<p>In this article, we describe several methods for approximating chance constraints on the duration of surgeries assigned to a surgical session. First, we extend the traditional assumption that surgery durations follow a normal distribution to both log-normal and gamma distributions. We use the Fenton–Wilkinson method to approximate the joint cumulative distribution function under these assumptions. Second, we use historical data to create an empirical distribution of the session duration and employ kernel density estimation to find the cumulative distribution function. We consider the situations where both the mean and variance of the surgeries’ durations are known, and when only the mean is known. Through numerical experiments, we demonstrate the accuracy of the cumulative distribution functions that we develop. In addition, we create piecewise linear constraints from the cumulative distribution functions to approximate chance constraints and compare their performance as binary classifiers to other approaches. The results show that the techniques we develop are equivalent to using the sample average approximation with a large sample size, while requiring fewer variables and constraints to be added to the optimisation problem.</p>