Optimal sensor placement in a hospital operating room

Abstract

Building ventilation systems are responsible for providing a favorable thermal condition, as well as maintaining acceptable indoor air quality. Thus, ventilation rates are extremely high in hospitals to avoid exposure to potentially fatal threads. This, of course, means higher energy consumption rates, making hospitals among the top energy intensive buildings. One approach to circumvent such a tradeoff is to design a smart ventilation system, where air quality is continuously measured by a series of sensors, whose real time readings help adjust the ventilation rates. In this paper, we introduce optimization problems to study the optimal number and location of sensors in a hospital operating room (OR). In particular, we formulate several optimization problems to find the optimal location and sensors to minimize the expected detection time. We propose three solution procedures to solve the said optimization problems. The first method extends and applies Monte Carlo simulation models to our problem and serves as a benchmark; the second method develops a novel decomposition approach along with a marginal benefit argument to provide solutions; and the third method develops an integer programing method for a discrete probability distribution of contamination on space. We apply our methods to a real data set from an OR of a hospital and our results show that our proposed algorithms are near-optimal, the optimal placement is sensitive to the probability density of contamination location, and optimal placement for sensors is near patient bed and OR doors.