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1、8.3 The wide application of AHP The analytic hierarchy process was introduced into China in the early 1980s,and it was quickly accepted by the majority of applied mathematicians and technicians in related fields.In economic planning and management,energy policy and distribution,talent selection and
2、evaluation,production decision transportation,research topics,industrial structure,education,medical care,environment,military and other fields have been successfully applied.application areas:economic planning and management,energy policy and distribution,talent selection and evaluation,production
3、decision-making,transportation,research topics,industrial structure,education,medical treatment,environment,military,etc.types of problems handled:decision-making,evaluation,analysis,prediction,etc.key steps:the establishment of an analytic hierarchy model is a key step,with the participation of mai
4、n decision-makers.quantitative basis:constructing paired comparison matrix is quantitative basis and should be given by an experienced and strong expert.The following are some application examples of AHP to illustrate its wide application.problems of selecting of leading cadres Supposing a unit plan
5、 to select a leader from three cadres.The selection criteria include policy level,work style,business knowledge,eloquence,writing ability and health status.The following uses the AHP method to comprehensively evaluate and quantify the three people.hierarchical structure model diagram(1)establish hie
6、rarchical structure model(2)constructed to compare matrix and hierarchical orderAssume that the pairwise comparison matrix given by an evaluator ispolicy levelwork stylepolicy leveleloquencewriting abilitybusiness knowledgehealth conditionhealth conditionbusiness knowledgewriting abilityeloquencewor
7、k style(3)make consistency check and calculate weight vectorcalculate the maximum eigenvalue of pairwise comparison matrix A:the corresponding eigenvector is:consistency index,look-up table shows that the random consistency index RI=1.24.Assume that the paired comparison matrix of the three criteria
8、 for the selection of cadres with regard to health status and business knowledge is:The consistency ratio CR=0.07/1.24=0.0565 0.1,pass the consistency test.By this calculation,the maximum eigenvalue and corresponding eigenvector of each attribute(or standard)pairwise comparison matrix are as follows
9、:writing ability business knowledge health conditioneloquence policy level work styleeigenvaluehealth conditionbusiness knowledgewriting ability eloquencepolicy levelwork style3.02 3.02 3.05 3.05 3.00 3.02maximum eigenvalue table of each attributeEasy to verify,the above comparisons all passed the c
10、onsistency test.(4)calculate the combination weight vector and make a combination consistency testcombinating weight vector to calculateTherefore,among the three persons,the first person should be selected for the leadership position.After calculation,it can pass the combination consistency test.Her
11、e are some decision-making problems that can be handled by the AHP method:national comprehensive strengthnational incomemilitary forcetechnology levelsocial stabilityforeign tradeUnited States,Russia,China,Japan,Germany and other major countriesjob selectioncontribution income develo-pmentreputa-tio
12、nrelati-onshippositionposts for selectionExample 1 National strength analysisExample 2 Job selectionbenefits of crossing the river Aeconomic benefit B1social benefit B2environmental benefits B3bridge D1tunnel D2ferry D3(1)hierarchical structure of benefits of crossing river Example 3 The choice of c
13、rossing rivers and straitssave time C1incomeC2onshore commercial C3local business C4building employment C5safe and reliable C6communication C7sense of pride C8comfort C9easy access C10beautify C11cost of crossing the river Aeconomic cost B1environmental cost B3social cost B2invest fundsC1operation a
14、nd main-tenance C2shock the ferry indust-ry C3imp-act lifes-tyle C4hea-vy traf-fic C5resid-ent reloc-ationC6car emiss-ions C7wat-er poll-utionC8ecological damage C9bridge D1tunnel D2ferry D3(2)hierarchical structure of crossing costsExample 3 The choice of crossing rivers and straitsscience and tech
15、nology achievements to be evaluateddirect economic benefit C11indirect economic benefit C12social benefit C13knowledge level C21academic innovation C22techinque level C23technological innovation C24benefit C1level C2scaleC3evaluation of scientific and technological achievementsExample 4 Comprehensiv
16、e evaluation of scientific and technological achievements？How to solve the problem of difficult calculation of the eigenvalue and eigenvector of the positive reciprocal matrix?8.3 The wide application of AHPBarrage problem1.When the evaluator constructs the pairwise comparison matrix,is it mainly ba
17、sed on his subjective view?(correct)a.construction of pairwise comparison matrixb.calculation of matrix eigenvalues and eigenvectorsc.consistency check d.calculation of combined weight vectors2.The main difficulty in applying analytic hierarchy process to solve the problem of solution evaluation is _.（b）