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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Stochastic environmental research and risk assessment 4 (1990), S. 277-294 
    ISSN: 1436-3259
    Keywords: Water distribution ; optimization ; nonlinear programming ; integer programming ; chance constraints ; rehabilation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper presents the mathematical development of an integer — nonlinear programming chance — constrained optimization model for the minimum cost rehabilitation/replacement of water distribution system components. Particular attention is given to the handling of uncertainties in the roughness factors and the loading conditions including both the random demand and preassure head requirements. The advantages of the proposed model include the ability to: 1) handle the optimal timing of rehabilitation/replacement for water distribution system components; 2) link a mixed-integer linear program solver, a nonlinear program solver, and a hydraulic simulator into an optimization framework; 3) handle the uncertainties of some of the variables; 4) incorporate various kinds of cost functions; and 5) handle multiple loading conditions.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 45 (1985), S. 113-122 
    ISSN: 1573-2878
    Keywords: Generalized upper bounds ; dual simplex method ; algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The dual simplex method for generalized upper bound (GUB) problems is presented. One of the major operations in the dual simplex method is to update the elements of therth row, wherer is the index for the leaving basic variable. Those updated elements are used for the ratio test to determine the entering basic variabble. A very simple formula for therth row update for the dual simplex method for a GUB problem is derived, which is similar to the formula for the standard linear program. This derivation is based on the change key operation, which is to exchange the key column and its counterpart in the nonkey section. The change key operation is possible because of a theorem that guarantees the existence of such a counterpart.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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