A mixed integer programming approach for allocating operating room capacity

We have developed a methodology for allocating operating room capacity to specialties. Our methodology consists of a finite-horizon mixed integer programming (MIP) model which determines a weekly operating room allocation template that minimizes inpatients' cost measured as their length of stay. A number of patient type priority (eg emergency over non-emergency patient) and clinical constraints (eg maximum number of hours allocated to each specialty, surgeon, and staff availability) are included in the formulation. The optimal solution from the analytical model is inputted into a simulation model that captures some of the randomness of the processes (eg surgery time, demand, arrival time, and no-show rate of the outpatients) and non-linearities (eg the MIP assumes proportional allocation of demand satisfaction (output) with room allocation (input)). The simulation model outputs the average length of stay for each specialty and the room utilization. On a case example of a Los Angeles County Hospital, we show how the hospital length of stay pertaining to surgery can be reduced.