Modeling and optimization of an effluent pollution surveillance system

A surveillance system for a given number of effluents, each with certain contaminants, is considered. An effluent can be sampled to determine whether any of the contaminants exceeds its standard, in which case a violation is said to have been detected. Damage costs are associated only with undetected violations. These costs depend upon pollutant loadings, the nature of the pollutants, and the assimilative capacity of the receiving water. The objective is the following: find the sampling frequencies for each effluent (during a certain monitoring period) such as to minimize the total cost of the undetected violations. This is to be done subject to a certain budget constraint for the monitoring period. The cost of an undetected violation is defined as the expected value of the damage. These expectations are evaluated using the statistical knowledge available prior to the beginning of the monitoring period. The statistics of the contaminants are updated at the end of each monitoring period. It is shown that a very simple optimization procedure, namely, the maximum marginal return method, can be used to obtain the optimal sampling frequencies.