Skip to main content

Optimal override policy for chemotherapy scheduling template via mixed-integer linear programming


Owing to treatment complexity in chemotherapy administration, nurses are usually required at the beginning, end, and at certain times during the treatment period to ensure high-quality infusion. It is, thus, critical for an outpatient chemotherapy unit to design a scheduling template that can effectively match nursing resources with treatment requirements. The template contains appointment slots of different lengths and thus allows schedulers to place patients into these slots according to the provider’s order. As the template is often used over a period of several months, there usually exists a mismatch between the daily patient mix and the fixed structure of the given template. Hence, override policies must be employed to adjust to demand. However, these policies are often manually performed by schedulers. We propose a mixed-integer linear programming model to systematically develop optimal override policies in place of the manual process to improve template utilization while maintaining template stability. Numerical experiments based on real-life data from a chemotherapy unit are conducted to demonstrate the effectiveness of the proposed approach.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2


  1. Bailey, N.T.: A study of queues and appointment systems in hospital out-patient departments, with special reference to waiting-times. Journal of the Royal Statistical Society. Series B (Methodological) pp. 185–199 (1952)

  2. Berg, B.P., Denton, B.T., Erdogan, S.A., Rohleder, T., Huschka, T.: Optimal booking and scheduling in outpatient procedure centers. Comput. Oper. Res. 50, 24–37 (2014)

    Article  MathSciNet  Google Scholar 

  3. Cayirli, T., Veral, E.: Outpatient scheduling in health care: a review of literature. Prod. Oper. Manag. 12(4), 519–549 (2003)

    Article  Google Scholar 

  4. Cayirli, T., Veral, E., Rosen, H.: Designing appointment scheduling systems for ambulatory care services. Health Care Manag. Sci. 9(1), 47–58 (2006)

    Article  Google Scholar 

  5. Denton, B., Gupta, D.: A sequential bounding approach for optimal appointment scheduling. IIE Trans. 35(11), 1003–1016 (2003)

    Article  Google Scholar 

  6. Erdogan, S.A., Denton, B.: Dynamic appointment scheduling of a stochastic server with uncertain demand. INFORMS J. Comput. 25(1), 116–132 (2013)

    Article  MathSciNet  Google Scholar 

  7. Fetter, R.B., Thompson, J.D.: Patients waiting time and doctors idle time in the outpatient setting. Health Serv. Res. 1(1), 66 (1966)

    Google Scholar 

  8. Gupta, D., Denton, B.: Appointment scheduling in health care: challenges and opportunities. IIE Trans. 40(9), 800–819 (2008)

    Article  Google Scholar 

  9. Gurvich, I., Luedtke, J., Tezcan, T.: Staffing call centers with uncertain demand forecasts: a chance-constrained optimization approach. Manag. Sci. 56(7), 1093–1115 (2010)

    Article  Google Scholar 

  10. Ho, C.J., Lau, H.S.: Minimizing total cost in scheduling outpatient appointments. Manag. Sci. 38(12), 1750–1764 (1992)

    Article  Google Scholar 

  11. Huang, Y.L., Bach, S.M., Looker, S.A.: Chemotherapy scheduling template development using an optimization approach. Int. J. Health Care Quality Assur. 5, 19 (2019)

    Google Scholar 

  12. Huang, Y.L., Bryce, A.H., Culbertson, T., Connor, S.L., Looker, S.A., Altman, K.M., Collins, J.G., Stellner, W., McWilliams, R.R., Moreno-Aspitia, A., et al.: Alternative outpatient chemotherapy scheduling method to improve patient service quality and nurse satisfaction. J. Oncol. Practice 14(2), e82–e91 (2018)

    Article  Google Scholar 

  13. Jiang, R., Ryu, M., Xu, G.: Data-driven distributionally robust appointment scheduling over wasserstein balls. arXiv preprint arXiv:1907.03219 (2019)

  14. Kaandorp, G.C., Koole, G.: Optimal outpatient appointment scheduling. Health Care Manag. Sci. 10(3), 217–229 (2007)

    Article  Google Scholar 

  15. Kall, P., Wallace, S.W.: Stochastic Programming. Springer, Berlin (1994)

    MATH  Google Scholar 

  16. Kong, Q., Lee, C.Y., Teo, C.P., Zheng, Z.: Scheduling arrivals to a stochastic service delivery system using copositive cones. Oper. Res. 61(3), 711–726 (2013)

    Article  MathSciNet  Google Scholar 

  17. Mak, H.Y., Rong, Y., Zhang, J.: Sequencing appointments for service systems using inventory approximations. Manuf. Serv. Oper. Manage. 16(2), 251–262 (2014)

    Article  Google Scholar 

  18. Mak, H.Y., Rong, Y., Zhang, J.: Appointment scheduling with limited distributional information. Manag. Sci. 61(2), 316–334 (2015)

    Article  Google Scholar 

  19. Muthuraman, K., Lawley, M.: A stochastic overbooking model for outpatient clinical scheduling with no-shows. IIE Trans. 40(9), 820–837 (2008)

    Article  Google Scholar 

  20. Shen, S., Wang, J.: Stochastic modeling and approaches for managing energy footprints in cloud computing service. Serv. Sci. 6(1), 15–33 (2014)

    Article  Google Scholar 

  21. Turkcan, A., Zeng, B., Lawley, M.: Chemotherapy operations planning and scheduling. IIE Trans. Healthcare Syst. Eng. 2(1), 31–49 (2012)

    Article  Google Scholar 

  22. Zacharias, C., Pinedo, M.: Managing customer arrivals in service systems with multiple identical servers. Manuf. Serv. Oper. Manag. 19(4), 639–656 (2017)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Guanglin Xu.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Huang, YL., Sikder, I. & Xu, G. Optimal override policy for chemotherapy scheduling template via mixed-integer linear programming. Optim Lett 16, 1549–1562 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Chemotherapy
  • Scheduling template
  • Override policy
  • Mixed-integer linear programming