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
Due to pollution in second water supply system (SWSS),nine renovation alternative plans were proposed and com-prehensive evaluations of different plan based on Analytical Hierarchy Process (AHP) were presented in this...Due to pollution in second water supply system (SWSS),nine renovation alternative plans were proposed and com-prehensive evaluations of different plan based on Analytical Hierarchy Process (AHP) were presented in this paper. Comparisons of advantages and disadvantages among the plans of SWSS renovations provided solid foundation for selecting the most appro-priate plan for engineering projects. In addition,a mathematical model of the optimal combination of renovation plans has been set up and software Lingo was used to solve the model. As a case study,the paper analyzed 15 buildings in Tianjin City. After simulation of the SWSS renovation system,an optimal scheme was obtained,the result of which indicates that 10 out of those 15 buildings need be renovated in priority. The renovation plans selected for each building are the ones ranked higher in the com-prehensive analysis. The analysis revealed that the optimal scheme,compared with two other randomly calculated ones,increased the percentage of service population by 19.6% and 13.6% respectively,which significantly improved social and economical benefits.展开更多
A problem of a hierarchy structure optimization is considered.Hierarchical structures arewidely used in the Analytic Hierarchy Process,conjoint analysis,and various other methods of multiplecriteria decision making.Th...A problem of a hierarchy structure optimization is considered.Hierarchical structures arewidely used in the Analytic Hierarchy Process,conjoint analysis,and various other methods of multiplecriteria decision making.The problem consists in finding a structure that needs a minimum number ofpair comparisons for a given total number of the alternatives.For an optimal hierarchy,the minimumefforts are needed for eliciting data and synthesizing the local preferences across the hierarchy to getthe global priorities or utilities.Special estimation techniques are developed and numerical simulationsperformed.Analytical and numerical results suggest optimal ways of priority evaluations for practicalmanagerial decisions in a complex environment.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.
基金Project (No.033113111) supported by Tianjin Science Association Key Project,China
文摘Due to pollution in second water supply system (SWSS),nine renovation alternative plans were proposed and com-prehensive evaluations of different plan based on Analytical Hierarchy Process (AHP) were presented in this paper. Comparisons of advantages and disadvantages among the plans of SWSS renovations provided solid foundation for selecting the most appro-priate plan for engineering projects. In addition,a mathematical model of the optimal combination of renovation plans has been set up and software Lingo was used to solve the model. As a case study,the paper analyzed 15 buildings in Tianjin City. After simulation of the SWSS renovation system,an optimal scheme was obtained,the result of which indicates that 10 out of those 15 buildings need be renovated in priority. The renovation plans selected for each building are the ones ranked higher in the com-prehensive analysis. The analysis revealed that the optimal scheme,compared with two other randomly calculated ones,increased the percentage of service population by 19.6% and 13.6% respectively,which significantly improved social and economical benefits.
文摘A problem of a hierarchy structure optimization is considered.Hierarchical structures arewidely used in the Analytic Hierarchy Process,conjoint analysis,and various other methods of multiplecriteria decision making.The problem consists in finding a structure that needs a minimum number ofpair comparisons for a given total number of the alternatives.For an optimal hierarchy,the minimumefforts are needed for eliciting data and synthesizing the local preferences across the hierarchy to getthe global priorities or utilities.Special estimation techniques are developed and numerical simulationsperformed.Analytical and numerical results suggest optimal ways of priority evaluations for practicalmanagerial decisions in a complex environment.