An approach to interval programming problems with left-hand-side stochastic coefficients: An application to environmental decisions analysis

Authors:
M. F. Cao;G. H. Huang;L. He
Affiliations:
Sino-Canada Center of Energy and Environmental Research, North China Electric Power University, Beijing 102206, PR China;Environmental Systems Engineering Program, Faculty of Engineering, University of Regina, Regina, Saskatchewan, Canada S4S 0A2;Department of Civil Engineering, Ryerson University, Ryerson, Ontario, Canada M5B 2K3
Venue:
Expert Systems with Applications: An International Journal
Year:
2011

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Abstract

An interval programming with stochastic coefficients (IPSC) model is developed for planning of regional air quality management. The IPSC model incorporates stochastic coefficients with multivariate normal distributions within an interval parameter linear programming (ILP) framework. In IPSC, system uncertainties expressed as stochastic coefficients and intervals are addressed. Since stochastic coefficients are the left-hand-side (LHS) parameters of the constraints in IPSC, a left-hand-side chance-constrained programming (LCCP) method is developed to solve the problem. The developed IPSC model is applied to a regional air quality management system. Uncertainties in both abatement efficiencies expressed as stochastic coefficients and environmental standards expressed as intervals are reflected. Interval solutions associated with different violation probability levels and/or different environmental standards have been obtained. Air quality managers can thus analyze the solutions with appropriate combinations of the uncertainties and gain insight into the tradeoffs between the abatement costs and the risks of violating different environmental standards.