  The distributed operating room (OR) scheduling problem aims to find an
assignment of surgeries to ORs across collaborating hospitals that share their
waiting lists and ORs. We propose a stochastic extension of this problem where
surgery durations are considered to be uncertain. In order to obtain solutions
for the challenging stochastic model, we use sample average approximation, and
develop two enhanced decomposition frameworks that use logic-based Benders
(LBBD) optimality cuts and binary decision diagram based Benders cuts.
Specifically, to the best of our knowledge, deriving LBBD optimality cuts in a
stochastic programming context is new to the literature. Our computational
experiments on a hospital dataset illustrate that the stochastic formulation
generates robust schedules, and that our algorithms improve the computational
efficiency.
