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Enhanced-interval linear programming

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  • Zhou, Feng
  • Huang, Gordon H.
  • Chen, Guo-Xian
  • Guo, Huai-Cheng

Abstract

An enhanced-interval linear programming (EILP) model and its solution algorithm have been developed that incorporate enhanced-interval uncertainty (e.g., A±, B± and C±) in a linear optimization framework. As a new extension of linear programming, the EILP model has the following advantages. Its solution space is absolutely feasible compared to that of interval linear programming (ILP), which helps to achieve insight into the expected-value-oriented trade-off between system benefits and risks of constraint violations. The degree of uncertainty of its enhanced-interval objective function (EIOF) would be lower than that of ILP model when the solution space is absolutely feasible, and the EIOF's expected value could be used as a criterion for generating the appropriate alternatives, which help decision-makers obtain non-extreme decisions. Moreover, because it can be decomposed into two submodels, EILP's computational requirement is lower than that of stochastic and fuzzy LP models. The results of a numeric example further indicated the feasibility and effectiveness of EILP model. In addition, EI nonlinear programming models, hybrid stochastic or fuzzy EILP models as well as risk-based trade-off analysis for EI uncertainty within decision process can be further developed to improve its applicability.

Suggested Citation

  • Zhou, Feng & Huang, Gordon H. & Chen, Guo-Xian & Guo, Huai-Cheng, 2009. "Enhanced-interval linear programming," European Journal of Operational Research, Elsevier, vol. 199(2), pages 323-333, December.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:2:p:323-333
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    2. Simic, Vladimir & Dimitrijevic, Branka, 2013. "Risk explicit interval linear programming model for long-term planning of vehicle recycling in the EU legislative context under uncertainty," Resources, Conservation & Recycling, Elsevier, vol. 73(C), pages 197-210.
    3. Elif Garajová & Milan Hladík, 2019. "On the optimal solution set in interval linear programming," Computational Optimization and Applications, Springer, vol. 72(1), pages 269-292, January.
    4. Adil Baykasoğlu & Burcu Kubur Özbel, 2021. "Explicit flow-risk allocation for cooperative maximum flow problems under interval uncertainty," Operational Research, Springer, vol. 21(3), pages 2149-2179, September.
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    6. Mehdi Allahdadi & Aida Batamiz, 2021. "Generation of some methods for solving interval multi-objective linear programming models," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 1077-1115, December.

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