Lee, B. H. and Deininger, R. A. (1992) “Optimal Locations of Monitoring Stations in Water Distribution Systems”, Journal of Environmental Engineering, 118(1) pp. 4-16.
Summary
The US EPA requires the monitoring of drinking water quality. This testing is typically done by testing stations. In the article, the authors attempt to use Linear Programming to mathematically calculate where to place the testing stations in the system so that the greatest percentage of water in the system will be tested. Their methodology is based on the fact that water at a downstream node must be of lower quality than at the node upstream where it came from. Also, the researchers used skeleton models of water distribution systems with constant flow directions.
Their LP used boolean (true/false) variables representing whether or not a testing station was at a particular node, and maximized the sum of (nodal demands)X(testing station t/f). The constraints used were related to the flow geometry and demand patterns and the number of testing stations being used.
This strategy was used for two water distribution systems, in Michigan and Connecticut, and the researchers found they were able to significantly increase the efficiency of the testing using their LP solutions.
Discussion
The article seemed to present a realistic example where a form of Linear Programming might be used on a real world problems. The methods used seemed to make sense intuitively, and the results were easy to understand. My one problem with the paper is the assumption of the flow patterns. This was clearly caused by lack of technology which forced the researchers to simplify the problem by using one (or four for the Connecticut system) flow pattern. As we all know, flow patterns can change throughout the day as demands at the different nodes change. I wonder whether using modern computers if you could calculate the coverage provided by a station at a particular node over the course of a day in order to better represent the dynamics of the system, and whether this would actually result in different solutions than those solutions the paper arrived at.
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That's a very good observation, that the flow pattern is changing throughout the day as demands change. I didn't think of that. I think a more complex way of modeling this system is definately needed now that better technology is available.
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