  We study the elective surgery planning problem in a hospital with operation
rooms shared by elective and emergency patients. This problem can be split in
two distinct phases. First, a subset of patients to be operated in the next
planning period has to be selected, and the selected patients have to be
assigned to a block and a tentative starting time. Then, in the online phase of
the problem, a policy decides how to insert the emergency patients in the
schedule and may cancel planned surgeries. The overall goal is to minimize the
expectation of a cost function representing the assignment of patient to
blocks, case cancellations, overtime, waiting time and idle time. We model the
offline problem by a two-stage stochastic program, and show that the
second-stage costs can be replaced by a convex piecewise linear surrogate model
that can be computed in a preprocessing step. This results in a mixed integer
program which can be solved in a short amount of time, even for very large
instances of the problem. We also describe a greedy policy for the online phase
of the problem, and analyze the performance of our approach by comparing it to
either heuristic methods or approaches relying on sampling average
approximation (SAA) on a large set of benchmarking instances. Our simulations
indicate that our approach can reduce the expected costs by as much as 30%
compared to heuristic methods and is able to solve problems with $1000$
patients in about one minute, while SAA-approaches fail to obtain near-optimal
solutions within 30 minutes, already for $100$ patients.
