Decision trees for decision making (2023)

Running a business i Stygian Chemical Industries, Ltd. will have to decide whether to build a small or large facility to produce a new product with a ten-year market life expectancy. The decision depends on how big the market for the product will be.

Demand can be high in the first two years, but drop to low levels thereafter, when many first-time users find the product unsatisfactory. Or high initial demand could indicate the possibility of a sustained high volume market. If demand is high and the company does not expand within the first two years, competing products will certainly be launched.

If the company builds a large facility, it has to live with it, regardless of the size of the market demand. If building a small plant, management has the option to expand the plant in two years if there is high demand in the initial phase; If demand is low during the introductory phase, the company will continue to operate in the small facility and make a decent profit on the low volume.

Management is not sure what to do. The company grew rapidly in the 1950s; kept pace with the chemical industry in general. If the market proves to be large, the new product offers the current management the opportunity to lead the company into a new phase of profitable growth. The development department, especially the development project engineer, is pushing to build the full-scale factory to take advantage of the first large-scale product development the department has produced in several years.

The president, a major shareholder, fears the possibility of unnecessary large factory capacity. He prefers a smaller installation commitment, but recognizes that further expansion to meet high demand would require more investment and be less efficient to operate. The president also recognizes that if the company does not act promptly to meet evolving demand, competitors will be tempted to introduce equivalent products.

The Stygian Chemical problem, simplified as it is, illustrates the uncertainties and problems that management must resolve when making investment decisions. (I use the term "investment" in the broadest sense, referring not only to expenditures for new plant and equipment, but also for large and risky contracts, special marketing facilities, research programs, and other purposes.) These decisions are being made. becoming increasingly important. while increasing in complexity. Countless executives want to make them better - but how?

In this article, I will introduce a newly developed concept called the "decision tree" that has tremendous potential as a decision-making tool. The decision tree, like no other analytical tool I've seen, can help management understand the choices, risks, objectives, monetary rewards, and information needs associated with an investment problem. We'll be hearing a lot more about decision trees in the years to come. While this is new to most business people today, it will certainly be mainstream management jargon before many years pass.

Later in this article, we'll come back to Stygian Chemical's problem and see how management can go about solving it using decision trees. First, however, some features of the decision tree approach will be illustrated with a simpler example.

show alternatives

Let's say it's a rather cloudy Saturday morning and in the afternoon 75 people come for a cocktail. You have a nice garden and your house isn't very big; So, weather permitting, you'll want to prepare refreshments in the garden and celebrate there. It would be more comfortable and your guests would feel more comfortable. On the other hand, if you're setting up your backyard party and it starts to rain after all the guests are gathered, the refreshments will go bad, your guests will get wet, and you'll be wishing you'd decided to party indoors. (We could complicate this problem by considering the possibility of a partial commitment to one course or another and ways to adjust time estimates throughout the day, but the simple problem is all we need.)

This particular decision can be presented in the form of a “paytable”:

Significantly more complex decision issues can be presented in the form of paytables. In the particular case of complex investment decisions, however, a different representation of the information relevant to the problem – the decision tree – makes sense to show the ways in which the various possible outcomes are achieved. Pierre Massé, Commissioner General of the National Agency for Productivity and Equipment Planning in France, says:

The decision problem does not arise either in terms of an isolated decision (since today's decision depends on tomorrow's decision) nor in terms of a sequence of decisions (since under uncertainty what will have influenced the decisions taken in the future already learned). The problem comes in the form of a decision tree.”¹

Figure I shows a decision tree for the cocktail problem. This tree is a different way of displaying the same information that is shown in the paytable. However, as later examples will show, when it comes to complex decisions, the decision tree is often a much clearer means of presenting the relevant information than a paytable.

The tree consists of a series of nodes and branches. At the first node on the left, the host has the option of having the party indoors or outdoors. Each branch represents an alternative course of action or decision. At the end of each branch or alternative route there is another node that represents a random event - whether it will rain or not. Each subsequent alternate stroke to the right represents an alternate outcome of that random event. Each complete alternative path through the tree has an associated return that is displayed at the end of the rightmost branch or at the end of the path.

When drawing decision trees, I like to draw the action or decision forks with square nodes and the random event forks with round nodes. Other symbols can be used instead, e.g. B. branching of one line and two lines, letters or special colors. It doesn't really matter which method of discrimination you use, as long as you use one or the other. A decision tree of any size always matches (a)actionOptions with (b) different possibleeventsorResultsActions influenced in part by chance or other uncontrollable circumstances.

Decision event chains

The previous example, while involving only a single decision stage, demonstrates the elementary principles upon which larger and more complex decision trees are built. Let's take a slightly more complicated situation:

You are trying to decide whether to approve a development budget for an improved product. You are incentivized to do so because the development, if successful, will give you a competitive advantage, but if you don't develop the product, your competitor could seriously erode your market share. You sketch a decision tree that looks like the one in Figure II.

Your initial decision is shown on the left. After the decision to go ahead with the project, if the development is successful, a second stage of decision-making at point A follows. Assuming the situation has not changed significantly between now and the time of point A, decide now which alternatives are important to you right now. On the right side of the tree are the results of various sequences of decisions and events. Again, these results are based on your current information. The bottom line is that you're saying, "If what I know now is true, then this will happen."

Of course, you are not trying to identify every event that might happen or every decision you must make about a topic to be analyzed. In the decision tree, you create only those decisions and events or outcomes that are important to you and have consequences that you want to compare. (More images can be found in the appendix.)

Adding financial data

Now we can return to the problems facing the management of Stygian Chemical. A decision tree that characterizes the investment problem outlined in the introduction is presented in Appendix III. Decision #1 requires the company to choose between a large and a small facility. That's all that needs to be decidednow🇧🇷 However, if the company decides to build a small facility and sees high demand in the initial phase, in two years - in decision #2 - it may decide to expand its facility.

But we go beyond a mere sketch of alternatives. When making decisions, leaders must consider the probabilities, costs, and returns that seem likely. Based on the data they now have, and assuming the company's situation hasn't changed significantly, they argue the following:

• Marketing estimates are 60%Large long-term market opportunity and 40%Possibility of low demand, which initially evolves as follows:

• Therefore, the probability that demand is initially high is 70%(60 + 10).What ifDemand is initially high, but the company estimates the chance of remaining at a high level at 86%(60 ÷ 70). comparison 86%bis 60%, it is clear that a high initial level of sales alters the estimated chance of high sales in subsequent periods. If sales are low in the first few days, chances are also 100%(30 ÷ 30) that sales will be low in subsequent periods. Therefore, it can be assumed that the level of sales in the initial period is a fairly accurate indicator of the level of sales in subsequent periods.

• Annual revenue estimates are made assuming each alternative outcome:

1. A tall, high-volume plant would yield$1,000,000 annually in cash flow.

2. A tall, low-volume plant would only produce$100,000 due to high fixed costs and inefficiencies.

3. A small, low-demand facility would be cost-effective and generate annual cash receipts of$400.000.

4. A small plant would generate income in an initial phase of high demand$450,000 a year, but that would fall on$300,000 annually over the long term due to competition. (The market would be larger than Alternative 3, but it would be divided among more competitors.)

5. If the small factory were expanded to meet the continued high demand, it would generate revenue$700,000 of cash flow annually and therefore would be less efficient than a large factory initially built.

6. If the small facility were expanded but not sustained, high demand would be the estimated annual cash flow$50.000.

• It is also estimated how much a large plant would cost$3 million to start would cost a small factory$1.3 million, and expanding the small facility would cost more$2.2 million.

When the above data is included, we have the decision tree shown in Appendix IV. Keep in mind that nothing is shown here that Stygian Chemical executives didn't know about beforehand; no number was drawn from hats. However, we are starting to see dramatic evidence of the value of decision trees.Put outwhat management knows in a way that allows for more systematic analysis and leads to better decisions. To summarize the requirements for creating a decision tree, management must:

1. Identify the decision points and the alternatives available at each point.

2. Identify points of uncertainty and the nature or range of alternative outcomes at each point.

3. Estimate the values ​​needed for the analysis, especially the probabilities of various events or outcomes of actions, and the costs and gains of various events and actions.

4. Review alternative values ​​to choose a course.

Selection of course of action

We are now ready for the next step in the analysis - comparing the consequences of different courses of action. A decision tree does not give management an answer to an investment problem; Rather, it helps management determine which alternative to a given selection point will produce the greatest expected financial gain, given the information and alternatives relevant to the decision.

Of course, the rewards must be weighed against the risks. At Stygian Chemical, as at many companies, managers have different perspectives on risk; therefore, they will reach different conclusions under the circumstances described by the decision tree presented in Appendix IV. The many people involved in a decision – those who provide capital, ideas, data or decisions and have different values ​​at stake – will see the uncertainty surrounding the decision in different ways. If these differences are not recognized and addressed, the decision maker, pays for it, provides data and analysis, and has to live with it, will judge the issue, the relevance of the data, the need for analysis, and the success criterion differently. and contradictory.

For example, a company's shareholders may see a particular investment as one of several possibilities, some of which will work and some of which will fail. A large investment can pose a risk to a middle manager—to his job and his career—regardless of the decision he makes. Another participant may gain a lot from the project's success but lose little from the project's failure. The nature of the risk - as each individual sees it - influences not only the assumptions they are willing to make, but also the strategy they follow in dealing with the risk.

The existence of multiple, unspoken and conflicting objectives will certainly contribute to the “politics” of Stygian Chemical's decision, and one can be sure that the political element is present whenever it comes to people's lives and ambitions. Here, as in similar cases, it is not bad practice to think about the parties involved in an investment decision and try to make the following assessments:

• What's at risk?Is it profit or equity, business survival, getting a job, opportunity for a great career?

• Who takes the risk?The shareholder generally assumes the risk in some form. Management, employees, the community - all carry different risks.

• What is the nature of the risk that each person runs?That's it,on your terms,unique, unique, sequential, insurable? Does it affect the economy, the industry, the company or part of the company?

Considerations like the above will certainly enter top management thinking, and the decision tree in Appendix IV will not eliminate them. But the tree shows management which decision today contributes most to its long-term goals. The tool for this next step of analysis is the concept of "reversal".

Concept of "reversal"

This is how reversal works in the described situation. At the time of Decision #1 (see Appendix IV), management does not need to make Decision #2 and does not know whether it will have the opportunity to do so. but if thatguerraTo have the option under Decision #2, based on current knowledge, the Company would expand the facility. The analysis is presented in Appendix V. (I will ignore the issue of discounting future earnings for now; this will be introduced later.) We see that the total expected value of the expansion alternative is$160,000 more than the no-expansion alternative over the remaining eight years. Therefore, given the information they had prior to decision #2, the alternative management would choose (thinking only of monetary gain as the standard of choice).

Readers may wonder why we started with Decision #2 when today's problem is Decision #1. The reason is this: we need to be able to put a monetary value on Decision #2 to "reverse" Decision #1 and profit from renting the lower branch ("Build Small Factory") with the profit from taking the upper branch ("Build Big Plant"). Let's call this monetary value for decision #2position value🇧🇷 The position value of a decision is the expected value of the preferred branch (in this case, the factory extension fork). The expected value is simply a sort of average of the results you would expect if you repeated the situation several times - you get a$5,600,000 equals 86%of time and one$400,000 equals 14%all the time.

In other words, it's worth it$2,672,000 to Stygian Chemical to position itself to make Decision #2. The question is, given that figure and the other data shown in Appendix IV, what now appears to be the best course of action for Decision #1?

Go now to Appendix VI. To the right of the branches in the top half, we see the yields of various events when a large installation is built (these are simply the Installation IV numbers multiplied). In the bottom half, we see the small plant counts, including the position value from Decision #2 plus the yield for the two years prior to Decision #2. If we subtract all these yields by their probabilities, we get the following comparison:

Therefore, the choice that maximizes expected total return in Decision #1 is to build the large facility first.

billing for time

And as for the differences inTempoof future income? The time between successive decision stages in a decision tree can be significant. At each stage, we may need to weigh differences in immediate costs or revenues against differences in value at the next stage. Whichever parameter is used, we can put the two alternatives on a comparable basis, discounting the value assigned to the next level by an appropriate percentage. The discount percentage is actually a deduction from the cost of capital and is similar to using a present value discount rate or discounted cash flow techniques that are well known to entrepreneurs.

If decision trees are used, the discounting method can be applied step by step. Both cash flows and position values ​​are discounted.

Let's assume for simplicity that a discount rate of 10%per year for all phases is determined by Stygian Chemical management. Using the reversal principle, we start again with decision #2. Let's take the same numbers used in the previous views and discount the cash flows by 10%, we obtain the data shown in Part A of Appendix VII. Please note in particular that these are cash amounts.from the moment decision No. 2 is taken.

Now let's follow the same procedure used in Appendix V when we got the expected values, only this time using the discounted yield numbers and getting a discounted expected value. The results are presented in Part B of Appendix VII. Since the discounted expected value of the unextended alternative is greater,aThe number becomes the position value of decision #2 this time.

Once this is done, we work with Decision No. 1 again, repeating the same analytical procedure as before, only with a discount. The calculations are presented in Annex VIII. Note that the Decision #2 position value at the time of Decision #1 is treated as if it were a lump sum received at the end of the two years.

The large plant alternative is again preferred based on discounted expected cash flow. But the scope of the difference compared to the small-scale alternative ($290,000) is less than without discount.

uncertainty alternatives

In illustrating the decision tree concept, I treated uncertainty alternatives as if they were discrete, well-defined possibilities. For my examples, I used uncertain situations that essentially depend on a single variable, such as the level of demand or the success or failure of a development project. I tried to avoid unnecessary complications while focusing on the main interrelationships between the current decision, future decisions, and intervening uncertainties.

In many cases, the uncertain elements take the form of discrete alternatives of a single variable. In others, however, cash flow opportunities during a phase can span a spectrum and depend on several independent or partially related variables that are subject to random influences – cost, demand, yield, economic climate, and so on. In these cases, we have found that the range of variability, or the probability that cash flow will fall within a certain range over a period, can be easily calculated from knowledge of the key variables and the uncertainties surrounding them. Then, the spectrum of cash flow opportunities during the phase can be divided into two, three or more "subsets" that can be used as discrete random alternatives.

Conclusion

Peter F. Drucker succinctly expressed the relationship between present planning and future events: “Long-term planning is not concerned with future decisions. It deals with the future of present decisions.”²Today's decision must be taken in view of the expected impact and outcome of uncertain events on future values ​​and decisions. Since today's decision sets the stage for tomorrow's decision, today's decision must balance economy with flexibility; There must be a balance between the need to seize opportunities as they arise and the ability to respond to future circumstances and needs.

The unique feature of the decision tree is that it allows management to combine analytical techniques such as discounted cash flow and present value methods with a clear representation of the implications of future decision alternatives and events. Management can use the decision tree to weigh multiple options for action more easily and clearly. Interactions between current decision alternatives, uncertain events, and future decisions and their outcomes become more visible.

Of course, there are many practical aspects of decision trees beyond what could be covered in just one article. When these other aspects are discussed in subsequent articles,³the whole range of possible gains for management is considered in more detail.

Certainly, the decision tree concept does not provide definitive answers for management making investment decisions in the face of uncertainty. We haven't reached that stage yet, and maybe we never will. However, the concept is valuable for illustrating the structure of investment decisions and can also provide excellent guidance in investment evaluation.occasions.

1.Optimal investment decisions: action rules and selection criteria(Englewood Cliffs, Nova Jersey, Prentice-Hall, Inc., 1962), p. 250.

2. "Long-Term Planning",business Administration,April 1959, S. 239.

3. We look forward to another article from Mr. Magee in an upcoming issue.—The editors

A version of this article appeared atjuly 1964problem ofHarvard Business Review.