A min-max optimization method is proposed as a new approach to deal with the weight determination problem in the context of the analytic hierarchy process. The priority is obtained through minimizing the maximal absol...A min-max optimization method is proposed as a new approach to deal with the weight determination problem in the context of the analytic hierarchy process. The priority is obtained through minimizing the maximal absolute difference between the weight vector obtained from each column and the ideal weight vector. By transformation, the. constrained min- max optimization problem is converted to a linear programming problem, which can be solved using either the simplex method or the interior method. The Karush-Kuhn- Tucker condition is also analytically provided. These control thresholds provide a straightforward indication of inconsistency of the pairwise comparison matrix. Numerical computations for several case studies are conducted to compare the performance of the proposed method with three existing methods. This observation illustrates that the min-max method controls maximum deviation and gives more weight to non- dominate factors.展开更多
基金The US National Science Foundation (No. CMMI-0408390,CMMI-0644552,BCS-0527508)the National Natural Science Foundation of China (No. 51010044,U1134206)+2 种基金the Fok YingTong Education Foundation (No. 114024)the Natural Science Foundation of Jiangsu Province (No. BK2009015)the Postdoctoral Science Foundation of Jiangsu Province (No. 0901005C)
文摘A min-max optimization method is proposed as a new approach to deal with the weight determination problem in the context of the analytic hierarchy process. The priority is obtained through minimizing the maximal absolute difference between the weight vector obtained from each column and the ideal weight vector. By transformation, the. constrained min- max optimization problem is converted to a linear programming problem, which can be solved using either the simplex method or the interior method. The Karush-Kuhn- Tucker condition is also analytically provided. These control thresholds provide a straightforward indication of inconsistency of the pairwise comparison matrix. Numerical computations for several case studies are conducted to compare the performance of the proposed method with three existing methods. This observation illustrates that the min-max method controls maximum deviation and gives more weight to non- dominate factors.
