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Optimal Food Safety Sampling Under a Budget Constraint

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  • Mark R. Powell
Abstract
Much of the literature regarding food safety sampling plans implicitly assumes that all lots entering commerce are tested. In practice, however, only a fraction of lots may be tested due to a budget constraint. In such a case, there is a tradeoff between the number of lots tested and the number of samples per lot. To illustrate this tradeoff, a simple model is presented in which the optimal number of samples per lot depends on the prevalence of sample units that do not conform to microbiological specifications and the relative costs of sampling a lot and of drawing and testing a sample unit from a lot. The assumed objective is to maximize the number of nonconforming lots that are rejected subject to a food safety sampling budget constraint. If the ratio of the cost per lot to the cost per sample unit is substantial, the optimal number of samples per lot increases as prevalence decreases. However, if the ratio of the cost per lot to the cost per sample unit is sufficiently small, the optimal number of samples per lot reduces to one (i.e., simple random sampling), regardless of prevalence. In practice, the cost per sample unit may be large relative to the cost per lot due to the expense of laboratory testing and other factors. Designing effective compliance assurance measures depends on economic, legal, and other factors in addition to microbiology and statistics.

Suggested Citation

  • Mark R. Powell, 2014. "Optimal Food Safety Sampling Under a Budget Constraint," Risk Analysis, John Wiley & Sons, vol. 34(1), pages 93-100, January.
    • Handle: RePEc:wly:riskan:v:34:y:2014:i:1:p:93-100
    DOI: 10.1111/risa.12054
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    References listed on IDEAS

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    1. S. Andrew Starbird, 2005. "Moral Hazard, Inspection Policy, and Food Safety," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 87(1), pages 15-27.
    2. Connelly, Luke B., 2003. "Balancing the Number and Size of Sites: An Economic Approach to the Optimal Design of Cluster Samples," MPRA Paper 14676, University Library of Munich, Germany.
    3. Harrington, Winston, 1988. "Enforcement leverage when penalties are restricted," Journal of Public Economics, Elsevier, vol. 37(1), pages 29-53, October.
    4. Vicki M. Bier & Shi‐Woei Lin, 2013. "Should the Model for Risk‐Informed Regulation be Game Theory Rather than Decision Theory?," Risk Analysis, John Wiley & Sons, vol. 33(2), pages 281-291, February.
    5. Starbird, S. Andrew, 2000. "Designing Food Safety Regulations: The Effect Of Inspection Policy And Penalties For Noncompliance On Food Processor Behavior," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 25(2), pages 1-20, December.
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    Cited by:

    1. Z. Wang & H. J. van der Fels‐Klerx & A. G. J. M. Oude Lansink, 2020. "Optimization of Sampling for Monitoring Chemicals in the Food Supply Chain Using a Risk‐Based Approach: The Case of Aflatoxins and Dioxins in the Dutch Dairy Chain," Risk Analysis, John Wiley & Sons, vol. 40(12), pages 2539-2560, December.
    2. Cuicui Chen & Rebecca S. Epanchin‐Niell & Robert G. Haight, 2018. "Optimal Inspection of Imports to Prevent Invasive Pest Introduction," Risk Analysis, John Wiley & Sons, vol. 38(3), pages 603-619, March.

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