  We study elective surgery planning in flexible operating rooms where
emergency patients are accommodated in the existing elective surgery schedule.
Probability distributions of surgery durations are unknown, and only a small
set of historical realizations is available. To address distributional
ambiguity, we first construct an ambiguity set that encompasses all possible
distributions of surgery duration within a Wasserstein distance from the
empirical distribution. We then define a data-driven distributionally robust
surgery assignment (DSA) problem, which seeks to determine optimal elective
surgery assigning decisions to available surgical blocks in multiple ORs to
minimize the sum of patient-related costs and the expectation of OR overtime
and idle time costs over all distributions residing in the ambiguity set. Using
DSA structural properties, we derive an equivalent mixed-integer linear
programming (MILP) reformulation of the min-max DSA model, that can be solved
efficiently using off-the-shelf optimization software. Using real-world surgery
data, we conduct extensive numerical experiments comparing the operational and
computational performance of our approach with two state-of-the-art approaches.
