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1、Logistics Decision Analysis Methods,Analytic Hierarchy ProcessTIAN Hong The Institute of Aeronautical Eng.T,Thomas L.Saaty,UNIVERSITY CHAIR,QUANTITATIVE GROUP Office:322 Mervis Hall Phone:412-648-1539E-mail:saatykatz.pitt.eduDegreesPhD in Mathematics,Yale University(1953)Postgraduate Study,Universit
2、y of Paris(195253),Prior to coming to the University of Pittsburgh,Thomas L.Saaty was professor at the Wharton School,University of Pennsylvania for 10 years and before that was for seven years in the Arms Control and Disarmament Agency at the U.S.State Department.He is a member of the National Acad
3、emy of Engineering.,He is the architect of the decision theory,the Analytic Hierarchy Process(AHP)and its generalization to decisions with dependence and feedback,the Analytic Network Process(ANP).He has published numerous articles and more than 12 books on these subjects.His nontechnical book on th
4、e AHP,Decision Making for Leaders,has been translated to more than 10 languages.His book,The Brain:Unraveling the Mystery of How It Works,generalizing the ANP further to neural firing and synthesis,appeared in the year 2000.,He is currently involved in extending his mathematical multicriteria decisi
5、on-making theory to how to synthesize group and societal influences.He is also developing the Super Decisions software that implements the ANP and it is available free at http:/,The AHP is used in both individual and group decision-making by business,industry,and governments and is particularly appl
6、icable to complex large-scale multiparty multicriteria decision problems The ANP has been applied to a variety of decisions involving benefits,costs,opportunities,and risks and is particularly useful in predicting outcomes.At the Katz School he teaches Decision Making in Complex Environments,using b
7、oth the AHP and the ANP and Creativity and Problem Solving.He has recently completed a book on the subject of creativity and problem solving that includes a CD of more than 140 colorful specially designed PowerPoint slides.,Motivation 1（动机之一）,In our complex world system,we are forced to cope with mo
8、re problems than we have the resources to handle.What we need is not a more complicated way of thinking but a framework that will enable us to think of complex problems in a simple way.The AHP provides such a framework that enables us to make effective decisions on complex issues by simplifying and
9、expediting our natural decision-making processes.,Motivation 2（动机之二）,Humans are not often logical creatures.Most of the time we base our judgments on hazy impressions（模糊的感觉）of reality and then use logic to defend（坚持）our conclusions.The AHP organizes feelings,intuition,and logic in a structured appro
10、ach to decision making.,Motivation 3（动机之三）,There are two fundamental approaches to solving problems:the deductive approach（演绎法）and the inductive(归纳法；or systems)approach.Basically,the deductive approach focuses on the parts whereas the systems approach concentrates on the workings of the whole.The AH
11、P combines these two approaches into one integrated,logic framework.,Introduction 1（介绍之一）,The analytic hierarchy process（AHP）was developed by Thomas L.Saaty.Saaty,T.L.,The Analytic Hierarchy Process,New York:McGraw-Hill,1980The AHP is designed to solve complex problems involving multiple criteria.An
12、 advantage of the AHP is that it is designed to handle situations in which the subjective judgments of individuals constitute an important part of the decision process.,Introduction 2（介绍之二）,Basically the AHP is a method of(1)breaking down a complex,unstructured situation into its component parts;(2)
13、arranging these parts,or variables into a hierarchic order;(3)assigning numerical values to subjective judgments on the relative importance of each variable;and(4)synthesizing the judgments to determine which variables have the highest priority and should be acted upon to influence the outcome of th
14、e situation.,Introduction 3（介绍之三）,The process requires the decision maker to provide judgments about the relative importance of each criterion and then specify a preference for each decision alternative on each criterion.The output of the AHP is a prioritized ranking（优先顺序排序）indicating the overall pr
15、eference for each of the decision alternatives.,Major Steps of AHP（主要步骤）,1)To develop a graphical representation of the problem in terms of the overall goal,the criteria,and the decision alternatives.(i.e.,the hierarchy of the problem)2)To specify his/her judgments about the relative importance of e
16、ach criterion in terms of its contribution to the achievement of the overall goal.3)To indicate a preference or priority for each decision alternative in terms of how it contributes to each criterion.4)Given the information on relative importance and preferences,a mathematical process is used to syn
17、thesize the information(including consistency checking)and provide a priority ranking of all alternatives in terms of their overall preference.,Constructing Hierarchies,Hierarchies are a fundamental mind toolClassification of hierarchiesConstruction of hierarchies,Establishing Priorities,The need fo
18、r prioritiesSetting prioritiesSynthesisConsistencyInterdependence,Advantages of the AHP,The AHP provides a single,easily understood,flexible model for a wide range of unstructured problems,The AHP integrates deductive and systems approaches in solving complex problems,The AHP can deal with the inter
19、dependence of elements in a system and does not insist on linear thinking,The AHP reflects the natural tendency of the mind to sort elements of a system into different levels and to group like elements in each level,The AHP provides a scale for measuring intangibles and a method for establishing pri
20、orities,The AHP tracks the logical consistency of judgments used in determining priorities,The AHP leads to an overall estimate of the desirability of each alternative,The AHP takes into consideration the relative priorities of factors in a system and enables people to select the best alternative ba
21、sed on their goals,The AHP does not insist on consensus but synthesizes a representative outcome from diverse judgments,The AHP enables people to refine their definition of a problem and to improve their judgment and understanding through repetition,Hierarchy Development MPG（油耗）,The first step in th
22、e AHP is to develop a graphical representation of the problem in terms of the overall goal,the criteria,and the decision alternatives.,Pairwise Comparisons,Pairwise comparisons are fundamental building blocks of the AHP.The AHP employs an underlying scale with values from 1 to 9 to rate the relative
23、 preferences for two items.,Pairwise Comparison Matrix,Element Ci,j of the matrix is the measure of preference of the item in row i when compared to the item in column j.AHP assigns a 1 to all elements on the diagonal of the pairwise comparison matrix.When we compare any alternative against itself(o
24、n the criterion)the judgment must be that they are equally preferred.AHP obtains the preference rating of Cj,i by computing the reciprocal(inverse)of Ci,j(the transpose position).The preference value of 2 is interpreted as indicating that alternative i is twice as preferable as alternative j.Thus,it
25、 follows that alternative j must be one-half as preferable as alternative i.According above rules,the number of entries actually filled in by decision makers is(n2 n)/2,where n is the number of elements to be compared.,Preference Scale 1（优先的尺度）,Preference Scale 2（优先顺序2）,Research and experience have
26、confirmed the nine-unit scale as a reasonable basis for discriminating between the preferences for two items.Even numbers(2,4,6,8)are intermediate values for the scale.A value of 1 is reserved for the case where the two items are judged to be equally preferred.,Synthesis（合成）,The procedure to estimat
27、e the relative priority for each decision alternative in terms of the criterion is referred to as synthesization（綜合；合成）.Once the matrix of pairwise comparisons has been developed,priority（優先次序；相對重要性）of each of the elements(priority of each alternative on specific criterion;priority of each criterion
28、 on overall goal)being compared can be calculated.The exact mathematical procedure required to perform synthesization involves the computation of eigenvalues and eigenvectors,which is beyond the scope of this text.,Procedure for Synthesizing Judgments,The following three-step procedure provides a go
29、od approximation of the synthesized priorities.Step 1:Sum the values in each column of the pairwise comparison matrix.Step 2:Divide each element in the pairwise matrix by its column total.The resulting matrix is referred to as the normalized pairwise comparison matrix.Step 3:Compute the average of t
30、he elements in each row of the normalized matrix.These averages provide an estimate of the relative priorities of the elements being compared.Example:,Example:Synthesizing Procedure-0,Step 0:Prepare pairwise comparison matrix,Example:Synthesizing Procedure-1,Step 1:Sum the values in each column.,Exa
31、mple:Synthesizing Procedure-2,Step 2:Divide each element of the matrix by its column total.All columns in the normalized pairwise comparison matrix now have a sum of 1.,Example:Synthesizing Procedure-3,Step 3:Average the elements in each row.The values in the normalized pairwise comparison matrix ha
32、ve been converted to decimal form.The result is usually represented as the(relative)priority vector.,Consistency-1,An important consideration in terms of the quality of the ultimate decision relates to the consistency of judgments that the decision maker demonstrated during the series of pairwise co
33、mparisons.It should be realized perfect consistency is very difficult to achieve and that some lack of consistency is expected to exist in almost any set of pairwise comparisons.Example:,Consistency-2,To handle the consistency question,the AHP provides a method for measuring the degree of consistenc
34、y among the pairwise judgments provided by the decision maker.If the degree of consistency is acceptable,the decision process can continue.If the degree of consistency is unacceptable,the decision maker should reconsider and possibly revise the pairwise comparison judgments before proceeding with th
35、e analysis.,Consistency Ratio,The AHP provides a measure of the consistency of pairwise comparison judgments by computing a consistency ratio（一致性比率）.The ratio is designed in such a way that values of the ratio exceeding 0.10 are indicative of inconsistent judgments.Although the exact mathematical co
36、mputation of the consistency ratio is beyond the scope of this text,an approximation of the ratio can be obtained.,Procedure:Estimating Consistency Ratio-1,Step 1:Multiply each value in the first column of the pairwise comparison matrix by the relative priority of the first item considered.Same proc
37、edures for other items.Sum the values across the rows to obtain a vector of values labeled“weighted sum.”Step 2:Divide the elements of the vector of weighted sums obtained in Step 1 by the corresponding priority value.Step 3:Compute the average of the values computed in step 2.This average is denote
38、d as lmax.,Procedure:Estimating Consistency Ratio-2,Step 4:Compute the consistency index(CI):Where n is the number of items being comparedStep 5:Compute the consistency ratio(CR):Where RI is the random index,which is the consistency index of a randomly generated pairwise comparison matrix.It can be
39、shown that RI depends on the number of elements being compared and takes on the following values.Example:,Random Index,Random index(RI)is the consistency index of a randomly generated pairwise comparison matrix.RI depends on the number of elements being compared(i.e.,size of pairwise comparison matr
40、ix)and takes on the following values:,Example:Inconsistency,Preferences:If,A B(2);B C(6)Then,A C(should be 12)(actually 8)Inconsistency,Example:Consistency Checking-1,Step 1:Multiply each value in the first column of the pairwise comparison matrix by the relative priority of the first item considere
41、d.Same procedures for other items.Sum the values across the rows to obtain a vector of values labeled“weighted sum.”,Example:Consistency Checking-2,Step 2:Divide the elements of the vector of weighted sums by the corresponding priority value.,Step 3:Compute the average of the values computed in step
42、 2(lmax).,Example:Consistency Checking-3,Step 4:Compute the consistency index(CI).,Step 5:Compute the consistency ratio(CR).,The degree of consistency exhibited in the pairwise comparison matrix for comfort is acceptable.,Development of Priority Ranking,The overall priority for each decision alterna
43、tive is obtained by summing the product of the criterion priority(i.e.,weight)(with respect to the overall goal)times the priority(i.e.,preference)of the decision alternative with respect to that criterion.Ranking these priority values,we will have AHP ranking of the decision alternatives.Example:,E
44、xample:Priority Ranking 0A,Step 0A:Other pairwise comparison matrices,Example:Priority Ranking 0B,Step 0B:Calculate priority vector for each matrix.,Example:Priority Ranking 1,Step 1:Sum the product of the criterion priority(with respect to the overall goal)times the priority of the decision alterna
45、tive with respect to that criterion.,Step 2:Rank the priority values.,Hierarchies:A Tool of the Mind,Hierarchies are a fundamental tool of the human mind.They involve identifying the elements of a problem,grouping the elements into homogeneous sets,and arranging these sets in different levels.Comple
46、x systems can best be understood by breaking them down into their constituent elements,structuring the elements hierarchically,and then composing,or synthesizing,judgments on the relative importance of the elements at each level of the hierarchy into a set of overall priorities.,Classifying Hierarch
47、ies,Hierarchies can be divided into two kinds:structural and functional.In structural hierarchies,complex systems are structured into their constituent parts in descending order according to structural properties(such as size,shape,color,or age).Structural hierarchies relate closely to the way our b
48、rains analyze complexity by breaking down the objects perceived by our senses into clusters,subclusters,and still smaller clusters.(more descriptive)Functional hierarchies decompose complex systems into their constituent parts according to their essential relationships.Functional hierarchies help pe
49、ople to steer a system toward a desired goal like conflict resolution,efficient performance,or overall happiness.(more normative)For the purposes of the study,functional hierarchies are the only link that need be considered.,Hierarchy,Each set of elements in a functional hierarchy occupies a level o
50、f the hierarchy.The top level,called the focus,consists of only one element:the broad,overall objective.Subsequent levels may each have several elements,although their number is usually small between five and nine.Because the elements in one level are to be compared with one another against a criter
