Operating rooms account for 40 percent of a hospital’s total revenue but run at only 69 percent of capacity, according to the Health Care Financial Management Association.

Most hospitals book a fixed amount of time for an operation, determine the number that can be performed in a day and assign each a starting time. If an operation runs late, it delays the starting time for each subsequent surgery.

Camilo Mancilla, a Ph.D. student, hopes to improve OR utilization with algorithms that account for the unpredictable durations of operations. He creates a sample of random times (or scenarios) for each procedure. By running a huge number of possible scenarios, the program eventually finds an optimal solution that accounts for randomness.

Improving OR utilization also requires determining the optimal order for surgeries. Common sense, says Robert Storer, professor of industrial and systems engineering, dictates scheduling a surgery of known duration before one whose length is harder to predict. But the problem becomes more complicated when determining the best sequence for 10 operations rather than two.

Some studies have examined the stochastic optimization of starting times for a given sequence of operations, but few have investigated the effect of changing the sequence. This requires an enormous amount of computing time.

Mancilla has developed a heuristic solution based on Benders’ decomposition, a technique that eliminates whole sets of poor sequences. His method reduces from days to minutes the computing time required to optimize a 10-operation-a-day schedule over a sample of 100 scenarios.

Mancilla and Storer have also developed a model for one surgeon performing procedures in two parallel ORs.

“In this case, there are two types of wasted time: when the OR is idle and staff is waiting for a surgeon or patient to arrive, and when a surgeon is waiting for the OR to be set up,” says Storer. “We estimate there would be about 60 percent less wasted time using our scheme rather than the current method.”