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) pg. 4-16.

Summary

The Environmental Protection Agency has had a requirement of monitoring water quality of potential drinking water. The guideline of the sampling frequency is based on the size of population that the distribution system serves. Furthermore, the EPA doesn’t prescribe a certain methodology in which monitoring stations should be chosen. This study by Lee and Deininger propose a integer programming model that introduces a rubric that optimizes locations of monitoring station(s).

First, a test model is introduced to explain in detail how the optimized model works. The model first creates a water fraction matrix in which the amount of water going through a certain node is contributed by a certain percentage from another node. From this matrix, a coverage matrix is created in which all the non-zero values above a certain “coverage criterion” are substituted by a 1. The “coverage criterion” is defined by the minimum percentage of flow contributed from node i to node j to be in order to be assigned a coverage value of 1.

The formulation of the optimization model includes an objective function that minimizes the product of the demand of node i and the binary integer that decides whether or not the sampling station will be location at node i. The constraints include the number of sampling stations wished to be used, along with the demand constraints for the nodes.

In the practical models, the demands of the nodes were the maximum daily flow demands for drinking water for the node. The demand coverage was optimized for a location in Michigan, in which the coverage increased from 18.5% to 54%. Also, this example incorporated multiple demand patterns, in which a two-scenario optimization problem was created. There was also a model created for a location in Connecticut that had incorporated four different flow scenarios that included demand nodes and pumping well fields.

Discussion

The authors argue that the EPA has strict requirements to monitor the quality of drinking water at specific locations in the system, however there is no formal procedures that are to be followed. It was interesting that the authors seemed to be completely uneducated about the previous methodologies of the past practices in this field. Surely they knew a little bit of information of why certain stations were monitored.

The authors introduced an integer programming model that optimized certain monitoring locations based on a “coverage criterion”. The authors believe that this factor is the optimal way to choose these specific locations. However is there a different criterion that other researchers have looked into? Also, it seems like a lot of information about the system is omitted, and nothing was added to the system to compensate. Lastly, I would be interested in the further development of this research, post 1992.