Summary
This study stems from the mandates of the Safe Drinking Water Act, put in place by the U.S. EPA in 1974. The Act identifies specific water quality parameters which must be measured, and the frequency with which these measurements must be taken. The Act also states that water quality measurements must be representative of the entire water distribution system from which they are taken. The EPA's language is very broad and sweeping, and contains no clear explanation or suggestion of how this mandate should be met. The authors turn to integer programming for a solution.
The authors conceptualize their model with a simplified WDS of seven nodes and five demands. It is assumed that flow quantities and directions in the WDS are known. The model centers around the idea of sufficiently estimating water quality at adjacent nodes by knowing the water quality at a sampled node. For example, if 80% of the water delivered to Node B comes from Node A, it is reasonable to assume that the water quality at Node A is equivalent or superior to the measurements obtained at Node B.
The authors begin their model by first constructing a Water Fraction Matrix, W. To construct W, one node in the WDS is assumed to be the sampling node, and the fractional amount of water passing through other nodes en route to the sampling node is identified. This process is then repeated for each node, resulting in an "n x n" matrix of water fractions, where "n" is the number of nodes in the system. From W, the knowledge-carrying matrix K is constructed based upon a decided fractional criterion. If fractional values in W are above a specified value, they are rounded to 1. If below, they are rounded to 0.
From K, the integer optimization problem can be outlined. The objective function seeks to maximize the "representativeness" of the water quality measurements taken. Constraints include a limited number of sampling nodes (which can be set by the user), and a set of conditions which monitor the relationship between sampling node location and demand coverage. The authors then apply this approach to more complicated systems in Flint, MI and Cheshire, CT, demonstrating significant coverage improvements over current monitoring systems.
Discussion
I found this article to be an interesting application of integer programming, although I am curious to know what was done to optimize water quality measurement between 1974 and 1992, when this article was written. The article doesn't give much insight into existing practices at the time, but it is obvious that the introduction of integer programming to this problem provided a significant step forward toward optimization.
Although the authors account for many of the complexities of a WDS, I feel their approach is held back by its simplifications. Reducing a WDS to less than 5 flow/demand patterns, arbitrary selection of a "coverage criterion", and crude rounding in the "knowledge-carrying" matrix are some of the major generalizations which I feel would lead to smaller coverage percentages than advertised in the authors' examples. Furthermore, even if optimization yields 60% coverage of the WDS, there is still 40% of the system which is consistently unmonitored. Although the authors' solution may have the best relationship between coverage and cost effectiveness, I feel it needs to be supplemented by another system to account for these unmonitored areas, whether it be randomized or more sophisticated.
This study stems from the mandates of the Safe Drinking Water Act, put in place by the U.S. EPA in 1974. The Act identifies specific water quality parameters which must be measured, and the frequency with which these measurements must be taken. The Act also states that water quality measurements must be representative of the entire water distribution system from which they are taken. The EPA's language is very broad and sweeping, and contains no clear explanation or suggestion of how this mandate should be met. The authors turn to integer programming for a solution.
The authors conceptualize their model with a simplified WDS of seven nodes and five demands. It is assumed that flow quantities and directions in the WDS are known. The model centers around the idea of sufficiently estimating water quality at adjacent nodes by knowing the water quality at a sampled node. For example, if 80% of the water delivered to Node B comes from Node A, it is reasonable to assume that the water quality at Node A is equivalent or superior to the measurements obtained at Node B.
The authors begin their model by first constructing a Water Fraction Matrix, W. To construct W, one node in the WDS is assumed to be the sampling node, and the fractional amount of water passing through other nodes en route to the sampling node is identified. This process is then repeated for each node, resulting in an "n x n" matrix of water fractions, where "n" is the number of nodes in the system. From W, the knowledge-carrying matrix K is constructed based upon a decided fractional criterion. If fractional values in W are above a specified value, they are rounded to 1. If below, they are rounded to 0.
From K, the integer optimization problem can be outlined. The objective function seeks to maximize the "representativeness" of the water quality measurements taken. Constraints include a limited number of sampling nodes (which can be set by the user), and a set of conditions which monitor the relationship between sampling node location and demand coverage. The authors then apply this approach to more complicated systems in Flint, MI and Cheshire, CT, demonstrating significant coverage improvements over current monitoring systems.
Discussion
I found this article to be an interesting application of integer programming, although I am curious to know what was done to optimize water quality measurement between 1974 and 1992, when this article was written. The article doesn't give much insight into existing practices at the time, but it is obvious that the introduction of integer programming to this problem provided a significant step forward toward optimization.
Although the authors account for many of the complexities of a WDS, I feel their approach is held back by its simplifications. Reducing a WDS to less than 5 flow/demand patterns, arbitrary selection of a "coverage criterion", and crude rounding in the "knowledge-carrying" matrix are some of the major generalizations which I feel would lead to smaller coverage percentages than advertised in the authors' examples. Furthermore, even if optimization yields 60% coverage of the WDS, there is still 40% of the system which is consistently unmonitored. Although the authors' solution may have the best relationship between coverage and cost effectiveness, I feel it needs to be supplemented by another system to account for these unmonitored areas, whether it be randomized or more sophisticated.
1 comment:
I agree with you Ian, the authors should have looked into the existing practices more than "it was uncertain why the existing stations were chosen to be monitored". I also concur with your statement that the unmonitored systems need to be supplemented with another model; it seems that the information left out needs to be compensated in some fashion.
Post a Comment