Health Care Management Science

, Volume 16, Issue 3, pp 197–216 | Cite as

A two-phase approach to scheduling multi-category outpatient appointments – A case study of a women’s clinic



In this paper, we propose a two-phase approach for designing a weekly scheduling template for outpatient clinics providing multiple types of services. In many outpatient clinics, various service types are categorized to address the operational challenge of substantial changeover time between certain pairs of services. In the first phase of our approach, a mixed-integer program is formulated to assign service categories to clinic sessions during a week and determine the optimal number of appointments reserved for each service type in each clinic session. The objective in the first phase is to balance the workload of the providers among clinic sessions. In the second phase, a stochastic mixed-integer program is formulated for each clinic session to assign each contained appointment with a starting time based on several time-based performance measures. To solve the formulated stochastic program, we develop a Monte Carlo sampling based genetic algorithm. The two-phase approach is tested numerically with cases derived from a real women’s clinic. Our results demonstrate that the two-phase approach can efficiently find promising weekly appointment scheduling templates for outpatient clinics. In addition, our results suggest that the best suboptimal scheduling templates found become more sensitive to the weighting coefficients of the time-based measures as the provider workload increases.


Appointment Scheduling Outpatient Clinics Stochastic Integer Programming Monte Carlo Sampling Genetic Algorithms 


  1. 1.
    Centers for Medicare & Medicaid Services (2012) National Health Expenditure data. Accessed March 2012
  2. 2.
    Institute of Medicine (2001) Crossing the quality chasm: A new health system for the 21st century. National Academy Press, Washington, DCGoogle Scholar
  3. 3.
    Cayirli T, Veral E (2003) Outpatient scheduling in health care: A review of literature. Prod Oper Manag 12(4):519–549CrossRefGoogle Scholar
  4. 4.
    Armstrong B, Levesque O, Perlin JB, Rick C, Shectman G (2005) Reinventing Veterans Health Administration: Focus on primary care. J Healthc Manag 50(6):399–408Google Scholar
  5. 5.
    LaGanga LR, Lawrence S (2007) Clinic overbooking to improve patient access and increase provider productivity. Decision Sci 38(2):251–276CrossRefGoogle Scholar
  6. 6.
    Gupta D, Denton B (2008) Appointment scheduling in health care: Challenges and opportunities. IIE Trans 40(9):800–819CrossRefGoogle Scholar
  7. 7.
    Santibáñez P, Chow VS, French J, Puterman ML, Tyldesley S (2009) Reducing patient wait times and improving resource utilization at British Columbia Cancer Agency’s ambulatory care unit through simulation. Health Care Manage Sci 12(4):392–407CrossRefGoogle Scholar
  8. 8.
    Rohleder TR, Lewkonia P, Bischak DP, Duffy P, Hendijani R (2011) Using simulation modeling to improve patient flow at an outpatient orthopedic clinic. Health Care Manage Sci 14(2):135–145CrossRefGoogle Scholar
  9. 9.
    Bailey NTJ (1952) A study of queue and appointment systems in hospital out-patient departments with special reference to waiting-times. J R Stat Soc B 14(2):185–199Google Scholar
  10. 10.
    Fetter RB, Thompson JD (1966) Patients’ waiting time and doctors’ idle time in the outpatient setting. Health Serv Res 1(2):66–90Google Scholar
  11. 11.
    Vissers J (1979) Selecting a suitable appointment system in an outpatient setting. Med Care 17(12):1207–1220CrossRefGoogle Scholar
  12. 12.
    Klassen KJ, Rohleder TR (1996) Scheduling outpatient appointments in a dynamic environment. J Oper Manag 14(2):83–101CrossRefGoogle Scholar
  13. 13.
    Rohleder TR, Klassen KJ (2000) Using client-variance information to improve dynamic appointment scheduling performance. Omega-Int J Manage S 28(3):293–302CrossRefGoogle Scholar
  14. 14.
    Ho C-J, Lau H-S (1992) Minimizing total cost in scheduling outpatient appointments. Manage Sci 38(12):1750–1764CrossRefGoogle Scholar
  15. 15.
    Ho C-J, Lau H-S (1999) Evaluating the impact of operating conditions on the performance of appointment scheduling rules in service systems. Eur J Oper Res 112(3):542–553CrossRefGoogle Scholar
  16. 16.
    Cayirli T, Veral E, Rosen H (2006) Designing appointment scheduling systems for ambulatory care services. Health Care Manage Sci 9(1):47–58CrossRefGoogle Scholar
  17. 17.
    Cayirli T, Yang KK, Quek SA (2012) A universal appointment rule for a single server system with walk-ins and no-shows. Prod Oper Manag 21(4):682–697CrossRefGoogle Scholar
  18. 18.
    Vanden Bosch PM, Dietz DC, Simeoni JR (1999) Scheduling customer arrivals to a stochastic service system. Nav Res Log 46(5):549–559CrossRefGoogle Scholar
  19. 19.
    Vanden Bosch PM, Dietz DC (2000) Minimizing expected waiting in a medical appointment system. IIE Trans 32(9):841–848CrossRefGoogle Scholar
  20. 20.
    Vanden Bosch PM, Dietz DC (2001) Scheduling and sequencing arrivals to an appointment system. J Serv Res-Us 4(1):15–25CrossRefGoogle Scholar
  21. 21.
    Kaandorp GC, Koole G (2007) Optimal outpatient appointment scheduling. Health Care Manage Sci 10(3):217–229CrossRefGoogle Scholar
  22. 22.
    Klassen KJ, Yoogalingam R (2009) Improving performance in outpatient appointment services with a simulation optimization approach. Prod Oper Manag 18(4):447–458CrossRefGoogle Scholar
  23. 23.
    Ahmadizar F, Ghazanfari M, Fatemi Ghomi SMT (2010) Group shops scheduling with makespan criterion subject to random release dates and processing times. Computers & Operations Research 37(1):152–162CrossRefGoogle Scholar
  24. 24.
    Al-Khamis T, M’Hallah R (2011) A two-stage stochastic programming model for the parallel machine scheduling problem with machine capacity. Computers & Operations Research 38(12):1747–1759CrossRefGoogle Scholar
  25. 25.
    Yen JW, Birge JR (2006) A Stochastic Programming Approach to the Airline Crew Scheduling Problem. Transportation Science 40(1):3–14CrossRefGoogle Scholar
  26. 26.
    Denton BT, Gupta D (2003) A sequential bounding approach for optimal appointment scheduling. IIE Trans 35(11):1003–1016CrossRefGoogle Scholar
  27. 27.
    Denton BT, Viapiano J, Vogl A (2007) Optimization of surgery sequencing and scheduling decisions under uncertainty. Health Care Manage Sci 10(1):13–24CrossRefGoogle Scholar
  28. 28.
    Batun S, Denton BT, Huschka TR, Schaefer AJ (2011) Operating room pooling and parallel surgery processing under uncertainty. Informs J Comput 23(2):220–237CrossRefGoogle Scholar
  29. 29.
    Robinson LW, Chen RR (2003) Scheduling doctors’ appointments: Optimal and empirically-based heuristic policies. IIE Trans 35(3):295–307CrossRefGoogle Scholar
  30. 30.
    Begen MA, Queyranne M (2011) Appointment scheduling with discrete random durations. Mathematics of Operations Research 36(2):240–257CrossRefGoogle Scholar
  31. 31.
    Begen MA, Levi R, Queyranne M (2012) A sampling-based approach to appointment scheduling. Operations Research 60(3):675–681CrossRefGoogle Scholar
  32. 32.
    Klein Haneveld WK, van der Vlerk MH (1999) Stochastic integer programming: General models and algorithms. Ann Oper Res 85:39–57CrossRefGoogle Scholar
  33. 33.
    Birge JR, Louveaux F (2011) Introduction to Stochastic Programming, 2nd edn. Springer, New York, NYCrossRefGoogle Scholar
  34. 34.
    O’Keefe RM (1985) Investigating outpatient departments: Implementable policies and qualitative approaches. J Oper Res Soc 36(8):705–712Google Scholar
  35. 35.
    Schultz R (2003) Stochastic programming with integer variables. Math Program ser B 97(1–2):285–309Google Scholar
  36. 36.
    Kleywegt AJ, Shapiro A, Homen-de-Mello T (2002) The sample average approximation method for stochastic discrete optimization. SIAM Journal On Optimization 12(2):479–502CrossRefGoogle Scholar
  37. 37.
    Mitchell M (1996) An Introduction to Genetic Algorithms. MIT Press, Cambridge, MAGoogle Scholar
  38. 38.
    MathWorks, Inc. (2012) R2012a Documentation – Version 7.12 (R2011a) MATLAB Software. Accessed August 2012
  39. 39.
    US Department of Labor (2012) National Occupational Employment and Wage Estimates in the United States. Accessed June 2012.

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of Industrial and Systems EngineeringNorth Carolina Agricultural and Technical State UniversityGreensboroUSA
  2. 2.Department of Industrial and Manufacturing EngineeringNorth Dakota State UniversityFargoUSA
  3. 3.Weldon School of Biomedical EngineeringPurdue UniversityWest LafayetteUSA

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