Targeting Threshold, Inspection Capacity and Net Benefit
At a container port, 2,000 customs declarations are processed each day. The targeting system produces a risk score from 0 to 100. Analysts estimate that 80 declarations each day involve a material violation. At a threshold of 70, 100 declarations are selected: 40 are violations and 60 are not. At a threshold of 50, 220 are selected: 55 are violations and 165 are not. Each selection costs $300 to inspect. Each true violation yields an average recovery of $4,000 in duty, penalties or seizure value. Each false positive imposes a $150 delay and facilitation cost on the trader and the port. The port can inspect 150 declarations per day without overtime; overtime costs an additional $100 per inspection above 150. The manager proposes lowering the threshold to 50 because it catches 15 more violations.
1. Calculate the net benefit per day at each threshold, including overtime, and compare them.
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Threshold 70: 100 selected, within capacity. Benefit = 40 × $4,000 = $160,000. Cost = inspection 100 × $300 = $30,000 plus false-positive burden 60 × $150 = $9,000, total $39,000. Net = $121,000. Threshold 50: 220 selected, 70 above the 150 capacity. Benefit = 55 × $4,000 = $220,000. Cost = inspection 220 × $300 = $66,000; false-positive burden 165 × $150 = $24,750; overtime 70 × $100 = $7,000; total $97,750. Net = $122,250. The lower threshold is marginally better on these figures, by $1,250 per day, not the large gain the manager implies. The marginal 15 extra violations cost $58,750 in additional cost, or about $3,917 each, almost equal to the $4,000 average recovery. Small changes in assumptions would reverse the result.
2. Compute precision, recall and the false omission rate at each threshold, and explain which metric matters for risk management.
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There are 80 true violations. At 70: TP 40, FN 40, FP 60. Precision = 40/100 = 40%. Recall = 40/80 = 50%. False omission rate = 40/80 = 50%. At 50: TP 55, FN 25, FP 165. Precision = 55/220 = 25%. Recall = 55/80 = 68.75%. False omission rate = 25/80 = 31.25%. The lower threshold raises recall by 18.75 points but cuts precision by 15 points and increases false positives from 60 to 165. For risk management, recall matters for security outcomes, but precision matters for trader burden and credibility. A single metric cannot decide the threshold; the cost-weighted net benefit and the nature of the missed risk (revenue versus safety or security) must be considered.
3. The manager says the higher threshold 'misses half the violations, so it is indefensible.' Evaluate this argument and recommend a threshold policy.
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The statement 'we miss half the violations' is arithmetically true at threshold 70, but 'indefensible' does not follow. The comparison ignores the cost of the additional 120 selections, the near-zero marginal net gain, and the 165 false positives that burden compliant traders. It also treats all violations as equal, when a missed security shipment may be far more costly than a missed duty payment. Recommendation: do not adopt 50 as a blanket threshold. Segment by risk type: use 50 or lower for security indicators, keep 70 for routine revenue risk, and use non-intrusive scanning and post-clearance audit for the middle band. If 50 is adopted, plan for overtime and a false-positive reduction strategy. Pilot the change for 30 days and measure seizure quality, not just count.