Annals of Operations Research

, Volume 275, Issue 2, pp 393–420 | Cite as

Optimally configuring a measurement system to detect diversions from a nuclear fuel cycle

  • Benjamin L. Johnson
  • Aaron T. Porter
  • Jeffrey C. King
  • Alexandra M. NewmanEmail author
Original - OR Modeling/Case Study


The civilian nuclear fuel cycle is an industrial process that produces electrical power from the nuclear fission of uranium. Using a measurement system to accurately account for possibly dangerous nuclear material, such as uranium, in a fuel cycle is important because of its possible loss or diversion. A measurement system is defined by a set of measurement methods, or “devices,” used to account for material flows and inventory values at specific locations at facilities in the fuel cycle. We develop a simulation-optimization algorithm and an integer-programming model to find the best, or near-best, resource-limited measurement system with a high degree of confidence. The simulation-optimization algorithm minimizes a weighted sum of false positive and false negative diversion-detection probabilities while accounting for material quantities and measurement errors across a finite, discrete time horizon in hypothetical non-diversion and diversion contexts. In each time period, the estimated cumulative material unaccounted for is compared to a fixed or an optimized threshold value to assess if a “significant amount of material” is lost from a measurement system. The integer-programming model minimizes the population variance of the estimated material loss, i.e., material unaccounted for, in a measurement system. We analyze three potential problems in nuclear fuel cycle measurement systems: (i) given location-dependent device precisions, find the configuration of n devices at n locations (\(n=3\)) that provides the lowest corresponding objective values using the simulation-optimization algorithm and integer-programming model, (ii) find the location at which improving device precision reduces objective values the most using the simulation-optimization algorithm (given the device accuracy is 100%), and (iii) determine the effect of measurement frequency on measurement system configurations and objective values using the simulation-optimization algorithm. We obtain comparable results for each problem at least an order of magnitude faster than existing methods do. Using an optimized, rather than a fixed, detection threshold in the simulation-optimization algorithm reduces the weighted sum of false positive and false negative probabilities.


Integer programming Simulation optimization Resource allocation Nuclear safeguards 



We acknowledge Nicolas Shugart, Ph.D. candidate in the Nuclear Engineering Department at the Colorado School of Mines, for developing relevant nuclear engineering problems and giving data support for our models. In addition, we are grateful for the insights provided by Dr. R. Kevin Wood, Distinguished Professor Emeritus of Operations Research at Naval Postgraduate School, and Dr. David Morton, Professor of Industrial Engineering and Management Sciences at Northwestern University. We thank the National Nuclear Security Administration for providing us support under Grant DE-NA0001730.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Benjamin L. Johnson
    • 1
  • Aaron T. Porter
    • 2
  • Jeffrey C. King
    • 3
  • Alexandra M. Newman
    • 1
    Email author
  1. 1.Operations Research with Engineering ProgramColorado School of MinesGoldenUSA
  2. 2.Department of Applied Mathematics and StatisticsColorado School of MinesGoldenUSA
  3. 3.Nuclear Engineering ProgramColorado School of MinesGoldenUSA

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