Assignment #4

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:
This article is meant to primarily address a potential method for determining sampling locations within distribution systems that will most efficiently ensure that the system meets water quality criteria. The need for this method was generated by SDWA requirements for sampling water within water distribution networks. As the system is made of various pipes with nodes and relevant demands (requirements for outflows at a node), many potential sampling locations are possible (at the nodes). At some nodes, water unused by the demands flows to other nodes, and it can be assumed that the water quality at nearby nodes is related. Thus, this system seeks to distinguish which nodes could be sampled such that the optimum amount of water within the system could be sampled (as much as possible) compared to the number of sampling locations (as few as possible).

To accomplish this goal, the analysts utilized linear programming with a binary system in the actual analysis; however, considerable effort went into developing their mathematical model to input into the LP program. For the mathematical model, they first analyzed the water distribution system based upon a set of demand patterns to determine which nodes related to adjacent nodes with respect to water quality. Then, a binary matrix was created such that if a sufficient percentage of the water flowing into a node would have similar water quality compared to another node, the matrix value would be 1 (this would then be completed for all nodes vs. all nodes). This could then be used to ensure that all nodes would contribute enough to the sampling such that the maximum amount of water would be tested.

Finally, the authors presented some case studies where they applied their method to various actual distribution systems, eventually trying to determine locations that could be optimized for variable demand patterns that would likely be seen in the system.

Discussion:
I initially thought the authors had found a very neat solution method to tackle a complex problem. In many ways, i still think that; however, I can also see that the model did make a couple of assumptions that may make the analysis less sure than they thought. One major thing that I would try to do in their analysis would be to determine if a means of looking at the time from the inflow into the system could be reached. In their process of trying to account for this aspect, they used a 0.5 assumption variable that seemed somewhat arbitrary. My basic question would probably wonder how their constraints worked in the model to prevent just sampling at the first location...all of the water goes through that point (and quality characteristics are met there), so without looking at quality decay measures, the most optimal point for sampling would to simply sample there (all water would then meet requirements).