Abstract
In this paper, we have introduced a new approach to solve a class of interval linear programming (ILP) problems. Firstly, the novel concept of an interval ordering relation is further developed to make desired solution feasible. Secondly, according to the 3\(\upsigma \) law of normal distribution, a new equivalent transformation for constraints with the interval-valued coefficients of ILP is justified. Accordingly, the uncertainty stemmed from interval number could be replaced by the uncertainty of random variables. Consequently, the classical methodology of stochastic linear programming, a chance constrained programming model based on normal distribution is designed to work out the equivalent form of the original problem. This is because it allows us to carry out the optimization operation with a certain calibrated probability. A typical numerical example is given to illustrate how to apply equivalent transformation in order to realize ILP. Finally, we conclude this paper by elaborated comparisons among our method and selected existing solutions to advance our confidence of our research results as to their correctness and effectiveness.
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Acknowledgments
The work was supported in part by the Industrial Guidance Project of Fujian Province (No. 2015H0020), China Scholarship Council and the NSF Grant of USA (No. 1115564), as well as NCDOT Research Grant (No. 2013-13).
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Chen, M., Wang, SG., Wang, P.P. et al. A new equivalent transformation for interval inequality constraints of interval linear programming. Fuzzy Optim Decis Making 15, 155–175 (2016). https://doi.org/10.1007/s10700-015-9219-3
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DOI: https://doi.org/10.1007/s10700-015-9219-3