Stochastic programming for outpatient scheduling with flexible inpatient exam accommodation


This study is concerned with the determination of an optimal appointment schedule in an outpatient-inpatient hospital system where the inpatient exams can be cancelled based on certain rules while the outpatient exams cannot be cancelled. Stochastic programming models were formulated and solved to tackle the stochasticity in the procedure durations and patient arrival patterns. The first model, a two-stage stochastic programming model, is formulated to optimize the slot size. The second model further optimizes the inpatient block (IPB) placement and slot size simultaneously. A computational method is developed to solve the second optimization problem. A case study is conducted using the data from Magnetic Resonance Imaging (MRI) centers of Lahey Hospital and Medical Center (LHMC). The current schedule and the schedules obtained from the optimization models are evaluated and compared using simulation based on FlexSim Healthcare. Results indicate that the overall weighted cost can be reduced by 11.6% by optimizing the slot size and can be further reduced by an additional 12.6% by optimizing slot size and IPB placement simultaneously. Three commonly used sequencing rules (IPBEG, OPBEG, and a variant of ALTER rule) were also evaluated. The results showed that when optimization tools are not available, ALTER variant which evenly distributes the IPBs across the day has the best performance. Sensitivity analysis of weights for patient waiting time, machine idle time and exam cancellations further supports the superiority of ALTER variant sequencing rules compared to the other sequencing methods. A Pareto frontier was also developed and presented between patient waiting time and machine idle time to enable medical centers with different priorities to obtain solutions that accurately reflect their respective optimal tradeoffs. An extended optimization model was also developed to incorporate the emergency patient arrivals. The optimal schedules from the extended model show only minor differences compared to those from the original model, thus proving the robustness of the scheduling solutions obtained from our optimal models against the impacts of emergency patient arrivals.


  • Timestamped operational data was analyzed to identify sources of uncertainty and delays.

  • Stochastic programming models were developed to optimize slot size and inpatient block placement.

  • A case study showed that the optimized schedules can reduce overall costs by 23%.

  • Distributing inpatient and outpatient slots evenly throughout the day provides the best performance.

  • A Pareto frontier was developed to allow practitioners to choose their own best tradeoffs between multiple objectives.

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Correspondence to Yifei Sun.

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Sun, Y., Raghavan, U.N., Vaze, V. et al. Stochastic programming for outpatient scheduling with flexible inpatient exam accommodation. Health Care Manag Sci (2021).

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  • Outpatient scheduling
  • Stochastic programming
  • Discrete-event simulation
  • Inpatient exam cancellation
  • Appointment scheduling/sequencing
  • Operations research