A variability reduction method for the operating room scheduling problem under uncertainty using CVaR

Uncertain surgery durations in Operating Rooms (OR) can cause a large deviation from the expected completion time of all surgery cases scheduled for each day. When the deviation is significantly large, it causes an extended overtime for the surgical team to complete the scheduled cases, and it often creates unnecessarily excessive idle times. As a result, the hospital will lose revenue opportunities. To address this issue, this paper presents a risk-based solution approach using the concept of Conditional Value-at-Risk (CVaR) to reduce variability on overtime, idle time, and associated costs in a daily OR scheduling problem. The OR scheduling problem is formulated as a stochastic mixed-integer linear programming (SMILP) model, where a surgery duration follows a probability distribution function. The objective of the SMILP model is to minimize the CVaR of overtime and idle time costs. Numerical experiments are conducted on real-life benchmark instances, and showed that CVaR outperformed the widely used expected value (EV) approach in reducing variance of the total cost. As compared to the EV in terms of the total cost, the CVaR reduced the variance by 37%, produced a 25% lower interquartile range, and 24% lower median absolute deviation at a slight increase (4%) in the expected value.