Events

Prof. Fernando G. Bernstein
Bob J. White Professor
The Fuqua School of Business
Duke University

We develop a stylized theoretical framework for the problem of tracking the population in a service system with noisy input and output observations.  The motivation for the project is the problem of tracking the population of passengers in the TSA area at an airport in real time using noisy data from people counters.  In the airport, such real-time population tracking can be useful for several operational decisions.  For example, when the number of passengers in the TSA area is large, the airport may need to deploy staff to manage the overflow from the designated queueing area.  This use suggests an objective that detects when the queue becomes large.  Other operational decisions, such as determining the number of security lanes to open or the number of officials to check IDs, rely on having an accurate estimate of the exact number of passengers in the TSA area. Our goal is to devise and analyze policies that use past people counter data to estimate the population in the system over a finite and discrete time horizon.  We evaluate the performance of policies in two distinct settings, each involving a different objective.  First, in the busyness tracking problem, the objective is to track whether the policy correctly detects if the system census is larger or smaller than a threshold.  Second, in the population tracking problem, the objective is to minimize the expected magnitude of the estimation error in each period (more precisely, the squared difference between the estimate and the true census in the system). We show that our problem is more challenging than dynamic learning problems typically studied in the bandit literature. In the busyness tracking problem, we derive a general lower bound on the cumulative expected loss that grows linearly with the time horizon.  In the population tracking problem, we prove another general lower bound on cumulative expected loss that is on the order of the square of the time horizon. Given this complexity, we develop and analyze policies that achieve the best possible performance in terms of the growth rate of cumulative expected loss.  Furthermore, we generalize our analysis to investigate the benefits of augmenting the people counter information with periodic inspections of the true census in the system.  Our motivating problem at the airport exemplifies a problem faced in other brick-and-mortar service settings in which – unlike in virtual service settings such as call centers – real-time occupancy information is not readily gathered but noisy signals may be available.

Fernando Bernstein is the William and Sue Gross Professor of Business Administration at the Fuqua School of Business, Duke University. He obtained a Ph.D. in Operations Management from the Graduate School of Business at Columbia University and joined Duke University in July 2000. Prof. Bernstein’s research interests include retail operations, supply chain management, production planning and inventory control, applications of game theory for production and distribution systems, and revenue management. Prof. Bernstein has published papers in leading journals such as Operations Research, Management Science and Manufacturing and Service Operations Management. He also serves as Associate Editor for these journals. Prof. Bernstein teaches the core Operations Management course for the Weekend Executive MBA program at Duke University, in addition to various Executive Education courses. He has earned the Excellence in Teaching Award for a core course for his teaching at Duke. Prof. Bernstein serves as Associate Dean for Global Initiatives for the strategic partnership between Duke University and Nazarbayev University.