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

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.

[1]  A. Stern.  Fundamentals of air pollution , 1973 .

[2]  Guohe Huang,et al.  The Perspectives of Environmental Informatics and Systems Analysis , 2003 .

[3]  G H Huang,et al.  An inexact fuzzy two-stage stochastic model for quantifying the efficiency of nonpoint source effluent trading under uncertainty. , 2005, The Science of the total environment.

[4]  Ross B. Corotis,et al.  Stochastic programs for identifying critical structural collapse mechanisms , 1991 .

[5]  Stefan Chanas,et al.  On the equivalence of two optimization methods for fuzzy linear programming problems , 2000, Eur. J. Oper. Res..

[6]  Guohe Huang,et al.  Optimization of regional waste management systems based on inexact semi-infinite programming , 2008 .

[7]  Julian Scott Yeomans,et al.  An Evolutionary Grey, Hop, Skip, and Jump Approach: Generating Alternative Policies for the Expansion of Waste Management , 2003 .

[8]  F. R. Holden,et al.  Air Pollution Handbook. , 1956 .

[9]  Li He,et al.  An Interval-Parameter Fuzzy-Stochastic Programming Approach for Air Quality Management under Uncertainty , 2008 .

[10]  Colin Rose,et al.  Mathematical Statistics with Mathematica , 2002 .

[11]  H. Brooks,et al.  Energy in transition 1985-2010 , 1980 .

[12]  Douglas A. Haith.  Environmental systems optimization , 1982 .

[13]  S. Y. Chang,et al.  Linear Programming Method for Investigating the Disposal Histories and Locations of Pollutant Sources in an Aquifer , 2009 .

[14]  David R. Cox,et al.  Testing multivariate normality , 1978 .

[15]  G. H. Huang,et al.  A fuzzy-stochastic robust programming model for regional air quality management under uncertainty , 2003 .

[16]  Anil K. Jain,et al.  A Test to Determine the Multivariate Normality of a Data Set , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Gordon H. Huang,et al.  An Inexact Chance-constrained Quadratic Programming Model for Stream Water Quality Management , 2009 .

[18]  J. Stedinger,et al.  Water resource systems planning and analysis , 1981 .

[19]  Guohe Huang,et al.  A GREY LINEAR PROGRAMMING APPROACH FOR MUNICIPAL SOLID WASTE MANAGEMENT PLANNING UNDER UNCERTAINTY , 1992 .

[20]  Guohe Huang,et al.  ITCLP: An inexact two-stage chance-constrained program for planning waste management systems , 2007 .

[21]  John H. Seinfeld,et al.  Fundamentals of Air Pollution Engineering , 1988 .

[22]  Julian Scott Yeomans.  Applications of Simulation-Optimization Methods in Environmental Policy Planning under Uncertainty , 2008 .

[23]  G. H. Huang,et al.  A hybrid inexact-stochastic water management model , 1998, Eur. J. Oper. Res..

[24]  Yan Li,et al.  An Inexact Two-Stage Quadratic Program for Water Resources Planning , 2007 .

[25]  Guohe Huang,et al.  Incorporation of Inexact Dynamic Optimization with Fuzzy Relation Analysis for Integrated Climate Change Impact Study , 1996 .

[26]  Li He,et al.  DIPIP: Dual Interval Probabilistic Integer Programming for Solid Waste Management , 2009 .

[27]  Guohe Huang,et al.  Grey Dynamic Programming for Waste‐Management Planning under Uncertainty , 1994 .

[28]  G. Huang,et al.  Grey integer programming: An application to waste management planning under uncertainty , 1995 .

[29]  Y. L. Tong.  The multivariate normal distribution , 1989 .

[30]  Jean-Michel Guldmann,et al.  Interactions between Weather Stochasticity and the Locations of Pollution Sources and Receptors in Air Quality Planning: A Chance- Constrained Approach , 2010 .

[31]  Ni-Bin Chang,et al.  A fuzzy goal programming approach for the optimal planning of metropolitan solid waste management systems , 1997 .

[32]  Hugh Ellis,et al.  Critical Loads and Development of Acid Rain Control Options , 1994 .

[33]  Edward A. McBean,et al.  A management model for acid rain abatement , 1983 .