Convex contractive interval linear programming for resources and environmental systems management

  • Guanhui Cheng
  • Guohe HuangEmail author
  • Cong Dong
Original Paper


It is likely that the most reliable estimation of system uncertainty in resources and environmental systems management (RESM) is a value range with an unknown distribution. Stochastic programming would be challenged by distortion of the original uncertain information through fabricating an inexistent probabilistic distribution function. Instead, interval linear programming (ILP), i.e. a synthesis of interval-set coefficients and the conventional linear programming, has been employed to identify the desired schemes for a number of RESM problems under interval uncertainty. However, its effectiveness is disabled by constraint violation which may lead to severe penalties on socio-economic or eco-environmental development. To mitigate such a challenge, a convex contractive interval linear programming (CCILP) approach is proposed in this study. It mainly consists of six modules: parameterizing an RESM problem as an ILP model, initializing a hyperrectangle decision space by two linear programming sub-models, revealing causes of constraint violation given a criterion, inferring feasibilities of potential solutions, finalizing a feasible hyperrectangle decision space by another linear programming sub-model, and supporting RESM of various complexities through alternative variants. A simple ILP model for RESM is introduced to demonstrate the procedures of CCILP and verify its advantages over existing ILP methods. The result indicates that CCILP is capable of robustly incorporating interval uncertainties into the optimization process, avoiding heavy computation burdens on complicated sub-models, eliminating occurrence of constraint violation, enabling provision of a hyperrectangle decision space, adapting to diverse system requirements, and increasing reliability of decision support for interval linear RESM problems.


Resources and environmental systems management Interval uncertainty Interval linear programming Constraint violation 



This research was supported by the Program for Innovative Research Team in University (IRT1127), the 111 Project (B14008) and the Natural Science and Engineering Research Council of Canada.


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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Faculty of Engineering and Applied ScienceUniversity of ReginaReginaCanada
  2. 2.Institute for Energy, Environment and Sustainability ResearchUniversity of ReginaReginaCanada

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