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

Abstract

Interval recourse linear programming (IRLP) is proposed 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 in IRLP. The 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 resolve 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. A postoptimality analysis is conducted to deal with the barriers for applying the IRLP approach to address real-world REM problems under interval uncertainties. A selected REM problem is introduced to demonstrate the procedures and effectiveness of the IRLP approach. Comparisons with existing ILP methods reveal that the IRLP approach is effective at avoiding constraint violation, reproducing the largest decision space which does not include infeasible solutions, and enhancing the reliability of decision support for REM.

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