Berry et al (2005)

Berry, J., Fleisher, L, Hart, W. Phillips, C. and Watson, J.-P. (2005) “Sensor Placement in Municipal Water Networks”, Journal of Water Resources Planning and Management, 131(3) pp. 237-243

This article shows a methodology for determining sensor placement in municipal water networks using mixed integer programming. These sensors are placed to determine the presence of contaminants, whether accidentally or intentionally occuring.

The article states that this type of problem can be solved with a variety of modeling approaches utilizing the latest technology in computing power, but the certainty of the results just won't be as good as mixed-integer optimization techniques that make many simplifying assumptions. This was an interesting point since in the last article review I did of Lee et al (1992) I made the comment (see below) that it might not be necessary to make so many assumptions for the sake of quick solutions considering today's technology and advancements in optimization techniques. However, Berry et al was able to answer my question by describing why simplifying assumptions are better, even today.

After making these simplifying assumptions, the authors describe the equations they used to model these problems and describe the three data sets they used to demonstrate their methodology. The sensitivity of their results was interesting since it was low when they had few sensors available to place in the network, high when there was a medium amount of sensors available, and low again when there were many sensors available. I can see how there would be low sensitivity with many sensors since the distances from a sensor to any point in the network is small, but I would expect that the sensitivity would be large with very few sensors since changing the location of a sensor would make big differences in distances to certain nodes, especially the nodes with higher populations and demands. I suppose that's why we have computers assisting us with these problems since they are too complex for a human to have an intuitive sense about it. Or it's just me. :)

For future work this could be applied to techniques for cleaning up contamination. It would be interesting to see how a slightly different application in the same setting might change the results.