风险评价教学3AHP1.ppt

Logistics Decision Analysis MethodsAnalytic Hierarchy ProcessTIAN Hong The Institute of Aeronautical Eng. Tianhongde@Thomas L. SaatylUNIVERSITY CHAIR, QUANTITATIVE GROUP lOffice: 322 Mervis Hall Phone: 412-648-1539E-mail: saaty@katz.pitt.edulDegreesPhD in Mathematics, Yale University (1953) Postgraduate Study, University of Paris (1952–53) lPrior 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 Academy of Engineering.lHe 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 the 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. lHe is currently involved in extending his mathematical multicriteria decision-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 l lThe AHP is used in both individual and group decision-making by business, industry, and governments and is particularly applicable 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 both 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）动机之一）lIn our complex world system, we are forced to cope with more problems than we have the resources to handle.nWhat 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.èThe AHP provides such a framework that enables us to make effective decisions on complex issues by simplifying and expediting our natural decision-making processes.Motivation – 2（（动机之二）动机之二）lHumans are not often logical creatures.nMost 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.èThe AHP organizes feelings, intuition, and logic in a structured approach to decision making.Motivation – 3（（动机之三）动机之三）lThere are two fundamental approaches to solving problems: the deductive approach（演绎法）and the inductive (归纳法；or systems) approach.nBasically, the deductive approach focuses on the parts whereas the systems approach concentrates on the workings of the whole.èThe AHP combines these two approaches into one integrated, logic framework.Introduction – 1（（介绍之一）介绍之一）lThe analytic hierarchy process （AHP） was developed by Thomas L. Saaty.nSaaty, T.L., The Analytic Hierarchy Process, New York: McGraw-Hill, 1980lThe AHP is designed to solve complex problems involving multiple criteria.lAn 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）介绍之二）lBasically the AHP is a method of (1) breaking down a complex, unstructured situation into its component parts; (2) 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 the situation.Introduction – 3（（介绍之三）介绍之三）lThe 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.lThe output of the AHP is a prioritized ranking （优先顺序排序）indicating the overall preference for each of the decision alternatives.Major Steps of AHP（（主要步骤）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 each 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 synthesize the information (including consistency checking) and provide a priority ranking of all alternatives in terms of their overall preference.Constructing HierarchieslHierarchies are a fundamental mind toollClassification of hierarchieslConstruction of hierarchiesEstablishing PrioritieslThe need for prioritieslSetting prioritieslSynthesislConsistencylInterdependenceAdvantages of the AHPUnityProcess RepetitionTradeoffsSynthesisConsistencyMeasurementInterdependenceComplexityAHPJudgment and ConsensusHierarchic StructuringThe AHP provides a single, easily understood, flexible model for a wide range of unstructured problemsThe AHP integrates deductive and systems approaches in solving complex problemsThe AHP can deal with the interdependence of elements in a system and does not insist on linear thinkingThe AHP reflects the natural tendency of the mind to sort elements of a system into different levels and to group like elements in each levelThe AHP provides a scale for measuring intangibles and a method for establishing prioritiesThe AHP tracks the logical consistency of judgments used in determining prioritiesThe AHP leads to an overall estimate of the desirability of each alternativeThe AHP takes into consideration the relative priorities of factors in a system and enables people to select the best alternative based on their goalsThe AHP does not insist on consensus but synthesizes a representative outcome from diverse judgmentsThe AHP enables people to refine their definition of a problem and to improve their judgment and understanding through repetitionHierarchy Development MPG（（油耗）油耗）lThe first step in the AHP is to develop a graphical representation of the problem in terms of the overall goal, the criteria, and the decision alternatives.Car ACar BCar CCar ACar BCar CCar ACar BCar CCar ACar BCar CPriceMPGComfortStyleSelect the Best CarOverall Goal:Criteria:Decision Alternatives:Pairwise ComparisonslPairwise comparisons are fundamental building blocks of the AHP.lThe AHP employs an underlying scale with values from 1 to 9 to rate the relative preferences for two items.Pairwise Comparison MatrixlElement Ci,j of the matrix is the measure of preference of the item in row i when compared to the item in column j.lAHP assigns a 1 to all elements on the diagonal of the pairwise comparison matrix.nWhen we compare any alternative against itself (on the criterion) the judgment must be that they are equally preferred.lAHP obtains the preference rating of Cj,i by computing the reciprocal (inverse) of Ci,j (the transpose position).nThe preference value of 2 is interpreted as indicating that alternative i is twice as preferable as alternative j. Thus, it follows that alternative j must be one-half as preferable as alternative i.lAccording 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）优先的尺度）Preference Scale – 2（（优先顺序优先顺序2））lResearch and experience have confirmed the nine-unit scale as a reasonable basis for discriminating between the preferences for two items.nEven numbers (2, 4, 6, 8) are intermediate values for the scale. nA value of 1 is reserved for the case where the two items are judged to be equally preferred.Synthesis（（合成）合成）lThe procedure to estimate the relative priority for each decision alternative in terms of the criterion is referred to as synthesization（綜合；合成）.nOnce 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 on overall goal) being compared can be calculated.nThe 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 JudgmentslThe following three-step procedure provides a good 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.uThe resulting matrix is referred to as the normalized pairwise comparison matrix.Step 3: Compute the average of the elements in each row of the normalized matrix.uThese averages provide an estimate of the relative priorities of the elements being compared.Example:Example: Synthesizing Procedure - 0Step 0: Prepare pairwise comparison matrixComfortCar ACar BCar CCar A128Car B1/216Car C1/81/61Example: Synthesizing Procedure - 1Step 1: Sum the values in each column.ComfortCar ACar BCar CCar A128Car B1/216Car C1/81/61Column totals13/819/615Example: Synthesizing Procedure - 2Step 2: Divide each element of the matrix by its column total.nAll columns in the normalized pairwise comparison matrix now have a sum of 1.ComfortCar ACar BCar CCar A8/1312/198/15Car B4/136/196/15Car C1/131/191/15Example: Synthesizing Procedure - 3Step 3: Average the elements in each row.nThe values in the normalized pairwise comparison matrix have been converted to decimal form.nThe result is usually represented as the (relative) priority vector.ComfortCar ACar BCar CRow Avg.Car A0.6150.6320.5330.593Car B0.3080.3160.4000.341Car C0.0770.0530.0670.066Total1.000Consistency - 1lAn 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 comparisons.nIt 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.nExample:Consistency - 2lTo handle the consistency question, the AHP provides a method for measuring the degree of consistency among the pairwise judgments provided by the decision maker.nIf the degree of consistency is acceptable, the decision process can continue.nIf the degree of consistency is unacceptable, the decision maker should reconsider and possibly revise the pairwise comparison judgments before proceeding with the analysis.Consistency RatiolThe AHP provides a measure of the consistency of pairwise comparison judgments by computing a consistency ratio（一致性比率）.nThe ratio is designed in such a way that values of the ratio exceeding 0.10 are indicative of inconsistent judgments.nAlthough the exact mathematical computation of the consistency ratio is beyond the scope of this text, an approximation of the ratio can be obtained.Procedure: Estimating Consistency Ratio - 1Step 1: Multiply each value in the first column of the pairwise comparison matrix by the relative priority of the first item considered. Same procedures 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 denoted as lmax.Procedure: Estimating Consistency Ratio - 2Step 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 shown that RI depends on the number of elements being compared and takes on the following values.Example: Random IndexlRandom index (RI) is the consistency index of a randomly generated pairwise comparison matrix.nRI depends on the number of elements being compared (i.e., size of pairwise comparison matrix) and takes on the following values:n12345678910RI0.00 0.00 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49Example: InconsistencyPreferences: If, A  B (2); B  C (6)Then, A  C (should be 12) (actually 8) ØInconsistencyComfortCar ACar BCar CCar A128Car B1/216Car C1/81/61Example: Consistency Checking - 1Step 1: Multiply each value in the first column of the pairwise comparison matrix by the relative priority of the first item considered. Same procedures for other items. Sum the values across the rows to obtain a vector of values labeled “weighted sum.” Example: Consistency Checking - 2Step 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 2 (lmax).Example: Consistency Checking - 3Step 4: Compute the consistency index (CI).Step 5: Compute the consistency ratio (CR).èThe degree of consistency exhibited in the pairwise comparison matrix for comfort is acceptable.Development of Priority RankinglThe overall priority for each decision alternative 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.lRanking these priority values, we will have AHP ranking of the decision alternatives.lExample:Example: Priority Ranking – 0AStep 0A: Other pairwise comparison matricesComfortCar ACar BCar CCar A128Car B1/216Car C1/81/61PriceCar ACar BCar CCar A11/3¼Car B31½Car C421MPGCar ACar BCar CCar A11/41/6Car B411/3Car C631StyleCar ACar BCar CCar A11/34Car B317Car C1/41/71CriterionPriceMPGComfortStylePrice1322MPG1/311/41/4Comfort1/2411/2Style1/2421Example: Priority Ranking – 0BStep 0B: Calculate priority vector for each matrix.PriceMPGComfortStyleCar ACar BCar CCriterionPriceMPGComfortStyleExample: Priority Ranking – 1Step 1: Sum the product of the criterion priority (with respect to the overall goal) times the priority of the decision alternative with respect to that criterion.Step 2: Rank the priority values.AlternativePriorityCar B0.421Car C0.314Car A0.265Total1.000Hierarchies: A Tool of the MindlHierarchies are a fundamental tool of the human mind.nThey involve identifying the elements of a problem, grouping the elements into homogeneous sets, and arranging these sets in different levels.nComplex 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 HierarchieslHierarchies can be divided into two kinds: structural and functional.lIn structural hierarchies, complex systems are structured into their constituent parts in descending order according to structural properties (such as size, shape, color, or age).nStructural hierarchies relate closely to the way our brains analyze complexity by breaking down the objects perceived by our senses into clusters, subclusters, and still smaller clusters. (more descriptive)lFunctional hierarchies decompose complex systems into their constituent parts according to their essential relationships.nFunctional hierarchies help people to steer a system toward a desired goal – like conflict resolution, efficient performance, or overall happiness. (more normative)lFor the purposes of the study, functional hierarchies are the only link that need be considered.HierarchylEach set of elements in a functional hierarchy occupies a level of the hierarchy.nThe top level, called the focus, consists of only one element: the broad, overall objective.nSubsequent levels may each have several elements, although their number is usually small – between five and nine.uBecause the elements in one level are to be compared with one another against a criterion in the next higher level, the elements in each level must be of the same order of magnitude. (Homogeneity)èTo avoid making large errors, we must carry out clustering process. By forming hierarchically arranged clusters of like elements, we can efficiently complete the process of comparing the simple with the very complex.èBecause a hierarchy represents a model of how the brain analyzes complexity, the hierarchy must be flexible enough to deal with that complexity.Types of Functional HierarchylSome functional hierarchies are complete, that is, all the elements in one level share every property in the nest higher level.lSome are incomplete in that some elements in a level do not share properties.Constructing Hierarchies - 1lOne’s approach to constructing a hierarchy depends on the kind of decision to be made.nIf it is a matter of choosing among alternatives, we could start from the bottom by listing the alternatives. (decision alternatives => criteria => overall goal)lOnce we construct the hierarchy, we can always alter parts of it later to accommodate new criteria that we may think of or that we did not consider important when we first designed it. (AHP is flexible and time-adaptable)nSometimes the criteria themselves must be examined in details, so a level of subcriteria should be inserted between those of the criteria and the alternatives.Constructing Hierarchies - 2nIf one is unable to compare the elements of a level in terms of the elements of the next higher level, one must ask in what terms they can be compared and then seek an intermediate level that should amount to a breakdown of the elements of the next higher level.uThe basic principle in structuring a hierarchy is to see if one can answer the question: “Can you compare the elements in a lower level in terms of some all all the elements in the next higher level?”nThe depth of detail (in level construction) depends on how much knowledge one has about the problem and how much can be gained by using that knowledge without unnecessarily tiring the mind.èThe analytic aspects of the AHP serve as a stimulus to create new dimensions for the hierarchy. It is a process for inducing cognitive awareness. A logically constructed hierarchy is a by-product of the entire AHP approach.Constructing Hierarchies II - 1lWhen constructing hierarchies one must include enough relevant detail to depict the problem as thoroughly as possible.nConsider environment surrounding the problem.nIdentify the issues or attributes that you feel contribute to the solution.nIdentify the participants associated with the problem.lArranging the goals, attributes, issues, and stakeholders in a hierarchy serves two purposes:nIt provides an overall view of the complex relationships inherent in the situation.nIt permits the decision maker to assess whether he or she is comparing issues of the same order of magnitude in weight or impact on the solution.（我們無法直接比較蘋果與橘子；卻可以根據它們的甜度、營養、價格來決定誰是比較好的水果。

Constructing Hierarchies II - 2lThe elements should be clustered into homogeneous groups of five to nine so they can be meaningfully compared to elements in the next higher level.nThe only restriction on the hierarchic arrangement of elements is that any element in one level must be capable of being related to some elements in the next higher level, which serves as a criterion for assessing the relative impact of elements in the level below.nElements that are of less immediate interest can be represented in general terms at the higher levels of the hierarchy and elements critical to the problem at hand can be developed in greater depth and specificity.nIt is often useful to construct two hierarchies, one for benefits and one for costs to decide on the best alternative, particularly in the case of yes-no decisions.Constructing Hierarchies II - 3lSpecifically, the AHP can be used for the following kinds of decision problems:Choosing the best alternativesGenerating a set of alternativesSetting prioritiesMeasuring performanceResolving conflictsAllocating resources (Benefit/Cost Analysis)Making group decisionsPredicting outcomes and assessing risksDesigning a systemEnsuring system reliabilityDetermining requirementsOptimizingPlanninglClearly the design of an analytic hierarchy is more art than science. But structuring a hierarchy does require substantial knowledge about the system or problem in question.Need for Priorities - 1lThe analytical hierarchy process deals with both (inductive and deductive) approaches simultaneously.nSystems thinking (inductive approach) is addressed by structuring ideas hierarchically, and causal thinking (deductive approach) is developed through paired comparison of the elements in the hierarchy and through synthesis.nSystems theorists point out that complex relationships can always be analyzed by taking pairs of elements and relating them through their attributes. The object is to find from many things those that have a necessary connection.uThe object of the system approach (,which complemented the causal approach) is to find the subsystems or dimensions in which the parts are connected.Need for Priorities - 2lThe judgment applied in making paired comparisons combine logical thinking with feeling developed from informed experience.lThe mathematical process described (in priority development) explains how subjective judgments can be quantified and converted into a set of priorities on which decisions can be based.Setting Priorities - 1lThe first step in establishing the priorities of elements in a decision problem is to make pairwise comparisons, that is, to compare the elements in pairs against a given criterion.nThe (pairwise comparison) matrix is a simple, well-established tool that offers a framework for [1] testing consistency, [2] obtaining additional information through making all possible comparisons, and [3] analyzing the sensitivity of overall priorities to changes in judgment.Setting Priorities - 2lTo begin the pairwise comparison, start at the top of the hierarchy to select the criterion (or, goal, property, attribute) C, that will be used for making the first comparison. Then, from the level immediately below, take the elements to be compared: A1, A2, A3, and so on.lTo compare elements, ask: How much more strongly does this element (or activity) possess (or contribute to, dominate, influence, satisfy, or benefit) the property than does the element with which it is being compared?nThe phrasing must reflect the proper relationship between the elements in one level with the property in the next higher level.lTo fill in the matrix of pairwise comparisons, we use numbers to represent the relative importance of one element over another with respect to the property.Synthesis IIlTo obtain the set of overall priorities for a decision problem, we have to pull together or synthesize the judgments made in the pairwise comparisons, that is, we have to do weighting and adding to give us a single number to indicate the priority of each element.lThe procedure is described earlier.Consistency II - 1lIn decision making problems, it may be important to know how good our consistency is, because we may not want the decision to be based on judgments that have such low consistency that they appear to be random.lHow damaging is inconsistency? nUsually we cannot be so certain of our judgments that we would insist on forcing consistency in the pairwise comparison matrix (except diagonal ones).nAs long as there is enough consistency to maintain coherence among the objects of our experience, the consistency need not be perfect.uWhen we integrate new experiences into our consciousness, previous relationships may change and some consistency is lost.uIt is useful to remember that most new ideas that affect our lives tend to cause us to rearrange some of our preferences, thus making us inconsistent with our previous commitments.Consistency II - 2lThe AHP measure the overall consistency of judgments by means of a consistency ratio.lThe procedure for determining consistency ratios is described earlier.lGreater inconsistency indicates lack of information or lack of understanding.lOne way to improve consistency when it turns out to be unsatisfactory is to rank the activities by a simple order based on the weights obtained in the first run of the problem. nA second pairwise comparison matrix is then developed with this knowledge of ranking in mind. nThe consistency should generally be better.（由於已有先入為主看法）Backup MaterialsInterdependencelSo far we have considered how to establish the priority of elements in a hierarchy and how to obtain the set of overall priorities when the elements of each level are independent.lHowever, often the elements are interdependent, that is, there are overlapping areas or commonalities among elements.lThere are two principal kinds of interdependence among elements of a hierarchy level:nAdditive interdependencenSynergistic interdependenceAdditive InterdependencelIn additive interdependence（累加性依賴性）, each element contributes a share that is uniquely its own and also contributes indirectly by overlapping or interacting with other elements.nThe total impact can be estimated by [1] examining the impacts of the independent and the overlapping shares and then [2] combining the impacts.nIn practice, most people prefer to ignore the rather complex mathematical adjustment for additive interdependence and simply rely on their own judgment (putting higher priority on those elements having more impacts).Synergistic Interdependence - 1lIn synergistic interdependence（綜效性依賴性）, the impact of the interaction of the elements is greater than the sum of the impacts of the elements, with due consideration given to their overlap.nThis type of interdependence occurs more frequently than additive interdependence and amounts to creating a new entity for each interaction.nMuch of the problem of synergistic interdependence arises from the fuzziness of words and even the underlying ideas they represent.uThe qualities that emerge cannot be captured by a mathematical process (such as Venn diagrams). What we have instead is the overlap of elements with other elements to produce an element with new priorities that are not discernible in its parent parts.Synergistic Interdependence - 2lWith synergistic interdependence, one needs to introduce (for evaluation) additional criteria (new elements) that reveal the nature of the interaction.nThe overlapping elements should be separated from its constituent parts. Its impact is added to theirs at the end to obtain their overall impact. Synergy of interaction is also captured at the upper levels when clusters are compared according to their importancelNote that if we increase the elements being compared by one more element and attempt to preserve the consistency of their earlier ranking, we must be careful how we make comparisons with the new element.nOnce we compare one of the previous elements with a new one, all other relationships should be automatically set; otherwise there would be inconsistency and the rank order might be changed.Synergistic Interdependence - 3lThe AHP provides a simple and direct means for measuring interdependence in a hierarchy.nThe basic idea is that wherever there is interdependence, each criterion becomes an objective and all the criteria are compared according to their contributions to that criterion.nThis generates a set of dependence priorities indicating the relative dependence of each criterion on all the criteria.nThese priorities are then weighted by the independence priority of each related criterion obtained from the hierarchy and the results are summed over each row, thus yielding the interdependence weights.Synergistic Interdependence - 4lNote that prioritization from the top of the hierarchy downward includes less and less synergy as we move from the larger more interactive clusters to the small and more independent ones.lInterdependence can be treated in two ways.nEither the hierarchy is structured in a way that identifies independent elements or dependence is allowed for by evaluating in separate matrices the impact of all the elements on each of them with respect to the criterion being considered.Advantages of the AHPUnityJudgment and ConsensusProcess RepetitionTradeoffsSynthesisConsistencyMeasurementHierarchic StructuringInterdependenceComplexityAHPResearch IssueslHierarchy constructionnMethod to deal with interdependencenFuzziness in relationships among elements?lPriority settingnScale vs. other scaling methodsnHow to make subjective judgment more objectivelApplicationnPerformance measurement via AHP vs. DEAnNetwork vs. hierarchic structurelHow to deal with situation when subjective judgment depends on relative weight of the criterion based? AHP AHP决策分析方法决策分析方法  概 述 美国运筹学家T. L. Saaty于20世纪70年代提出的AHP决策分析法（Analytic Hierarchy Process，简称AHP方法），是一种定性与定量相结合的决策分析方法。

它常常被运用于多目标、多准则、多要素、多层次的非结构化的复杂决策问题，特别是战略决策问题的研究，具有十分广泛的实用性定性问题定量化定性问题定量化）AHP决策分析法，是一种将决策者对复杂问题的决策思维过程模型化、数量化的过程通过这种方法，可以将复杂问题分解为若干层次和若干因素，在各因素之间进行简单的比较和计算，就可以得出不同方案重要性程度的权重，从而为决策方案的选择提供依据本章节主要内容：lAHP决策分析方法的基本原理与计算方法决策分析方法的基本原理与计算方法l三个应用研究实例三个应用研究实例 1. 甘肃省两西地区扶贫开发战略决策定量分析甘肃省两西地区扶贫开发战略决策定量分析 2. 兰州市主导产业选择的决策分析兰州市主导产业选择的决策分析 3. 晋陕内蒙古三角地区晋陕内蒙古三角地区综合开发治理战略决策分析综合开发治理战略决策分析 §1 AHP决策分析的基本原理与计算方法 一、一、 基本原理基本原理 AHP决策分析方法的基本原理，可以用以下的简单事例分析来说明 假设有n个物体A1，A2，…，An，它们的重量分别记为W1，W2，…，Wn。

现将每个物体的重量两两进行比较如下： 若以矩阵来表示各物体的这种相互重量关系， A＝ A称为判断矩阵 若取重量向量W＝[W1，W2，… ， Wn]T，则有： AW＝n•WW是判断矩阵A的特征向量，n是A的一个特征值 根据线性代数知识可以证明，n是矩阵是矩阵A的唯一非零的，也是最大的特的唯一非零的，也是最大的特征值 l 上述事实告诉我们，如果有一组物体，需要知道它们的重量，而又没有衡器，那么就可以通过两两比较它们的相互重量，得出每一对物体重量比的判断，从而构成判断矩阵；然后通过求解判断矩阵的最大特征值λmax和它所对应的特征向量，就可以得出这一组物体的相对重量l这一思路提示我们这一思路提示我们—— 在复杂的决策问题研究中，对于一些无法度量的因素，只要引入合理的度量标度，通过构造判断矩阵，就可以用这种方法来度量各因素之间的相对重要性，从而为有关决策提供依据 这一思想，实际上就是AHP决策分析方法的基本思想，AHP决策分析方法的基本原理也由此而来。

二、二、AHP决策分析方法的基本过程决策分析方法的基本过程 AHP决策分析方法的基本过程，大体可以分为如下六个基本步骤： （（一一））明确问题明确问题即弄清问题的范围，所包含的因素，各因素之间的关系等，以便尽量掌握充分的信息 （（二二））建立层次结构模型建立层次结构模型 （（三三））构造判断矩阵构造判断矩阵 （（四四））层次单排序层次单排序 （（五五））层次总排序层次总排序 （（六六））一致性检验一致性检验 l在这一个步骤中，要求将问题所含的要素进行分组，把每一组作为一个层次，并将它们按照：最高层（目标层）——若干中间层（准则层）——最低层（措施层/方案层）的次序排列起来 l这种层次结构模型常用结构图来表示（图1.1），图中要标明上下层元素之间的关系二）建立层次结构模型建立层次结构模型图图1.1 AHP决策分析法层次结构示意图决策分析法层次结构示意图 n如果某一个元素与下一层的所有元素均有联系，则称这个元素与下一层次存在有完全层次的关系n如果某一个元素只与下一层的部分元素有联系，则称这个元素与下一层次存在有不完全层次的关系 n层次之间可以建立子层次，子层次从属于主层次中的某一个元素，它的元素与下一层的元素有联系，但不形成独立层次。

（三）构造判断矩阵三）构造判断矩阵 ①①判断矩阵表示针对上一层次中的某元素而言，评定该层次中各有关元素相对重要性（优先性）程度的判断其具体形式如下： 这一个步骤是这一个步骤是AHP决策分析中一个关键的步骤决策分析中一个关键的步骤②②其中，bij 表示对于A Ak k 而言，元素Bi 对Bj 的相对重要性程度的判断值 一般取1，3，5，7，9等5个等级标度，其意义为：1表示Bi与B j同等重要；3表示Bi较B j重要一点；5表示Bi较B j重要得多；7表示Bi较B j更重要；9表示Bi较B j极端重要 而2，4，6，8表示相邻判断的中值，当5个等级不够用时，可以使用这几个数 ③③ 显然，显然，对于任何判断矩阵都应满足 （i，j＝1，2，…，n） ④④ 一般而言，判断矩阵的数值判断矩阵的数值 是根据数据资料、专家意见和分析者的认识，加以平衡后给出的 ⑤⑤ 如果判断矩阵存在关系： bij＝ （i，j，k＝1，2，3，…，n）则称它具有完全一致性。

为了考察AHP决策分析方法得出的结果是否基本合理，需要对判断矩阵进行一致性检验 四、层次单排序①①目的目的：确定本层次与上层次中的某元素有联系的各元素重要性次序的权重值 ②②任务任务：计算判断矩阵的特征根和特征向量即对于判断矩阵B，计算满足： （1.5）的特征根和特征向量 在（1.5）式中，λmax为判断矩阵B的最大特征根，W为对应于λmax的正规化特征向量，W的分量Wi就是对应元素单排序的权重值  通过前面的分析，我们知道，如果判断矩阵B具有完全一致性时，λmax＝n但是，在一般情况下是不可能的为了检验判断矩阵的一致性，需要计算它的一致性指标： ③③检验判断矩阵的一致性：检验判断矩阵的一致性：（1.6） 在（1.6）式中，当CI＝0时，判断矩阵具有完全一致性；反之，CI愈大，就表示判断矩阵的一致性就越差  为了检验判断矩阵是否具有令人满意的一致性，需要将CI与平均随机一致性指标RI（见表8.1.1）进行比较 一般而言，1或2阶的判断矩阵总是具有完全一致性的。

对于2阶以上的判断矩阵，其一致性指标CI与同阶的平均随机一致性指标RI之比，称为判断矩阵的随机一致性比例，记为CR 一般地，当 （8.1.7） 时，就认为判断矩阵具有令人满意的一致性；否则，当CR 0.1时，就需要调整判断矩阵，直到满意为止 表表1.1 平均随机一致性指标平均随机一致性指标 五、层次总排序①①定义定义：利用同一层次中所有层次单排序的结果，就可以计算针对上一层次而言，本层次所有元素的重要性权重值，这就称为层次总排序 ②②层次总排序需要从上到下逐层顺序进行对于最高层而言，其层次单排序的结果也就是总排序的结果 假如上一层的层次总排序已经完成，元素A1，A2，…，Am得到的权重值分别为a1，a2，…，am；与Aj对应的本层次元素B1，B2，…，Bn的层次单排序结果为[ ]T（当Bi与Aj无联系时， ＝0）；那么，B层次的总排序结果见表1.2 表表8.1.2 8.1.2 层次总排序表层次总排序表 显然： （8.1.8）即层次总排序是归一化的正规向量。

CI＝RI＝CR＝ CI为层次总排序的一致性指标；CIj为与aj对应的B层次中判断矩阵的一致性指标；RI为层次总排序的随机一致性指标；RIj为与aj对应的B层次中判断矩阵的随机一致性指标；CR为层次总排序的随机一致性比例六)、层次总排序的一致性检验 为了评价层次总排序结果的一致性，类似于层次单排序，也需要进行一致性检验为此，需要分别计算下列指标：  当CR<0.10时，则认为层次总排序的计算结果具有令人满意的一致性；否则，就需要对本层次的各判断矩阵进行调整，直至层次总排序的一致性检验达到要求为止 返回返回三、计算方法 通过前面的介绍，我们知道，在AHP决策分析方法中，最根本的计算任务是求解判断矩阵的最大特征根最大特征根 及其所对应的特征向量特征向量 这些问题可以用线性代数知识去求解，并且能够利用计算机求得任意高精度的结果但事实上，在AHP决策分析方法中，判断矩阵的最大特征根及其对应的特征向量的计算，并不需要追求太高的精度这是因为判断矩阵本身就是将定性问题定量化的结果，允许存在一定的误差范围。

l  常常用如下两种近似算法求解判断矩阵的最大特征根及其所对应的特征向量n方根法方根法 n和积法和积法 (1) 方根法 l计算判断矩阵每一行元素的乘积 l计算 的n次方根 l将向量 ＝ 归一化： 则 即为所求的特征向量 l计算最大特征根 表示向量AW的第个分量 (2) 和积法l将判断矩阵每一列归一化： l对按列归一化的判断矩阵，再按行求和： l将向量 ＝ 归一化： 则 即为所求的特征向量 l计算最大特征根： 表示向量AW的第个分量 四、对AHP方法的简单评价 优点优点：思路简单明了，它将决策者的思维过程条理化、数量化，便于计算，容易被人们所接受 所需要的定量化数据较少，但对问题的本质，问题所涉及的因素及其内在关系分析得比较透彻、清楚。

缺点缺点：存在着较大的随意性 譬如，对于同样一个决策问题，如果在互不干扰、互不影响的条件下，让不同的人同样都采用AHP决策分析方法进行研究，则他们所建立的层次结构模型、所构造的判断矩阵很可能是各不相同的，分析所得出的结论也可能各有差异  为了克服这种缺点，在实际运用中，特别是在多目标、多准则、多要素、多层次的非结构化的战略决策问题的研究中，对于问题所涉及的各种要素及其层次结构模型的建立，往往需要多部门、多领域的专家共同会商、集体决定；在构造判断矩阵时，对于各个因素之间的重要程度的判断，也应该综合各个专家的不同意见，譬如，取各个专家的判断值的平均数、众数或中位数判断值的平均数、众数或中位数层次分析法建模举例1 1旅游问题旅游问题2(1)建立层次模型分别分别表示景色、费用、居住、饮食、旅途分别表示德国、意大利、法国 （2）构造成对比较矩阵(3)计算层次单排序的权向量和一致性检验成对比较矩阵 的最大特征值表明 通过了一致性验证故则该特征值对应的归一化特征向量 对成对比较矩阵 可以求层次总排序的权向量并进行一致性检验，结果如下： 计算 可知 通过一致性检验。

对总目标的权值为：（4）计算层次总排序权值和一致性检验又决策层对总目标的权向量为：同理得， 对总目标的权值分别为：故，层次总排序通过一致性检验可作为最后的决策依据故最后的决策应为去法国法国又 分别表示德国、意大利、法国，即各方案的权重排序为四四 层次分析法的优点和局限性层次分析法的优点和局限性1 、系统性 层次分析法把研究对象作为一个系统，按照分解、比较判断、综合的思维方式进行决策，成为继机理分析、统计分析之后发展起来的系统分析的重要工具 2 、实用性 层次分析法把定性和定量方法结合起来，能处理许多用传统的最优化技术无法着手的实际问题，应用范围很广，同时，这种方法使得决策者与决策分析者能够相互沟通，决策者甚至可以直接应用它，这就增加了决策的有效性3 简洁性 具有中等文化程度的人即可以了解层次分析法的基本原理并掌握该法的基本步骤，计算也非常简便，并且所得结果简单明确，容易被决策者了解和掌握以上三点体现了层次分析法的优点，该法的局限性主要表现在以下几个方面：第一第一 只能从原有的方案中优选一个出来，没有办法得出更好的新方案。

第二第二 该法中的比较、判断以及结果的计算过程都是粗糙的，不适用于精度较高的问题第三第三 从建立层次结构模型到给出成对比较矩阵，人的主观因素对整个过程的影响很大，这就使得结果难以让所有的决策者接受当然采取专家群体判断的办法是克服这个缺点的一种途径思考：多名专家的综合决策问题思考：多名专家的综合决策问题 ？？？？？？五五 正互反阵最大特征值和特征向量实用算法正互反阵最大特征值和特征向量实用算法用定义计算矩阵的特征值和特征向量相当困难，特别是阶数较高时；成对比较矩阵是通过定性比较得到的比较粗糙的结果，对它的精确计算是没有必要的寻找简便的近似方法定理定理对于正矩阵 A （A的所有元素为正）1） A 的最大特征根为正单根 ；2） 对应正特征向量 w（w的所有分量为正）；3）其中是对应 的归一化特征向量1 幂法幂法 步骤如下a) 任取 n 维归一化初始向量b) 计算c) 归一化，即令d) 对于预先给定的精度 ，当下式成立时即为所求的特征向量；否则返回b；e) 计算最大特征值这是求特征根对应特征向量的迭代方法迭代方法，其收敛性由定理的3）保证。

2 和法和法 步骤如下a) 将A的每一列向量归一化得b) 对c) 归一化按行求和得d) 计算3 根法根法步骤与和法基本相同，只是将步骤 b 改为对按行求积并开n次方，即三方法中，和法最为简便看下列例子e) 计算，最大特征值的近似值列向量归一化求和归一化精确计算，得§2 AHP决策分析方法应用实例 l甘肃省两西地区扶贫开发战略决策定量分析甘肃省两西地区扶贫开发战略决策定量分析 l兰州市主导产业选择的决策分析兰州市主导产业选择的决策分析 l晋陕蒙三角地区综合开发治理战略决策分析晋陕蒙三角地区综合开发治理战略决策分析 一、甘肃省两西地区扶贫开发战略决策定量分析  甘肃省两西地区，包括以定西为代表的中部半干旱区及以河西走廊干旱区 其中，中部地区，属黄土高原西部半干旱区，资源贫乏，生态环境脆弱，植被稀少，水土流失严重，自然灾害频繁，人口严重超载，经济、文化落后，是一个集中连片的区域性贫困地区 河西走廊地区，地处西北干旱区，降水稀少，水资源紧缺，荒漠面积广阔，沙漠化严重，人口稀少；然而，丰富的光热资源、发源于祁连山冰川的灌溉水源以及成片的宜农荒地孕育了历史悠久绿洲农业，独特的自然风光（如，七一冰川等）和丝绸古道上的历史文化遗产（如，敦煌莫高窟等）是国内外著名的旅游景点，我国著名的镍都——金昌市与钢铁工业基地之一——嘉峪关市也位于本区。

（1）总目标总目标：A —— 使甘肃省两西地区稳定解决温饱， 彻底脱贫致富，改变落后面貌2）战略目标战略目标，包括： O1 —— 改善生态环境，力争达到良性循环； O2 —— 发展大农业生产； O3 —— 积极发展第二、三产业一）层次结构模型（3）发展战略，包括： C1 —— 移民； C2 —— 建设河西商品粮基地；C3 —— 建设中部自给粮基地；C4 —— 种树种草，大力发展林牧业；C5 —— 扩大经济作物种植面积，发展名优农副生产基地；C6 —— 充分利用当地资源，发展多样化产业4）制约因素制约因素，有： S1 —— 资金不足； S2 —— 水资源不足； S3 —— 有效灌溉面积不足； S4 —— 技术力量缺乏（包括农业技术人员、工程技术人员、科研人员、教员等）；S5 —— 交通运输条件差；S6 —— 自然条件恶劣，自然灾害频繁，水土流失严重；  S7 —— 饲料严重不足； S8 —— 人口自然增长率高。

5）方针措施方针措施，包括： P1 —— 国家投入专项基金； P2 —— 省财政设立农业专项开发资金； P3 —— 当地对资源实行有偿使用，以便积累资金； P4 —— 向国际金融机构申请贷款； P5 —— 采取联合开发的方式，弥补资金、技术力量的不足； P6 —— 实施高扬程引黄提灌工程； P7 —— 积极修建河西蓄水工程； P8 —— 开采地下水资源； P9 —— 发展节水农业，提高水资源利用率；  P10 —— 开垦荒地； P11 —— 建设基本农田； P12 —— 努力提高粮食单产； P13 —— 退耕还林、还牧； P14 —— 开展科技培训、提高劳动者科技素质； P15 —— 建立健全科技服务网络； P16 —— 兴办集体企业，壮大集体经济实力； P17 —— 改善公路运输条件，兴建公路； P18 —— 修建铁路，提高铁路运输能力； P19 —— 抓紧抓好计划生育工作 根据上述各因素及其之间的相互关系，可以建立如图8.2.1所示的决策层次结构模型。

O1O2O3C1C2C3C6C5C4AS1S2S4S3S5S6S7S8P1P2P3P4P5P6P7P8P9P10P11P12P13P14P15P16P17P18P19图图8.2.1 8.2.1 甘肃省两西地区扶贫开发战略决策分析层次结构模型甘肃省两西地区扶贫开发战略决策分析层次结构模型（二）模型计算 ①① 计算三个战略目标O1，O2，O3的相对权重（既是层次单排序，也是层次总排序）——它们表示各战略目标对实现总目标的重要程度 ②② 计算每一个发展战略C1，C2，……，C6对每个战略目标的相对权重（层次单排序），并用O1，O2，O3的权重对发展战略的相应权重加权后相加，计算各发展战略的组合权重（层次总排序）——它们表示各发展战略对实现总目标的重要程度 ③③ 计算每个制约因素S1，S2，……，S8对每个发展战略的相对权重（层次单排序），并用发展战略C1，C2，……，C6的组合权重对制约因素的相应权重加权后相加，计算各制约因素的组合权重（层次总排序）——它们表示各制约因素对实现总目标的制约程度 ④④ 计算各方针措施P1，P2，……，P19对每个制约因素的相对权重（层次单排序），并用各制约因素的组合权重对措施的相应权重加权后相加，计算各方针措施的组合权重（层次总排序），——它们表示各方针措施对实现总目标重要程度。

权重越大越重要，因此在实现总目标的过程中，应该首先考虑实施那些权重较大的措施计算结果：计算结果：（（1）） A—O判断矩阵及单判断矩阵及单/总层次排序结果总层次排序结果 λ=3.018，，CI=0.009，，RI=0.58，， CR=0.015<0.10 （（2））O1-C判断矩阵及层次单排序结果判断矩阵及层次单排序结果λ=5.179，CI=0.045，RI=1.12，CR=0.040<0.10 （（3）） O2-C判断矩阵及层单排序结果判断矩阵及层单排序结果λ=6.524，CI=0.105，RI=1.24，CR=0.085<0.10（（4））O3-C判断矩阵及层次单排序结果判断矩阵及层次单排序结果 λ=2，CI=RI=0 （（5 5））发展战略的层次总排序结果发展战略的层次总排序结果 CI=0.059，RI=1.022，CR=0.058<0.10（（6）） C1—S判断矩阵及层次单排序结果判断矩阵及层次单排序结果 λ=4.259，CI=0.086，RI=0.9，CR=0.096<0.10  （（7））C2—S判断矩阵及层次单排序结果 λ=4.145，CI=0.048，RI=0.9，CR=0.047<0.10（（8）） C3—S判断矩阵及层次单排序结果判断矩阵及层次单排序结果 λ=6.290，CI=0.058，RI=1.24，CR=0.047<0.10 （（9））C4—S判断矩阵及层次单排序结果 λ=5.338，CI=0.084，RI=1.12，CR=0.075<0.10（（10））C5—S判断矩阵及层次单排序结果判断矩阵及层次单排序结果 λ=5.314，CI=0.078，RI=1.12，CR=0.07<0.10 （（11））C6—S判断矩阵及层次单排序结果判断矩阵及层次单排序结果 λ=3.01，CI=0.005，RI=0.58，CR=0.009<0.10（（12））制约因素的层次总排序结果制约因素的层次总排序结果 CI=0.063，RI=0.956，CR=0.066<0.10 （（13））S1—P判断矩阵及层次单排序结果判断矩阵及层次单排序结果 λ=6.394，CI=0.079，RI=1.24，CR=0.064<0.10（（14））S2—P判断矩阵及层次单排序结果判断矩阵及层次单排序结果 λ=4.143，CI=0.048，RI=0.9，CR=0.053<0.10 （（15））S3—P判断矩阵及层次单排序结果 λ=5.183，CI=0.046，RI=1.12，CR=0.041<0.10（（16））S4—P判断矩阵及层次单排序结果判断矩阵及层次单排序结果 λ=3.054，CI=0.027，RI=0.58，CR=0.046<0.10 （（17））S5—P判断矩阵及层次单排序结果判断矩阵及层次单排序结果 （（18））S6—P判断矩阵及层次单排序结果判断矩阵及层次单排序结果 （（19））S7—P13：W=1，λ=1，CI=RI=0（（20）） S8—P19：W=1，λ=1，CI=RI=0 λ=2，CI=RI=0 λ=2，CI=RI=0（（21））方针措施的层次总排序结果方针措施的层次总排序结果( (见下页）见下页） CI=0.054，RI=0.952，CR=0.057<0.10 （三）结果分析 （1）从战略目标来看，要实现两西地区扶贫开发的总目标， 首先要积极改善生态环境，尽快恢复生态平衡，使之走上良性循环的轨道，其权重为0.558；但必须采取开发与治理并重的总方针，边开发边治理，以开发促治理，大力发展农业生产，计算结果表明这一目标的权重为0.320，其重要程度处在第二位。

当然，第二、第三产业的发展也应得到相应的重视，其权重为0.122  （2）从发展战略上来讲，首先要在定西地区继续实施以扶贫为目标的移民工程，其权重为0.262；河西商品粮基地的建设与发展也占有举足轻重的地位，其权重为0.220；两区积极发展林业和畜牧业也应放到重要的位置上来，权重值为0.168 随着两区社会经济的不断发展，建设名优农副产品基地和积极发展乡镇企业这两条战略的重要性将逐渐显示出来，其权重值分别为0.128和0.127 定西地区的粮食生产基地也有待积极建设，保证自给，缓解粮食供求的紧张局面，其权重值为0.094  （3）从制约因素来看，资金短缺这一点对两西地区扶贫开发影响最大，其权重为0.472；水资源不足与有效灌溉面积不足也是两个至关重要的问题，二者的权重分别为0.172和0.147；技术力量不足，交通运输条件差也对总目标的实现有较为严重的制约，其权重分别为0.081和0.051；饲料严重不足，自然条件恶劣、人口自然增长率高三者的权重分别为0.036、0.023和0.016  （4）从方针措施来看，当前急待解决的几个问题： ①① 采取联合开发的形式，弥补资金、技术力量的不足，权重为0.193；②② 省财政继续设立农业专项开发资金，权重为0.119； ③③ 继续实施高扬程引黄灌溉工程，解决中部严重缺水的问题，权重为0.072； ④④ 在以河西为重点的两西地区，积极发展节水农业，各行业应努力提高水资源利用率，权重为0.069； ⑤⑤ 退耕还林、还牧、保持生态平衡，控制水土流失，积极发展林牧业，其权重值为0.065； ⑥⑥ 国家投入专项扶贫资金，以及向国际金融机构申请贷款，对于筹集资金也很重要，二者的权重均为0.058；⑦⑦ 积极开垦荒地、加强资源的有偿使用，提高使用效益，逐步积累基金，建设基本农田，继续修建河西蓄水工程，改建或新建公路这五条措施也是需要抓紧抓好、尽快落实的几点措施，它们的权重依次为0.055，0.0554，0.052，0.036和0.034；⑧⑧ 从长远角度考察，为了克服两西扶贫开发中的阻碍还需要采取的一些措施有：兴办集体企业，壮大集体经济实力；对劳动力积极培训；开采地下水资源；提高铁路运输能力；抓紧抓好计划生育工作；建立健全科技服务网络；努力提高单产等等。

二、兰州市主导产业选择的决策分析 地处甘肃省中部、黄河上游的兰州市，是甘肃省的省会，全省政治、经济、文化、医疗卫生、教育和科技中心兰州经济的发展，无疑在全省、乃至全国占有着十分重要的地位在国家实施西部大开发战略之际，兰州究竟如何抓住时机，发挥地区优势，促进城市经济的全面发展，并使之尽快成为中国西北地区的核心增长极？ 为了解决这一问题，必须以市场为导向，结合本市的自然、经济、社会和技术条件，综合各种有利和不利因素，选择一批能发挥地区优势，具有较高效益的主导产业，从而带动全市经济的腾飞 n目标层（A）： 选择带动兰州市经济全面发展的主导产业 n准则层（C）： 主导产业选择的准则，主要应该以如下三个方面的准则为判断标准： C1 —— 市场需求（包括市场需求现状和远景市场潜力）； C2 —— 效益准则（这里主要考虑产业的经济效益） ；C3 —— 发挥地区优势，合理利用资源 （一）层次结构模型（一）层次结构模型l 对象层（P） 主导产业选择的对象主要包括如下十四个方面： P1 —— 能源工业 P2 —— 交通运输业P3 —— 冶金工业 P4 —— 化工工业P5 —— 纺织工业 P6 —— 建材工业P7 —— 建筑业 P8 —— 机械工业P9 —— 食品加工业 P10 ——信息产业 P11 —— 电器电子工业 P12 —— 农业P13 —— 旅游业 P14 —— 饮食服务 图图8.2.2 8.2.2 兰州市主导产业选择的兰州市主导产业选择的AHPAHP层次结构图层次结构图 （二）模型计算过程 l构造判断矩阵A－C 、C－P ，进行层次单排序。

λmax=3.038，CI=0.019，RI=0.58，CR=0.0328<0.10表表8.2.208.2.20 A－－C判断矩阵及排序结果判断矩阵及排序结果 表表8.2.21 C1－－P判断矩阵及层次单排序结果判断矩阵及层次单排序结果 λmax =15.65，CI=0.127，RI=1.58 ，CR=0.0804<0.10 表表8.2.22 C2－－P判断矩阵及层次单排序结果判断矩阵及层次单排序结果 λmax =15.94，CI=0.149，RI=1.58，CR=0.0943<0.10 表表8.2.23 C3－－P判断矩阵及层次单排序结果判断矩阵及层次单排序结果 λmax =15.64，CI=0.126，RI=1.58，CR=0.0797<0.10 l层次总排序层次总排序表表8.2.24 对象层（对象层（P））的层次总排序结果的层次总排序结果 （三）基本结论 l从准则层的排序结果来看，兰州市主导产业选择，首先考虑产业的效益（主要是经济效益）；其次考虑市场需求和远景市场潜力；第三考虑发挥地区优势和资源合理利用问题 l从对象层总排序的结果来看，兰州市主导产业选择的先后顺序应该是：P1（能源工业）> P2（交通运输业）> P4（化工工业）> P3（冶金工业）> P5（纺织工业）> P7（建筑业）> P11（电器、电子工业）> P8（机械工业）> P12（农业）> P6（建材工业）> P10（信息产业）> P13（旅游业）> P14（饮食服务业）> P9（食品加工业）。

 三、晋陕内蒙古三角地区 综合开发治理战略决策分析 晋陕蒙三角地区包括山西省的河曲、保德、偏关、兴县，陕西省的神木、府谷、榆林县，内蒙古自治区德伊金霍洛旗、东胜市、准格尔旗、清水河县、达拉特旗，共12个县（市，旗） 本区自然环境恶劣，水资源缺乏，水土流失及风沙危害严重，农、林、牧业都不发达但是，本区煤炭资源十分丰富，拥有我国和世界上罕见的特大煤田，探明储量共计2576亿吨为了给本区综合开发治理决策提供依据 倪建华等（1992）曾运用AHP决策分析法，按总目标、战略目标、发展战略、制约因素和方针措施等五个层次，分析了它们之间的相互联系与相互制约关系，计算出了各层的相对权重，从而得出了这些因素对实现总目标影响的重要程度，为制定切实可行的方针措施和克服不利因素提供了必要的依据 （一）模型的层次结构 l总目标：对晋陕蒙三角地区进行综合开发与治理 l战略目标： O1 ——煤炭开发；O2 —— 发展农林牧生产；O3 —— 改善生态环境，力争达到良性循环l发展战略：C1——发展统配煤矿； C2——发展地方、乡镇煤矿； C3——发展电力工业； C4——发展重工业、化工工业； C5——发展地方工业乡镇企业； C6——发展粮食生产； C7——建设肉蛋奶基地； C8——建设果品蔬菜基地； C9——水土保持； C10——沙漠化治理。

l制约因素 S1——运输能力低下；S2——资金严重不足； S3——人力、技术力量（包括技术工人，工程技术人员，科研人员，教员等）缺乏；S4——水资源不足；  S5——地方乡镇经济不发达； S6——粮食及农副畜产品供应紧张； S7——水土流失严重，风沙危害大； S8——厂矿建设要占用大部分良田l方针措施 ：P1 —— 引入国外资金，引进技术；P2 —— 国家投资； P3 —— 地方集资； P4 —— 现有水资源开发节流，合理使用； P5 —— 引黄河水； P6 —— 开发地下水； P7——种草种树，发展畜牧；P8——加强农田基建，提高单产；P9 —— 对可能污染环境的厂矿，提前采取措施；P10 —— 各省内自行解决人才、技术问题；P11 —— 从全国引进人才，引进技术；P12 —— 本地区自行解决人才、技术问题；P13 —— 各省内解决农副畜产品供应问题；P14 —— 地方解决粮食供应；P15 —— 省内解决粮食供应；P16 —— 从全国调人粮食；P17 —— 改善公路运输条件，新建公路；P18 —— 修建铁路；P19 —— 对重点工矿，加强水保工作及沙化治理。

图图8.2.3 晋陕蒙三角地区综合开发治理战略决策模型层次结构图晋陕蒙三角地区综合开发治理战略决策模型层次结构图 （二）模型计算及结果 l计算3个战略目标O1，O2，O3的相对权重及每个发展战略C1，C2，…，C10 对每个战略目标的相对权重，并用O1，O2，O3的权重对发展战略的相对权重加权后相加，得到各发展战略C1，C2，…，C10的组合权重，它们表示各发展战略对实现总目标的重要程度计算结果见表8.2.25 表表8.2.25 8.2.25 l计算每个制约因素S1，S2，…，S8对每个发展战略的相对权重，并用发展战略C1，C2，…，C10的组合权重对制约因素的相对权重加权后相加，得到各制约因素的组合权重，它们表示各制约因素对实现总目标的制约程度计算结果见表8.2.26 表表8.2.26 8.2.26 l计算各方针措施P1，P2，…，P10对每个制约因素的相对权重，并用各制约因素的组合权重对方针措施的相对权重加权后相加，得到方针措施的组合权重，们表示各方针措施对实现总目标的重要程度计算结果见表8.2.27 表8.2.27（三）基本结论 l从战略目标来看，要实现晋陕蒙三角地区综合开发与治理，首先要发挥本地区煤炭资源的优势，其权重为0.595。

但不容忽视的是，必须采取开发与治理并重的总方针，边开发边治理，以开发促治理，从计算结果看，O3的权重为0.276，其重要程度排在第二位当然，农林牧生产也应得到相应的重视，其权重为0.128l从发展战略上来讲，首先应该发展统配煤矿，其权重为0.151；地方乡镇煤矿的发展也占有重要地位，其权重为0.139；水土保持和粮食生产的权重分别为0.134和0.133，处在第三位和第四位 沙漠化治理、肉蛋奶基地及果品蔬菜基地建设也应放在重要的位置上，其权重分别为0.129 、0.114和0.108 另外，发展电力工业与发展地方工业乡镇企业的权重分别为0.039和0.032从计算结果可以看出，发展重化工业的权重为0.022，在10个发展战略中，其权重处在最后一位，这说明本区不宜发展重工业和化工工业l从制约因素来看，本区资金短缺这一制约因素的影响最为严重，权重为0.36；其次，水资源不足对总目标的制约程度也十分严重，其权重为0.234另外，粮食和农副产品供应问题、水土流失、风沙危害以及运输能力的不足，也对总目标的实现有较为严重的制约，其权重分别为0.106，0.093，0.084。

人才技术缺乏、地方经济不发达、厂矿建设占地过多等制约因素的权重依次为0.053，0.040，0.029 l从方针措施来看，通过各种渠道解决资金不足的矛盾是最为重要的，包括国家投资、地方集资，其权重分别为0.242和0.119 由于本区干旱少雨，地表径流少且中小型水库很快就会被泥沙淤满，因此为了解决水资源供需矛盾，从长远观点来看，必须从黄河提水、引水，其权重为0.117 其次本区交通运输问题也是急待解决的矛盾，其中修建铁路的权重为0.063，大于修建公路的权重 另外，农田基本建设工作也不容忽视，其权重为0.052。