Linear/Integer Programming to Allocate Operating Room Time


How a Linear/Integer Programming Model Works


Linear/Integer Programming: The Basics

Linear/Integer Programming is used to help managers make decisions in allocating valuable resources. It accomplishes this by either maximizing or minimizing specific resource variables (type of products, personnel, shortest distances, etc.) within determined constraints (available raw material, available hours, requirements, etc.). Provided is a simple model (2 variables and 2 constraints) to demonstrate how the program generates the answer. Many times in the real world, problems are far more complicated utilizing over 2,000 variables and 2,000 constraints. At StrategyGen, we provide this service (click here).

Real World Application: Mount Sinai Allocating Operating Room Time

Mount Sinai in Toronto has 14 operating rooms that serve five surgical departments. The surgical departments include surgery, gynecology, ophthalmology, otolaryngology, and oral surgery. The surgery department also consists of five subareas including orthopedics, general surgery, plastic surgery, vascular surgery, and urology. The hospital only has 397.50 operating room hours available per week. Is there a way to schedule the operating blocks to be more efficient with time, personnel resources, and unbiased? The answer is yes.

Results: Improved Schedule, Saved Costs, and Better Allocation of Resources

Mount Sinai developed a Master Surgical Schedule, using a Linear/Integer Programming model, to allocate operating room time to meet the needs of the patients and doctors.

The Linear/Integer Programming model developed the best sequence for the master surgical schedule by reducing wasted layover time, maximizing the amount of input available, and meeting all the necessary criteria. In return, this reduced the clerical time for producing a schedule saving $20,000 per year. The new schedule provided the hospital with greater flexibility, increased ability to explore creative scheduling techniques, and improved the quality of the schedules. But perhaps the greatest benefit was the staff has been now provided with unbiased, equitable schedules through a consistent, identifiable process that resulted in reducing conflict between departments and surgeons.



J.T. Blake and J. Donald, “Mount Sinai Hospital Uses Integer Programming to Allocate Operating Room Time,” Interfaces 32, no. 2 (March-April 2002): 63-73


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