Decision Analysis Comes of Age

In the early 1970s, C. Jackson Grayson, onetime head of the Wage and Price Commission and also author of one of the first books on applied decision analysis, urged analysts to “put people, time, power, data accessibility, and response time into models and create crude, workable solutions” if they wanted busy people like himself to use them.1 At the time, decision analysis was still an experimental management technique, a fairly straightforward application of statistical decision theory. 2 The choice facing a decision maker was expressed as a mathematical function of probability and utility numbers, which measured the person’s uncertainties and value judgments. (The best option was the one with the highest expected utility.) Although decision analysis was well established as a way to quantify logically the considerations that go into any choice among options, it had just begun to move out of the business schools and into practical application in the business world. Only a handful of corporations provided in-house expertise, and consultants specializing in decision analysis were rarely called on. Now, after ten years of sometimes humbling feedback from the real world, analysts have learned to be more flexible and modest in how to make the basic decision theory formulation useful to managers. The technology has been enhanced to capture more considerations relevant to sound decision making, notably through multiattribute utility analysis and improved interaction with the user. Decision analysis has emerged as a complement to older decision-making techniques such as systems modeling and operations research. In addition to statistical decision theory, the new technology draws on psychology, economics, and social science. What is retained and is distinctive about the approach is that the quantitative models incorporate personal judgments. To distinguish this approach from other ways of analyzing decisions in widespread use (such as those that depend only on “objective” inputs), we call it personalized decision analysis. Analysts have learned to use the data and expertise that are immediately available to the decision maker and to play back conclusions to the manager in close to real time. In 1970, an analysis was rarely completed within three months. Now, meaningful analysis of a problem can be generated in an afternoon, and a succession of analyses can be presented in intervals of one or two days. Without greatly disturbing their schedule of meetings or reflective process, managers can now respond to these analyses and provide input for other rounds. Although such decision analysis has not become the dominant analytic discipline that some people expected, its use has grown dramatically since 1970. Personalized decision analysis has become an accepted part of the staff services that major corporations draw on routinely, much as they do industrial psychology, cost analysis, marketing research, and economic analysis. And virtually all the major areas of government have adopted decision analysis in one form or another. The case studies that we present in this article illustrate how managers use the three major variants of decision analysis currently in use—decision tree analysis, probabilistic forecasting, and multiattribute utility analysis. Decision Tree Analysis Decision tree analysis is the oldest and most widely used form of decision analysis. Managers have used it in making business decisions in uncertain conditions since the late 1950s, and its techniques are familiar.3 Over the past several years, however, the manner in which people conduct decision tree analysis has expanded. Today’s analyst has at his or her disposal not only an array of computer supports that make quick turnaround possible but also the accumulated wisdom of analysts over the last 20 years. The following case illustrates some of the components of a successful decision tree analysis. They include the use of simple displays, sensitivity analysis to guide refinements, and subsidiary models to ensure completeness. Also important are the direction and integration the analysis gives to the contributions of experts as well as the involvement of top managers. Should AIL Purchase Rights to a New Patent? Late in 1974, the AIL Division of Cutler-Hammer, Inc. (now a division of Eaton Corporation) was offered the opportunity to acquire the defense market rights to a new flight-safety system patent. The inventor claimed he had a strong patent position as well as technical superiority, but the market for the product was very uncertain, mostly because of pending legislative action. Because the inventor wished to make an offer to other companies if AIL was not interested, he asked AIL to make the decision in a few weeks, a period of time clearly inadequate to resolve any uncertainties it was aware of. AIL had not used formal decision analysis before. Top managers were, however, familiar with the theory and its typical applications through the literature and interested in trying these techniques on an actual decision to evaluate their worth. The patent decision appeared to be a good candidate for such a trial. A team of AIL personnel and outside analysts spent two weeks developing an analysis of the patent idea. All the while, the team stayed in continual contact with top management. AIL’s analysis The analysts used standard decision tree techniques. Exhibit I shows the immediate choice, to purchase a six-month option on the patent rights or not, and the main uncertainties that affected the decision. The attractiveness of each outcome, or path through the tree, is represented by its present value earnings. These range from a loss of $ 700,000 to a gain of $ 10.5 million. The expected value at each node in the tree is calculated by taking a probability-weighted average of its branches. Working these values gives an expected value of $ 100,425. That is, AIL could expect to be better off by $ 100,425 if it purchased the six-month option. Exhibit I AIL’s Decision Tree The mechanics of the analysis—specifying the tree, assigning values, and calculating results—are straightforward. The usefulness of the analysis, however, depends more on how the analysis process is managed than on the mechanics. Five features that are often absent in unsuccessful attempts to apply decision analysis marked this implementation as a success. A simple display. The focus of the analysis was the simple tree shown in Exhibit I. The most common mistake that a beginner at decision analysis makes is to include everything the choice involves in the tree. This is a sure way to end up with a mess, which only the analyst, if anyone, can understand. Such a tree is unlikely to influence any manager’s decision. The trick is to design a simple tree that captures the essence of the problem by including its most important elements. In this case, the most important elements affecting earnings were the probabilities of exercising the option, receiving an initial contract, and continuing on a second contract. Refining the elements. By means of an interactive computer program, the analysts determined how sensitive the results were to changes in the inputs to the tree. The analysis was then expanded in a way that would be most responsive to what the decision maker needed to know. Use of subsidiary models. The analysts at AIL developed models to refine estimates of the most sensitive inputs. Using a simple tree does not make the analysis coarse or incomplete; subsidiary models can ensure any desired level of detail and sophistication. In this case, the analysts used three subsidiary models. They used one to determine yearly earnings and calculate present values and another to assess the probability of receiving a contract. The latter model reflected important factors such as the timing and terms of a possible legislative mandate for the system, the strength of possible competitive systems, and the likelihood of a crash or near crash of a plane within the next several months. The analysts used a third model to assess probability distributions of earnings from the contracts that reflected uncertainties in the number of units, the price per unit, and the profit margin. Each subsidiary model was compact and could be displayed on a single chart, which the analysts used to answer top managers’ questions about how the figures in the main model had been determined. Team input. At AIL various people were involved with each aspect of the model, so that each expert could focus on the area of his expertise. Those most knowledgeable about the chances of winning the second contract, for example, addressed this aspect of the problem but did not consider other aspects. The combined contributions of all the experts formed a unified picture for top management. Contact with top management. The most important factor was the close work of top management with the analysis team throughout the analysis. This interaction ensured that: 1. The choices modeled were in fact the choices under consideration. (In this case, as a result of the modeling, the analysts identified a new choice—waiting and seeking a sublicense.) 2. All important concerns were addressed. For AIL, the issues included the impact that decision factors other than direct earnings have (in this case, return on capital). 3. The level of modeling was right. That is, some aspects were modeled formally, but others were left to informal consideration. For example, the analysts explored AIL’s attitude toward risk taking by displaying risk profiles of the choices rather than by assessing and using a utility function.4 (Because answering the hypothetical questions about preferences for uncertain returns that are required to establish a utility function strikes many managers as gambling, many of them are reluctant to do it. In this case, the uncertainties of the decision could be sufficiently characterized in simple risk profiles.) Exhibit II shows the risk profiles of the alternatives AIL faced. Purchasing the option would give an expected net present value of earnings of about $ 100,000, a 60 % chance of losing about $ 700,000, a 29 % chance of losing about $ 125,000, and an 11 % chance of having a positive return from a distribution with an expectation of about $ 5.25 million. (This picture corresponds to a more detailed analysis of the earnings from a defense contract.) Exhibit II Risk Profiles for AIL’s Patent Purchasing Decision distribution of incremental discounted earnings in millions of dollars The alternative, waiting and seeking a sublicense, would have a 94 % chance of producing no gain (or loss) and a 6 % chance of producing a distribution with an expectation of about $ 830,000 and would result in an expected value of about $ 50,000. This display facilitated a unanimous decision by the decision-making group (the president and his vice presidents for business development and operations) to go with the less risky strategy even though it offered a slightly lower expected value. Other Companies’ Experiences Companies in a wide range of industries are using decision tree analysis to make a variety of decisions. For example: Through this kind of analysis, Ford has determined whether to produce its own tires and whether to stop producing convertibles. The defense systems division of Honeywell uses decision tree analysis to evaluate the attractiveness of new weapons programs. On a regular basis, program managers and the director of planning develop models to help decide which programs to pursue and how they should allocate internal research and development funds. With decision tree analysis, Pillsbury’s grocery products division has evaluated major decisions, such as whether to switch from a box to a bag for a certain grocery product. In this case, even when analysts used pessimistic assessments expressed by a manager who initially recommended remaining with the box, the analysis showed that the profitability would be greater with the bag. The analysis also showed that the value of making a market test, as urged by some executives, could not remotely approach its cost. The bag was introduced, and the profits on the product climbed. Faced with a decision to electrify part of its system, which would involve capital expenditures of several hundred million dollars, Southern Railway carried out an analysis that gave managers a better understanding of the interactions of variables influencing the decision. Many major oil and gas companies, such as Union Texas Petroleum, the Champlin oil and gas subsidiary of Union Pacific, and Gulf Oil, apply decision analysis regularly to choose appropriate sites for exploration and evaluate the economics of field development. ITT uses decision analysis at many levels of the company, especially for capital investment decisions. Probabilistic Forecasting The previous section illustrates how personalized decision analysis can capture all the thinking that goes into a particular decision. The technique has other uses as well. Analysts can develop certain aspects of decision analysis into analytic tools that can be used in a variety of contexts. Analysts can use the probabilistic modeling aspects of decision analysis to develop forecasts of, for instance, future sales and profits, which in turn can be used to support decisions about planning, investment, and marketing. Developing a single aspect of personalized decision analysis to support decisions in a variety of contexts is likely to become very popular. Because its cost can be spread over many uses, a company can afford to use enough computerization and staff time to do this type of analysis properly. The following example illustrates how personalized decision analysis can be used for forecasting. Of course, this kind of analysis is not the only way to carry out quantitative forecasting. What is distinctive about this approach’s contribution to the problem is that, rather than limit a forecast to statistical extrapolation from the past, it can combine assessments of judgment with data. In cases where little or no relevant history is available on which to base a forecast and where each product’s success depends on a combination of events about which personal judgment is virtually the only source of information, this form of analysis is particularly helpful. How Will Honeywell’s Defense Division Grow? In late 1979, the manager of planning for the defense systems division of Honeywell, Inc. faced the task of planning the division’s growth over the next ten years. A major part of the work involved finding how to stay within the R&D budget and yet pursue new product opportunities to increase the division’s sales and profits. After he screened the new product opportunities according to their fit with the rest of the division, the manager needed forecasts of the products’ sales, profits, and investment requirements. The products’ successful development, the strength of competition, and their eventual market success were all uncertain. In addition, the chances for success of some of the products were interrelated, and several products offered the chance of significant collateral business. The approach the analysts took was to build a composite forecast for the division by combining decision tree analyses of individual products. During the project, Honeywell’s planners worked closely with decision analysis consultants and, by the time they had finished, had acquired the skills needed to carry out the analyses in-house. This type of analysis is now a regular part of Honeywell’s project evaluation, planning, and forecasting activity. The analysts developed a model for each product along lines similar to AIL’s. The analysis team worked closely with each project manager and his staff to build the decision tree, assess probabilities and values, and discuss results and sensitivities. The two analyses differed significantly, however, in a number of ways. First, the results of Honeywell’s analysis were to be used for forecasting as well as for decision making. This use meant that the analysts would need to model additional factors and would have to make the form the outputs took suitable for forecasting. Second, because the success of some products was related to the success of others, the analysts had to include in the analysis such factors as common investments, collateral business opportunities, and marketing interactions. Third, Honeywell’s problem presented no clear single criterion according to which management could make a decision. Honeywell considered several financial criteria such as internal rate of return, net present value, and yearly streams of profits, investments, and return on investment. Honeywell’s forecasts Exhibit III shows the probabilistic sales forecast for one group of interrelated products. This forecast is based on decision tree analyses of three main products and two collateral business opportunities. The analysts first developed decision trees for each product to determine the distributions of sales in the event that a market sufficient to support full production both did and did not emerge. Then they developed a second level of analysis to model the key interdependencies among the products; specifically, the probability of any particular product being in full production depended on which other products were also in full production. Exhibit III Distribution of Sales for a Group of Interrelated Products The forecast shows that low sales are expected from the products for the first seven years. After that, sales for the next six years are expected to be about $ 75 million per year. This amount is not certain, however. The forecast, for instance, shows a 24 % chance of sales being below $ 25 million in 1989. The supporting decision tree analyses were useful for explaining the shape of each year’s forecast. Exhibit IV shows that because of uncertainty about which products would have sufficient markets to support full production by 1988, the forecast for sales is “lumpy.” The reasons for these uncertainties are detailed in the decision tree analyses. Exhibit IV Detailed Forecast of Sales in 1988 This analysis helped Honeywell to assess the chances that these products would meet sales goals, the uncertainties in the assessment, and the reasons for the uncertainties. By detailing the chain of events that would produce different levels of sales, it also identified points of leverage—places where Honeywell could take action to change probabilities and improve sales. The analysts also used the decision trees to forecast yearly profits, fund flows, assets, research and development investments, and the related financial quantities of net present value, internal rate of return, and annual return on investment. Their forecasts indicated that these products could be expected to exceed requirements on all factors and that, unless Honeywell was very risk averse, they were attractive. Honeywell’s managers compared forecasts to decide which product opportunities to pursue. These comparisons provided an additional screen since some products were clearly worse than others on all factors. But because the analysis didn’t show the relative importance of each factor—some products were projected to perform better on certain factors (for example, internal rate of return and net present value) and other products were projected to perform better on other factors (for example, return on investment)—an unambiguous ordering of the products was impossible. Honeywell’s managers might have had such an ordering if their analysts had used some of the newer techniques of multiattribute utility. Multiattribute Utility Analysis In trying to determine where to place its European subsidiary, the top management of one company completely ignored a decision tree analysis that showed careful consideration of the financial implications of possible locations. When pressed for an explanation, top management confided that the choice was dominated by the fact that key personnel wanted to be near the International School in Geneva. Somehow, that consideration seemed too non-economical and nonrational to be included in the analysis—yet it did dominate the decision. At the time the decision was made, the technology of decision analysis was ill equipped to handle the tradeoffs between financial effects and intangibles. A new technique, multiattribute utility analysis, makes such modeling possible by precisely specifying the factors that affect the choice, making trade-offs among the factors, and choosing the alternative that offers the best balance. Multiattribute utility analysis evolved out of decision analysis that supported government decisions, in which the need to balance multiple objectives is most obvious. As the case of the company deciding where to put its plant shows, however, its usefulness for business decision making is evident. For example, plant sites usually differ in such intangibles as the skill of the local work force, the ability of local management, and the management problems of operating plants in the locations under consideration. These are important factors to consider in the decision of where to locate the plant, yet it is virtually impossible to specify their impact on profit with any precision. Many factors also arise in strategic decisions. For example, Michael E. Porter has argued that, when considering the strategic decisions of vertical integration, major capacity expansion, and entry into new businesses, managers should go beyond cost and investment analyses to consider broad strategic issues and perplexing administrative problems and that these are very hard to quantify.5 Multiattribute utility analysis, which is illustrated in the following case, provides a way to quantify and trade off such factors. Which Bomb Detection System Should the FAA Choose? Over the past few years, the Federal Aviation Administration has been supporting research and development on a system to detect bombs in airplane baggage. In early 1980, the program manager for this project had to decide which of several candidate systems to continue funding. The candidates differed greatly in their potential performance and technical characteristics. Since none was clearly superior in all respects, the program manager sought a method for weighing the various characteristics to arrive at a measure of overall value. A team of outside analysts worked closely with the program manager and other FAA personnel to develop a comprehensive model of the value of each system. To determine an efficient allocation of budgeted funds, they combined these values with assessments of the probabilities of success and development costs. The FAA’s analysis The analysts’ primary goal was to develop a comprehensive model for evaluating and comparing candidates. This development involved four activities—defining attributes of value, assessing performance of the candidates on each attribute, determining trade-offs across attributes, and calculating overall values.6 Defining preference attributes. The analysts sought to define attributes with four characteristics. The attributes were to be comprehensive enough to account for most of what is important in evaluating the candidates, to highlight the differences among the candidates, to reflect separate, nonoverlapping values to avoid double counting, and to be independent of each other. When the analysts had identified attributes that satisfied these four requirements, they then arranged the attributes in a hierarchy showing the logical relationships among attributes. This is shown in Exhibit V. Exhibit V Hierarchy of Attributes in the FAA’s Analysis in preference weights The first main attribute is the effectiveness of the device at detecting bombs. This is subdivided into the type of explosive, the size of the bomb, and the detection-false alarm ratio. The second main attribute, development considerations, is divided into four subcategories—time to develop a prototype, production lead time, operating size (which would determine a system’s location in an airport), and transportability. Cost to employ the system in an airport, the third main attribute, is divided into initial costs and recurring costs. Initial costs reflect a basic cost estimate based on technical considerations and an estimate of the effects of competition. Recurring costs include maintenance, operating personnel, and material consumed during operation. The fourth main attribute is the system’s acceptability to passengers. Assessing performance of candidates on each attribute. To assess preference, the analysts required scales for all attributes. They used two types of measure—scales with natural standard units (including dollars for costs, months or hours for time, and percentages for detection rates) and relative scales. Wherever possible, the performance of a candidate was first assessed in natural units. These assessments were then transformed into 0-to-100-point scales for standardization. The candidate with the best performance (the lowest cost, for example) received a score of 100; the one with the worst performance (the highest cost, for instance) received a score of 0; and the others received intermediate scores. Where no natural measure existed (for example, for “public acceptance”), performance was assessed directly on a 0-to-100-point scale. Again, a score of 100 was assigned to the candidate with the best performance, 0 to the worst performance, and so forth. Exhibit VI shows, for instance, the scores for the six candidates on each development consideration. Candidate A was assessed to have the best “time to develop” since it was fully developed at the time of the analysis. It was assigned a value of 100. Candidate C would take the longest time to develop—four years. It received a value of 0. Other candidates would take intermediate amounts of time to develop and thus received intermediate scores. Exhibit VI Performance of the FAA’s Bomb Detection Candidates on Development Considerations on a scale of 0 to 100 Determining trade-offs across attributes. By assessing a set of weights to represent the decision maker’s judgment about the relative importance of improving performance from the worst to the best level for each attribute, analysts could determine trade-offs across attributes. The analysts assessed the weights by referring to the range of performance the scales reflected instead of to abstract notions of importance. Consider, for example, the weights of the development considerations shown in Exhibit V. For these attributes, the ranges of possible variation in “production lead time” (18 months) and in “operating size” were considered most important. The variation of “time to develop” (4 years) was assessed to be half as important (as important as a variation of 9 months on “production lead time”). Finally, the variation of “transportability” (32 hours) was assessed to be one-tenth as important as “time to develop” (or about as important as 5 months of development time). These assessments are represented by weights that are in the ratios of .5:1:1:.05 for time to develop, production lead time, operating size, and transportability. Normalized weights of .20:.39:.39:.02 (which retain these ratios) were used for standardization. The analysts assessed weights both directly, as we explained earlier, and indirectly. They used an indirect method to assess the weight between initial and recurring costs. This method determined weights that were consistent with a 10 % discount rate and a ten-year operating horizon. Calculating overall values. The fourth modeling activity was to calculate a weighted-average score for each candidate by working up through the hierarchy. Thus, using the values in Exhibit VI and the weights in Exhibit V, analysts calculated the value of candidate A on “development considerations” as: Similar calculations produced the values for the candidates on each main attribute that are shown in Exhibit VII. The analysts next calculated the overall value of each candidate by taking a weighted average of these scores. For example, the overall value of candidate A is: Exhibit VII Overall Value of Candidates on a scale of 0 to 100 Overall value is a measure of the attractiveness of each candidate that can be compared with measures for other candidates. The result of the analysis shows that candidate B offers the best balance of characteristics, that C and D are almost as attractive, and that candidates E and F offer the worst balances. The value of the analysis The FAA’s primary use of the analysis was to quantify each candidate’s value in a way that permitted comparison. To determine an efficient allocation of R&D funds, the analysts combined these evaluations with estimates of each candidate’s probability of success and cost of development. The FAA’s analysis also facilitated several aspects of the decision-making process. First, it helped resolve disagreements. The disaggregation of the elements of the decision clarified the source of a disagreement—was it about facts (for example, the cost of a system) or a difference in judgment (for instance, the relative importance of cost in comparison with detection performance)? Once the disagreements were clear, managers could deal with them by, for example, gathering additional supporting information. If the disagreement persisted, the model could determine its importance. For each input, the model could show whether the disagreement significantly affected the overall evaluation. Even if a disagreement was significant, the model at least isolated its cause. This clarification enabled the ultimate decision maker to make a better judgment. The disaggregation also allowed the analyst to make a comprehensive analysis of the candidates. The team could investigate each attribute thoroughly yet keep its contribution to the overall evaluation in perspective. This arrangement prevented the analysts from wasting attention on unimportant issues. To give a balanced picture of the whole, the multiattribute analysis synthesized the various pieces of the assessment. The analysts considered the impact of all important factors before they came up with a recommendation. Business Use of Multiattribute Utility Analysis Multiattribute utility analysis has been used widely to aid government decision makers. For instance, it has been used to select military systems, set water-supply policy, site nuclear facilities, allocate nuclear inspection resources, determine fire department operations, evaluate crime-prevention programs, and prepare international negotiators. Its use as an aid in making business decisions has not been as widespread, but the next few years should see a dramatic increase. Multiattribute analysis is useful for any decision in which multiple factors are important, no alternative is clearly best on all factors, and some factors are difficult to quantify. Several business decisions have these characteristics: Where to put a plant Sites often differ in many important aspects. Some factors, such as differences in capital costs (land, plant, and equipment) and in operating revenue and expenses (access to markets, labor rates, tax benefits, shipping costs), are easily reduced to financial terms. Other factors that may be crucial to the decision are more difficult to reduce to dollars. These include the availability and skill of local labor, the degree of unionization, the difficulty of managing geographically dispersed units, and legal restrictions on operations. Multiattribute analysis can highlight the sources of differences and enable managers to make quantitative trade-offs between financial factors and “intangibles.” Whether to integrate vertically A decision to integrate an operation or not requires that management consider a multitude of factors, many of which are difficult to quantify with standard financial techniques: access to new information, access to new technologies, ability to control specifications of products or raw materials, economies of combined operations, difficulty in balancing “upstream” and “downstream” units, and increased fixed costs of doing business. Whether and how to enter a new business This decision can involve considerations that are often ignored in capital budgeting: The production or marketing “fit” between new and existing businesses or technologies. Special skills or technologies required to operate the new business. “Cultural fit” between new and old businesses (especially important if entry is by acquisition). Relative strengths of competitors in the new business. By using multiattribute utility analysis, managers can balance these factors against financial considerations to derive a comprehensive evaluation of alternatives. What and whether to negotiate Many negotiations—labor, real estate, and sales, for example—may involve several issues. A labor negotiation could include issues of wage rates, length of agreement, grievance procedures, work rules, seniority, job security, union security, vacations, fringe benefits, and pension fund contributions. Both sides’ opening positions on the issues are often clear, but how they view the trade-offs across issues is not. Using multiattribute analyses of their own preferences and trade-offs and those of the other side, negotiators can uncover opportunities to give a small concession in return for a large benefit.7 How to allocate research and development budgets Research and development projects often exhibit a variety of performance characteristics that managers may need to balance to determine the best project. Multiattribute utility analysis can help them do this. They can also combine such an analysis with a decision tree analysis to address uncertainties and risks. The Forecast for Decision Analysis If the trends of the past decade continue at their present rate, then over the next decade we can certainly expect to see personalized decision analysis spread and become firmly established as a staff function throughout industry. Virtually all corporations of any substance will have in-house staffs or outside consultants to analyze decisions and report findings to top management. The big question is, however, whether decision analysis will become an integrated part of management’s decision making. As C. Jackson Grayson has persuasively argued, the integration requires that the cultural gap between management scientists and managers be bridged. Without the bridge, personalized decision analysis, like operations research and other analytic techniques, may never be more than an optional aid, albeit interesting. For the integration to take place, managers will have to become more skilled at using decision analysis and its practitioners more effective than they are now. In other words, analysts and managers-to-be need to undergo extensive training in the integration of decision analysis with existing organizational and personal decision processes. (This training would go far beyond the teaching of particular techniques, which is as far as most business schools go now.) The integration may also require organizational changes in control and reward structures in business. At present, appropriate professional training is not readily available to either the manager or the specialized decision analyst. What is needed is a course of study (and supporting research) that integrates the logical, the psychological, and the organizational aspects of applied subjective decision analysis. This will probably not become available until there is at least one institute of research and teaching devoted to all aspects of decision-aiding technology (including personalized analysis) and to their integration. This training would require overcoming the institutional rigidities associated with partitioning universities along such traditional departmental lines as engineering, psychology, business, and statistics. Even within single departments such as business, the feeder disciplines—organizational behavior, applied mathematics, finance, business policy, and marketing—are usually kept jealously apart. If these can be adequately synthesized, management science in general, and personalized decision analysis in particular, can at last achieve full-fledged assimilation into the day-to-day business of management. The Tables Turned Up! up! my friend, and quit your books, / Or surely you’ll grow double: / Up! up! my friend, and clear your looks; / Why all this toil and trouble? The sun, above the mountain’s head, / A refreshing lustre mellow / Through all the long green fields has spread, / His first sweet evening yellow. Books! ’tis a dull and endless strife: / Come, hear the woodland linnet, / How sweet his music! on my life / There’s more of wisdom in it. And hark! how blithe the throstle sings! / He, too, is to mean preacher: / Come forth into the light of things, / Let Nature be your teacher. She has a world of ready wealth, / Our minds and hearts to bless— / Spontaneous wisdom breathed by health, / Truth breathed by cheerfulness. One impulse from a vernal wood / May teach you more of man, / Of moral evil and of good, / Than all the sages can. Sweet is the lore which Nature brings; / Our meddling intellect / Misshapes the beauteous forms of things:— / We murder to dissect. Enough of science and of art! / Close up those barren leaves; / Come forth, and bring with you a heart / That watches and receives. William Wordsworth, 1798 References 1. See C. Jackson Grayson, Decisions Under Uncertainty (Boston: Division of Research, Harvard University Graduate School of Business Administration, 1960) and “Management Science and Business Practice,” HBR July–August 1973, p. 41. 2. See Rex V. Brown, “Do Managers Find Decision Theory Useful?” HBR May–June 1970, p. 78, and Howard Raiffa and Robert O. Schlaifer, Applied Statistical Decision Theory (Boston: Division of Research, Harvard University Graduate School of Business Administration, 1962). 3. See, for example, John F. Magee, “Decision Trees for Decision Making,” HBR July–August 1964, p. 126, or the more recent article by Samuel E. Bodily, “When Should You Go to Court?” HBR May–June 1981, p. 103. 4. See David B. Hertz, “Risk Analysis in Capital Investment,” HBR January–February 1964, p. 95, and John S. Hammond III, “Better Decisions with Preference Theory,” HBR November–December 1967, p. 123, for descriptions of risk profiles and utility functions, respectively. 5. Michael E. Porter, Competitive Strategy (New York: The Free Press, 1980), pp. 299–357. 6. A comprehensive treatment of multiattribute utility analysis is provided by Ralph L. Keeney and Howard Raiffa in Decisions with Multiple Objectives: Preferences and Value Trade-offs (New York: Wiley, 1976). Our example illustrates only the basic ideas of the method and the simplest form of analysis, linear and additive. 7. The Art and Science of Negotiation, a forthcoming book by Howard Raiffa (Cambridge: Belknap Press of Harvard University Press) will contain an extensive treatment of this subject. Jacob W. Ulvila’s doctoral dissertation, “Decisions with Multiple Objectives in Integrative Bargaining” (Harvard Business School, 1979), also addresses this topic.

Decision Analysis Comes of Age

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