An Incentive System for Salmonella Control in the Pork Supply Chain

with a bacteriological prevalence distribution associated with the mix of control packages reflecting the
steady state distribution of producers over production history states and the plant’s own control
package. Let cpi, μij, and σij² be the percentage of producers using control package i and the mean and
variance of producer level bacteriological prevalence for package i, where i ∈ {1, 2, 3}, when the plant
has selected plant control package j, where j ∈ {1, 2, 3}. Assuming producer level prevalence is
identically and independently distributed for producers using the same control package, the plant-level
expected bacteriological prevalence for this group of producers will be normally distributed with mean
and variance, μSij, and σSij², defined by the following expressions:

(5)      ИSij = Иij

(6)     σ Sij² = σ ij² /(cpi^dhogd)

The overall plant-level expected bacterological prevalence will also be normally distributed with mean
and variance, μSj, and σSj², defined by the following expressions:

(7)     и Sj = Σ cpi и Sij

i=1

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(8)     ^σSj² = Σ^cPi^2σSij² = Σ^cPi^σij² /^dhogd

i=1                            i=1

The plant receives no premium when the plant level prevalence in hogs delivered exceeds BPREV^*.
Knowing the plant-level bacteriological prevalence distribution, the expected slaughter plant premium
is the product of QPS and the probability the plant-level prevalence will be less than or equal to
BPREV^*. The plant pays Salmonella control costs, quality premiums to producers and Salmonella

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