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Interval Recourse Linear Programming for Resources and Environmental Systems Management under Uncertainty

G. H. Cheng1, G. H. Huang2,*, C. Dong1, B. W. Baetz3 and Y. P. Li4

  1. Center for Energy, Environment and Ecology Research, UR-BNU, Faculty of Engineering and Applied Science, University of Regina, Regina, Saskatchewan S4S 0A2, Canada
  2. Center for Energy, Environment and Ecology Research, UR-BNU, Beijing Normal University, Beijing 100875, China
  3. Faculty of Engineering, McMaster University, Ontario L8S 4L8, Canada
  4. State Key Laboratory of Water Environment Simulation, School of Environment, Beijing Normal University, Beijing 100875, China

*Corresponding author. Tel.: +1 306 5854095; fax: +1 306 3373205. Email address: (G. H. Huang).


An interval recourse linear programming (IRLP) approach is proposed in this study for mitigating constraint violation problems in resources and environmental systems management (REM) under interval uncertainties. Based on a review of interval linear programming (ILP) and its significances to REM, two linear programming sub-models are employed to initialize a decision space for IRLP. Causes of constraint violation are examined based on identification of a violation criterion. Contraction ratios are defined after revelation of violation ranges of constraints. As a recourse measure to constraint violation problems, another two linear programming sub-models are constructed given a series of contraction ratios. A hypercube decision space where infeasible solutions are excluded is obtained. Post-optimality analysis is conducted to deal with barriers for applying the IRLP approach to real-world ILP models for REM. An REM problem is introduced to demonstrate procedures and effectiveness of the IRLP approach. Comparisons with existing ILP methods reveal that the IRLP approach is effective at resolving the constraint-violation problem, reproducing the largest decision space which does not include infeasible solutions, and enhancing reliability of decision support for REM.

Keywords: resources and environmental management; interval linear programming; constraint violation

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