The Solution of Interval Linear Programming with Max-min Satisfaction Degree

摘要

Linear programming (LP) is widely used and well-established tool in Operations Research and Management Science. In the practical applications, especially in the decision-making domain, we usually obtain the data that are lack of imprecision. in particular these obtained data are interval-valued numbers which are caused by computation soundings, confidence ranges or perdition errors. The problems of dealing with interval-valued numbers in LP is named Interval-Valued Linear Program (IVLP). Although the best and worst objective values of IVLP have been studied in the literature, a specific values of IVLP have been studied in the literature, a specific value within these two extremes must be selected for implementation. Instead of fixing the upper and lower bounds of interval coefficients to develop an extreme version, in this study, we proposed an intermediate version of interval relationship on inequalities, which applies a satisfaction index for each constraints and the objective function to reflect a risk-reverse strategy. Based on the principle of maximizing the minimal degree of all satisfaction functions, a generalized fractional programming (GFP) model was formulated. To solve this GFP problem, Dinkelbach-type-2 algorithm was employed. Finally, a numerical example was demonstrated. Because the proposed modeling approach utilizes the objective index to derive an acceptable solution, it nevertheless is quicker than the post-optimization approach in terms of sensitivity analysis or parametric programming.