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Determining the optimal surgical case start times is a challenging stochastic optimization problem that shares a key feature with many other healthcare operations problems. Namely, successful problem solutions require using a vast array of available historical data to create distributions that accurately capture a case duration's uncertainty for integration into an optimization model. Distribution fitting is the conventional approach to generate these distributions, but it can only employ a limited, aggregate portion of the detailed patient features available in Electronic Medical Records systems today. If all the available information can be taken advantage of, then distributions individualized to every case can be constructed whose precision would support higher quality solutions in the presence of uncertainty. Our individualized stochastic optimization framework shows how the quantile regression forest (QRF) method predicts individualized distributions that are integrable into sample-average approximation, robust optimization, and distributionally robust optimization models for problems like surgery scheduling. In this paper, we present some related theoretical performance guarantees for each formulation. Numerically, we also study our approach's benefits relative to three other traditional models using data from Memorial Sloan Kettering Cancer Center in New York, NY, USA. [ABSTRACT FROM AUTHOR]