A stochastic optimization and simulation approach for scheduling operating rooms and recovery beds in an orthopedic surgery department

• A knapsack followed by a mixed integer program and discrete event simulation approach.
• Minimizing the makespan and the waiting time of stochastic surgeries duration schedule.
• A case study with real data and observation of the head surgeon's work.
• We outperform the head surgeon's method. A gain of about 100 operations/year even with fewer selections.

This paper studies the problem of scheduling elective surgery patients in the orthopedic surgery division of Habib Bourguiba hospital in Tunisia. Two types of resources are considered: Operating Rooms (OR) and Recovery Beds (RB). The problem consists of optimizing the assignment of surgeries to OR’s and planning the recoveries in order to avoid them in the OR’s when no bed is available in the recovery room. The proposed solution takes into account the uncertainty in surgery and recovery durations and the capacity of resources. In a first phase, an additive slack was given to the total duration of each surgery in the waiting list. Then a knapsack model is proposed to choose operations to be scheduled in the selected day. The selected operations are assigned to the different operating rooms using a mixed integer programming model with the aim of wisely using the operating rooms’ time and minimizing the makespan. In a second phase, a discrete event simulation model is suggested to compare the new model and the head surgeon actual practise to evaluate the global performance of the proposed model. The efficiency of the suggested solution is then validated by an illustrating example which shows that a substantial amount of operations and hence cost can be saved. Larger instances with sizeable waiting lists are solved to convince surgery schedulers of the utility of the approach.