 179–188CrossRefGoogle Scholar
  27. 27.
    Testi A, Tànfani E (2009) Tactical and operational decisions for operating room planning: efficiency and welfare implications. Health Care Management Science 12(4):363CrossRefGoogle Scholar
  28. 28.
    Testi A, Tanfani E, Valente R, Ansaldo G, Torre G (2008) Prioritizing surgical waiting lists. J Eval Clin Pract 14(1):59–64CrossRefGoogle Scholar
  29. 29.
    Thompson S, Nunez M, Garfinkel R, Dean MD (2009) Or practice—efficient short-term allocation and reallocation of patients to floors of a hospital during demand surges. Operations Research 57(2):261–273CrossRefGoogle Scholar
  30. 30.
    Vissers J, Adan IJ, Bekkers JA (2005) Patient mix optimization in tactical cardiothoracic surgery planning: a case study. IMA J Manag Math 16(3):281–304CrossRefGoogle Scholar
  31. 31.
    Vissers JM, Adan IJ, Dellaert NP (2007) Developing a platform for comparison of hospital admission systems: an illustration. Eur J Oper Res 180(3):1290–1301CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Industrial and Systems Engineering, School of EngineeringPontificia Universidad Católica de ChileSantiagoChile
  2. 2.Center for Energy Science and TechnologySkolkovo Institute of Science and TechnologyMoscowRussia
  3. 3.Institute for Mathematical and Computational EngineeringPontificia Universidad Católica de ChileSantiagoChile

Personalised recommendations