An Incentive System for Salmonella Control in the Pork Supply Chain

The probability distribution for package 1 has most of its probability mass at a bacteriological
prevalence level of 0%. With higher serological herd prevalence levels the probability distribution is
more dispersed with non-zero probabilities up to bacteriological prevalence levels of 80%.

5. Solution Procedures

General purpose MATLAB routines developed by Miranda and Fackler (2002: 155-188) were
adapted to solve the producer’s stochastic discrete time/discrete state infinite horizon dynamic
programming problem for a given set of parameters. The program uses policy iteration to identify an
optimal steady state control policy - i.e., the optimal Salmonella control package for each possible
production history state. The solution procedure also identifies the state transition matrix associated
with the optimal policy, which can be used to determine a long-run probability for each possible state
under the optimal policy. This, in turn can be used along with the optimal policy to calculate expected
control costs, testing costs, penalties, and prevalence levels for a representative producer operating
under the optimal policy.

In order to solve the slaughter plant manager’s problem of selecting an optimal plant control
package and set of incentive system parameters, the producer problem for each system was embedded
in a grid search program that systematically explored the relevant plant control package and incentive
parameter space, as defined in table 3.

The optimal parameters for the manager problem combined with the optimal producer control
policy for those parameters, define a Nash equilibrium. As noted in the description of the model, we
consider two ownership structures - denoted IOF and COOP - as well as an efficiency benchmark for
the production chain operations - denoted CHAIN. The relevant performance measure for the manager

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