Optimal pinging frequencies in the search for an immobile beacon

ABSTRACT

We consider a search for an immobile object that can only be detected if the searcher is within a given range of the object during one of a finite number of instantaneous detection opportunities; i.e., “pings.” More specifically, motivated by naval searches for battery-powered flight data recorders of missing aircraft, we consider the trade-off between the frequency of pings for an underwater locator beacon and the duration of the search. First, assuming that the search speed is known, we formulate a mathematical model to determine the pinging period that maximizes the probability that the searcher detects the beacon before it stops pinging. Next, we consider generalizations to discrete search speed distributions under a uniform beacon location distribution. Lastly, we present a case study based on the search for Malaysia Airlines Flight 370 that suggests that the industry-standard beacon pinging period—roughly 1 second between pings—is too short.

Keywords:

• Immobile hider
• linear search problem
• definite range law
• periodic detection

Acknowledgements

We wish to thank Sheldon Jacobson, Laura McLay, an anonymous Associate Editor, and two anonymous referees for their insightful and encouraging comments. In particular, one referee’s suggestions helped clarify the proof of Lemma 1.

Funding

This research was supported by National Science Foundation grants CMMI-1100082, CMMI-1100421, CMMI-1333758, and CMMI-1400009, as well as Research Experience for Undergraduates supplements to National Science Foundation grants CMMI-1131172 and CMMI-1333758.

Additional information

Notes on contributors

David J. Eckman

David J. Eckman is a Ph.D. student in the School of Operations Research and Information Engineering at Cornell University. He received a B.S. in Industrial Engineering from the University of Pittsburgh. His research interests include optimization via simulation and decision-making under uncertainty.

Lisa M. Maillart

Lisa Maillart is an Associate Professor in the Industrial Engineering Department at the University of Pittsburgh. Prior to joining the faculty at Pitt, she served on the faculty of the Department of Operations in the Weatherhead School of Management at Case Western Reserve University. She received her M.S. and B.S. in Industrial and Systems Engineering from Virginia Tech and her Ph.D. in Industrial and Operations Engineering from the University of Michigan. Her primary research interest is in sequential decision-making under uncertainty, with applications in medical decision-making, health care operations, and maintenance optimization. She is a member of INFORMS, SMDM, and IIE.

Andrew J. Schaefer

Andrew Schaefer is Noah Harding Chair and Professor of Computational and Applied Mathematics at Rice University. Previously he was Swanson Chair at the University of Pittsburgh. He received his Ph.D. in Industrial and Systems Engineering from Georgia Tech in 2000. His research interests include stochastic optimization methodology and its application to health care problems. In particular, he is interested in optimizing decisions arising in the treatment of a variety of diseases, including end-stage liver disease, HIV/AIDS, and influenza.