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Optimal Group Testing with Processing Times and Incomplete Identification

Author

Listed:
  • Shaul K. Bar-Lev

    (University of Haifa)

  • Wolfgang Stadje

    (University of Osnabrück)

  • Frank A. van der Duyn Schouten

    (Tilburg University)

Abstract

We consider the group testing problem for a finite population of possibly defective items with the objective of sampling a prespecified demanded number of nondefective items at minimum cost. Group testing means that items can be pooled and tested together; if the group comes out clean, all items in it are nondefective, while a “contaminated” group is scrapped. Every test takes a random amount of time and a given deadline has to be met. If the prescribed number of nondefective items is not reached, the demand has to be satisfied at a higher (penalty) cost. We derive explicit formulas for the distributions underlying the cost functionals of this model. It is shown in numerical examples that these results can be used to determine the optimal group size.

Suggested Citation

  • Shaul K. Bar-Lev & Wolfgang Stadje & Frank A. van der Duyn Schouten, 2004. "Optimal Group Testing with Processing Times and Incomplete Identification," Methodology and Computing in Applied Probability, Springer, vol. 6(1), pages 55-72, March.
    • Handle: RePEc:spr:metcap:v:6:y:2004:i:1:d:10.1023_b:mcap.0000012415.00394.66
    DOI: 10.1023/B:MCAP.0000012415.00394.66
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    References listed on IDEAS

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    1. Ming-Chin Hung & William H. Swallow, 2000. "Use of Binomial Group Testing in Tests of Hypotheses for Classification or Quantitative Covariables," Biometrics, The International Biometric Society, vol. 56(1), pages 204-212, March.
    2. Lawrence M. Wein & Stefanos A. Zenios, 1996. "Pooled Testing for HIV Screening: Capturing the Dilution Effect," Operations Research, INFORMS, vol. 44(4), pages 543-569, August.
    3. Shaul K. Bar‐Lev & Arnon Boneh & David Perry, 1990. "Incomplete identification models for group‐testable items," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(5), pages 647-659, October.
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    Cited by:

    1. Bar-Lev, Shaul K. & Boxma, Onno & Kleiner, Igor & Perry, David & Stadje, Wolfgang, 2017. "Recycled incomplete identification procedures for blood screening," European Journal of Operational Research, Elsevier, vol. 259(1), pages 330-343.
    2. Claeys, Dieter & Walraevens, Joris & Laevens, Koenraad & Bruneel, Herwig, 2010. "A queueing model for general group screening policies and dynamic item arrivals," European Journal of Operational Research, Elsevier, vol. 207(2), pages 827-835, December.
    3. Shaul K. Bar-Lev & Hans Blanc & Onno Boxma & Guido Janssen & David Perry, 2013. "Tandem Queues with Impatient Customers for Blood Screening Procedures," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 423-451, June.
    4. Jiejian Feng & Michael Zhang, 2017. "Reducing cost and abandoned E-components in incomplete identification," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(3), pages 281-290, March.
    5. Shaul K. Bar‐Lev & Onno Boxma & Andreas Löpker & Wolfgang Stadje & Frank A. Van der Duyn Schouten, 2012. "Group testing procedures with quantitative features and incomplete identification," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(1), pages 39-51, February.

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