Abstract
An optimization model for use in the planning stage of the water quality management process was developed. The model determined the optimal removal of coliform bacteria in accordance with an objective function which reflects the uncertainty aspects of the problem. Several management options are available through model use thereby providing a decision-maker with considerable latitude to evaluate the relative importance of the conflicting objectives of the problem.
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Abbreviations
- A:
-
matrix of constraint coefficients,
- b:
-
vector of constraint right-hand side values,
- d ij :
-
scalar transfer coefficient from source i to receptor j,
- D j :
-
background pollutant concentration at location j,
- I j :
-
index set of sources impacting receptor location j,
- k :
-
first-order decay coefficient for coliform bacteria decay model,
- N o :
-
initial concentration of coliform bacteria,
- N t :
-
concentration of coliform bacteria after travel time t,
- S j :
-
pollutant standard at location j,
- I ij :
-
travel time in the water body from location i to location j,
- v ij :
-
the element in row i and column j of the variance-covariance matrix,
- V c :
-
variance-covariance matrix of the objective function vector,
- W i :
-
pollutant loading to source i,
- x:
-
decision vector for an optimization problem,
- x ij :
-
treatment imposed on source i,
- z o :
-
aspiration level for water quality objective,
- μ c :
-
mean value vector of the objective function coefficients,
- ϱ ij :
-
the correlation between the ith and jth objective function coefficients,
- σ i :
-
the ith element of the vector σ c ,
- τ:
-
the constraint limit for the equity constraints.
References
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Burn, D.H., McBean, E.A. Nonlinear optimization modeling of coliform bacteria. Water Air Soil Pollut 32, 183–200 (1987). https://doi.org/10.1007/BF00227693
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DOI: https://doi.org/10.1007/BF00227693