Reducing post-surgery recovery bed occupancy with a probabilistic forecast model

Abstract

Operations Research approaches to surgical scheduling are becoming increasingly popular in both theory and practice. Often these models neglect stochasticity in order to reduce the computational complexity of the problem. We wish to provide practitioners and hospital administrative staff with a start-of-day probabilistic forecast for the occupancy of post-surgery recovery spaces. The model minimises the maximum expected occupancy of the recovery unit, thus levelling the workload of hospital staff, and reducing the likelihood of bed shortages and bottlenecks. We show that a Poisson binomial random variable models the number of patients in the recovery when parameterised by the surgical case sequence. A mixed integer nonlinear programming model for the surgical case sequencing problem reduces the maximum expected occupancy in post-surgery recovery spaces. Simulated Annealing produces good solutions in short amounts of computational time. We evaluate the methodology with a full year of historical data. The solution techniques reduce maximum expected recovery occupancy by 18% on average. This alleviates a large amount of stress on staff in the postsurgery recovery spaces, reduces the likelihood of bottlenecks, and improves the quality of care provided to patients.