How to make a decision

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1、_HOW TO MAKE A DECISIONThomas L. SaatyUniversity of PittsburghSaatyvms.cis.pitt.edu1. IntroductionThe Analytic Hierarchy Process (AHP) for decision making uses objective mathematics to process the inescapably subjective and personal preferences of an individual or a group in making a decision. With

2、the AHP and its generalization, the Analytic Network Process (ANP), one constructs hierarchies or feedback networks, then makes judgments or performs measurements on pairs of elements with respect to a controlling element to derive ratio scales that are then synthesized throughout the structure to s

3、elect the best alternative.Nearly all of us, in one way or another, have been brought up to believe that clear-headed logical thinking is our only sure way to face and solve problems. We also believe that our feelings and our judgments must be subjected to the acid test of deductive thinking. But ex

4、perience suggests that deductive thinking is not natural. Indeed, we have to practice, and for a long time, before we can do it well. Since complex problems usually have many related factors, traditional logical thinking leads to sequences of ideas that are so tangled that their interconnections are

5、 not readily discerned. We note that people have been making decisions as long as they have been around and did not need mathematics and technology to do it well. How can we capture what people do naturally with our mathematics of today? The lack of a coherent procedure to make decisions is especial

6、ly troublesome when our intuition alone cannot help us to determine which of several options is the most desirable, or the least objectionable, and neither logic nor intuition are of help. Therefore, we need a way to determine which objective outweighs another, both in the near and long terms. Since

7、 we are concerned with real-life problems we must recognize the necessity for tradeoffs to best serve the common interest. Therefore, this process should also allow for consensus building and compromise.Individual knowledge and experience are inadequate in making decisions concerning the welfare and

8、 quality of life for a group. Participation and debate are needed both among individuals and between the groups affected. Here two aspects of group decision making have to be considered. The first is a rather minor complication, namely, the discussion and exchange within the group to reach some kind

9、 of consensus on the given problem. The second is of much greater difficulty. The holistic nature of the given problem necessitates that it be divided into smaller subject-matter areas within which different groups of experts determine how each area affects the total problem. A large and complex pro

10、blem can rarely be decomposed simply into a number of smaller problems whose solutions can be combined into an overall answer. If this process is successful, one can then reconstruct the initial question and review the proposed solutions. A last and often crucial disadvantage of many traditional dec

11、ision-making methods is that they require specialized expertise to design the appropriate structure and then to embed the decision-making process in it.A decision-making approach should have the following characteristics: be simple in construct, be adaptable to both groups and individuals, be natura

12、l to our intuition and general thinking, encourage compromise and consensus building, and not require inordinate specialization to master and communicate.In addition, the details of the processes leading up to the decision-making process should be easy to review. At the core of the problems that our

13、 method addresses is the need to assess the benefits, the costs, and the risks of the proposed solutions. We must answer such questions as the following: Which consequences weigh more heavily than others? Which aims are more important than others? What is likely to take place? What should we plan fo

14、r and how do we bring it about? These and other questions demand a multicriteria logic. It has been demonstrated over and over by practitioners who use the theory discussed in this paper, that multicriteria logic gives different and often better answers to these questions than ordinary logic and doe

15、s it efficiently. To make a decision one needs various kinds of knowledge, information, and technical data. These concern: details about the problem for which a decision is needed, the people or actors involved, their objectives and policies, the influences affecting the outcomes, and, the time hori

16、zons, scenarios, and constraints.The set of potential outcomes and the alternatives from which to choose are the essence of decision making. In laying out the framework for making a decision, one needs to sort the elements into groupings or clusters that have similar influences or effects. One must

17、also arrange them in some rational order to trace the outcome of these influences. Briefly, we see decision making as a process that involves the following steps:(1) Structure a problem with a model that shows the problems key elements and their relationships.(2)Elicit judgments that reflect knowled

18、ge, feelings, or emotions.(3)Represent those judgments with meaningful numbers.(4)Use these numbers to calculate the priorities of the elements of the hierarchy.(5)Synthesize these results to determine an overall outcome.(6) Analyze sensitivity to changes in judgment.The decision-making process desc

19、ribed in this paper meets these criteria. I call it the analytic hierarchy process (AHP). The AHP is about breaking a problem down and then aggregating the solutions of all the sub-problems into a conclusion. It facilitates decision making by organizing perceptions, feelings, judgments, and memories

20、 into a framework that exhibits the forces that influence a decision. In the simple and most common case, the forces are arranged from the more general and less controllable to the more specific and controllable. The AHP is based on the innate human ability to make sound judgments about small proble

21、ms. It has been applied in a variety of decisions and planning projects in nearly 20 countries.Here rationality is Focusing on the goal of solving the problem; Knowing enough about a problem to develop a complete structure of relations and influences; Having enough knowledge and experience and acces

22、s to the knowledge and experience of others to assess the priority of influence and dominance (importance, preference, or likelihood to the goal as appropriate) among the relations in the structure; Allowing for differences in opinion with an ability to develop a best compromise.2. How to Structure

23、a HierarchyPerhaps the most creative part of decision making that has a significant effect on the outcome is modeling the problem. In the AHP, a problem is structured as a hierarchy. It is then followed by a process of prioritization, which we describe in detail later. Prioritization involves elicit

24、ing judgments in response to questions about the dominance of one element over another when compared with respect to a property. The basic principle to follow in creating this structure is always to see if one can answer the following question: Can I compare the elements on a lower level using some

25、or all of the elements on the next higher level as criteria or attributes of the lower level elements?A useful way to proceed in structuring a decision is to come down from the goal as far as one can by decomposing it into the most general and most easily controlled factors. One can then go up from

26、the alternatives beginning with the simplest subcriteria that they must satisfy and aggregating the subcriteria into generic higher level criteria until the levels of the two processes are linked in such a way as to make comparison possible. Here are some suggestions for an elaborate design of a hie

27、rarchy: (1) Identify the overall goal. What are you trying to accomplish? What is the main question? (2) Identify the subgoals of the overall goal. If relevant, identify time horizons that affect the decision. (3) Identify criteria that must be satisfied to fulfill the subgoals of the overall goal.

28、(4) Identify subcriteria under each criterion. Note that criteria or subcriteria may be specified in terms of ranges of values of parameters or in terms of verbal intensities such as high, medium, low. (5) Identify the actors involved. (6) Identify the actors goals. (7) Identify the actors policies.

29、 (8) Identify options or outcomes. (9) For yes-no decisions, take the most preferred outcome and compare the benefits and costs of making the decision with those of not making it. (10) Do a benefit/cost analysis using marginal values. Because we are dealing with dominance hierarchies, ask which alte

30、rnative yields the greatest benefit; for costs, which alternative costs the most, and for risks, which alternative is more risky. 3. The Hospice ProblemWestmoreland County Hospital in Western Pennsylvania, like hospitals in many other counties around the nation, has been concerned with the costs of

31、the facilities and manpower involved in taking care of terminally ill patients. Normally these patients do not need as much medical attention as do other patients. Those who best utilize the limited resources in a hospital are patients who require the medical attention of its specialists and advance

32、d technology equipment, whose utilization depends on the demand of patients admitted into the hospital. The terminally ill need medical attention only episodically. Most of the time such patients need psychological support. Such support is best given by the patients family, whose members are able to

33、 supply the love and care the patients most need. For the mental health of the patient, home therapy is a benefit. From the medical standpoint, especially during a crisis, the hospital provides a greater benefit. Most patients need the help of medical professionals only during a crisis. Some will al

34、so need equipment and surgery. The planning association of the hospital wanted to develop alternatives and to choose the best one considering various criteria from the standpoint of the patient, the hospital, the community, and society at large. In this problem, we need to consider the costs and ben

35、efits of the decision. Cost includes economic costs and all sorts of intangibles, such as inconvenience and pain. Such disbenefits are not directly related to benefits as their mathematical inverses, because patients infinitely prefer the benefits of good health to these intangible disbenefits. To s

36、tudy the problem, one needs to deal with benefits and with costs separately.4. Approaching the ProblemI met with representatives of the planning association for several hours to decide on the best alternative. To make a decision by considering benefits and costs, one must first answer the question:

37、In this problem, do the benefits justify the costs? If they do, then either the benefits are so much more important than the costs that the decision is based simply on benefits, or the two are so close in value that both the benefits and the costs should be considered. Then we use two hierarchies fo

38、r the purpose and make the choice by forming the ratio from them of the (benefits priority/cost priority) for each alternative. One asks which is most beneficial in the benefits hierarchy (Figure 1) and which is most costly in the costs hierarchy (Figure 2). If the benefits do not justify the costs,

39、 the costs alone determine the best alternative, that which is the least costly. In this example, we decided that both benefits and costs had to be considered in separate hierarchies. In a risk problem, a third hierarchy is used to determine the most desired alternative with respect to all three: be

40、nefits, costs, and risks. In this problem, we assumed risk to be the same for all contingencies. Whereas for most decisions one uses only a single hierarchy, we constructed two hierarchies for the hospice problem, one for benefits or gains (which model of hospice care yields the greater benefit) and

41、 one for costs or pains (which model costs more). Figure 1: To choose the best hospice plan, one constructs a hierarchy modeling the benefits to the patient, to the institution, and to society. This is the benefits hierarchy of two separate hierarchies.Physical0.16Psycho-social0.23Economic0.03Psycho

42、-social0.44Economic0.04direct care of patients0.02palliative care0.14volunteer support0.02networking in families0.06relief of post-death distress0.12emotional support to family and patient0.21alleviation of guilt0.03reduced costs0.01improved productivity0.03publicity and public relations0.19voluntee

43、r recruitment0.03professional recruitment and support0.06reduced length of stay0.006better utilization of resources0.023professional recruitment and support0.06death as a social issue0.02rehumanization of medical, professional and health institutions0.08Choosing Best HospiceBenefits HierarchyRecipie

44、nt benefits0.64Institutional benefits0.26Societal benefits0.10Tertiary subcriteruaGoalGeneralcriteruaSecondarysubcriteruaAlternativesModel 10.43Unit of beds with team giving home care (as in hospital or nursing home)Model 20.12Mixed bed, contractual home care (partly in hospital for emergency care a

45、nd partly in home when better-no nurses going to the house)Model 30.45Hospital and home care share case management (with visiting nurses to the home; if extremely sick patient goes to the hospital)-(each alternative model below is connected to every tertiary subcriterion)-Figure 2: To choose the bes

46、t hospice plan, one constructs a hierarchy modeling the community, institutional, and societal costs. This is the costs hierarchy of two separate hierarchies.Choosing Best HospiceCosts HierarchyCommunity costs0.14Institutional costs0.71Societal costs0.15Education0.07Recruitment0.03Bad debt0.15Capita

47、l0.03Operating0.40Tertiary subcriteruaGoalGeneralcriteruaSecondarysubcriteruaAlternativesModel 10.58Unit of beds with team giving home care (as in hospital or nursing home)Model 20.19Mixed bed, contractual home care (partly in hospital for emergency care and partly in home when better-no nurses goin

48、g to the house)Model 30.23Hospital and home care share case management (with visiting nurses to the home; if extremely sick patient goes to the hospital)Training staff0.06Community0.01Staff0.05Volunteers0.01-(each alternative model below is connected to every tertiary subcriterion)-The planning asso

49、ciation thought the concepts of benefits and costs were too general to enable it to make a decision. Thus, the planners and I further subdivided each (benefits and costs) into detailed subcriteria to enable the group to develop alternatives and to evaluate the finer distinctions the members perceive

50、d between the three alternatives. The alternatives were to care for terminally ill patients at the hospital, at home, or partly at the hospital and partly at home. For each of the two hierarchies, benefits and costs, the goal clearly had to be choosing the best hospice. We placed this goal at the to

51、p of each hierarchy. Then the group discussed and identified overall criteria for each hierarchy; these criteria need not be the same for the benefits as for the costs.The two hierarchies are fairly clear and straightforward in their description. They descend from the more general criteria in the se

52、cond level to secondary subcriteria in the third level and then to tertiary subcriteria in the fourth level on to the alternatives at the bottom or fifth level. At the general criteria level, each of the hierarchies, benefits or costs, involved three major interests. The decision should benefit the

53、recipient, the institution, and society as a whole, and their relative importance is the prime determinant as to which outcome is more likely to be preferred. We located these three elements on the second level of the benefits hierarchy. As the decision would benefit each party differently and the i

54、mportance of the benefits to each recipient affects the outcome, the group thought that it was important to specify the types of benefit for the recipient and the institution. Recipients want physical, psycho-social and economic benefits, while the institution wants only psychosocial and economic be

55、nefits. We located these benefits in the third level of the hierarchy. Each of these in turn needed further decomposition into specific items in terms of which the decision alternatives could be evaluated. For example, while the recipient measures economic benefits in terms of reduced costs and impr

56、oved productivity, the institution needed the more specific measurements of reduced length of stay, better utilization of resources, and increased financial support from the community. There was no reason to decompose the societal benefits into a third level subcriteria, hence societal benefits conn

57、ects directly to the fourth level. The group considered three models for the decision alternatives, and they are at the bottom (or fifth level in this case) of the hierarchy: in Model 1, the hospital provided full care to the patients; in Model 2, the family cares for the patient at home, and the ho

58、spital provides only emergency treatment (no nurses go to the house); and in Model 3, the hospital and the home share patient care (with visiting nurses going to the home).In the costs hierarchy there were also three major interests in the second level that would incur costs or pains: community, ins

59、titution, and society. In this decision the costs incurred by the patient were not included as a separate factor. Patient and family could be thought of as part of the community. We thought decomposition was necessary only for institutional costs. We included five such costs in the third level: capi

60、tal costs, operating costs, education costs, bad debt costs, and recruitment costs. Educational costs apply to educating the community and training the staff. Recruitment costs apply to staff and volunteers. Since both the costs hierarchy and the benefits hierarchy concern the same decision, they bo

61、th have the same alternatives in their bottom levels, even though the costs hierarchy has fewer levels.5. Judgments and ComparisonsA judgment or comparison is the numerical representation of a relationship between two elements that share a common parent. The set of all such judgments can be represen

62、ted in a square matrix in which the set of elements is compared with itself. Each judgment represents the dominance of an element in the column on the left over an element in the row on top. It reflects the answers to two questions: which of the two elements is more important with respect to a highe

63、r level criterion, and how strongly, using the 1-9 scale shown in Table 1 for the element on the left over the element at the top of the matrix. If the element on the left is less important than that on the top of the matrix, we enter the reciprocal value in the corresponding position in the matrix.

64、 It is important to note that the lesser element is always used as the unit and the greater one is estimated as a multiple of that unit. From all the paired comparisons we calculate the priorities and exhibit them on the right of the matrix. For a set of n elements in a matrix one needs n(n-1)/2 comparisons because there are n 1s on the diagonal for comparing elements with