The management of a company that I shall call Stygian Chemical Industries, Ltd., must decide whether to build a small plant or a large one to manufacture a new product with an expected market life of ten years. The decision hinges on what size the market for the product will be.

Possibly demand will be high during the initial two years but, if many initial users find the product unsatisfactory, will fall to a low level thereafter. Or high initial demand might indicate the possibility of a sustained high-volume market. If demand is high and the company does not expand within the first two years, competitive products will surely be introduced.

If the company builds a big plant, it must live with it whatever the size of market demand. If it builds a small plant, management has the option of expanding the plant in two years in the event that demand is high during the introductory period; while in the event that demand is low during the introductory period, the company will maintain operations in the small plant and make a tidy profit on the low volume.

Management is uncertain what to do. The company grew rapidly during the 1950’s; it kept pace with the chemical industry generally. The new product, if the market turns out to be large, offers the present management a chance to push the company into a new period of profitable growth. The development department, particularly the development project engineer, is pushing to build the large-scale plant to exploit the first major product development the department has produced in some years.

The chairman, a principal stockholder, is wary of the possibility of large unneeded plant capacity. He favors a smaller plant commitment, but recognizes that later expansion to meet high-volume demand would require more investment and be less efficient to operate. The chairman also recognizes that unless the company moves promptly to fill the demand which develops, competitors will be tempted to move in with equivalent products.

The Stygian Chemical problem, oversimplified as it is, illustrates the uncertainties and issues that business management must resolve in making investment decisions. (I use the term “investment” in a broad sense, referring to outlays not only for new plants and equipment but also for large, risky orders, special marketing facilities, research programs, and other purposes.) These decisions are growing more important at the same time that they are increasing in complexity. Countless executives want to make them better—but how?

In this article I shall present one recently developed concept called the “decision tree,” which has tremendous potential as a decision-making tool. The decision tree can clarify for management, as can no other analytical tool that I know of, the choices, risks, objectives, monetary gains, and information needs involved in an investment problem. We shall be hearing a great deal about decision trees in the years ahead. Although a novelty to most businessmen today, they will surely be in common management parlance before many more years have passed.

Later in this article we shall return to the problem facing Stygian Chemical and see how management can proceed to solve it by using decision trees. First, however, a simpler example will illustrate some characteristics of the decision-tree approach.

Displaying Alternatives

Let us suppose it is a rather overcast Saturday morning, and you have 75 people coming for cocktails in the afternoon. You have a pleasant garden and your house is not too large; so if the weather permits, you would like to set up the refreshments in the garden and have the party there. It would be more pleasant, and your guests would be more comfortable. On the other hand, if you set up the party for the garden and after all the guests are assembled it begins to rain, the refreshments will be ruined, your guests will get damp, and you will heartily wish you had decided to have the party in the house. (We could complicate this problem by considering the possibility of a partial commitment to one course or another and opportunities to adjust estimates of the weather as the day goes on, but the simple problem is all we need.)

This particular decision can be represented in the form of a “payoff” table:

Much more complex decision questions can be portrayed in payoff table form. However, particularly for complex investment decisions, a different representation of the information pertinent to the problem—the decision tree—is useful to show the routes by which the various possible outcomes are achieved. Pierre Massé, Commissioner General of the National Agency for Productivity and Equipment Planning in France, notes:

Exhibit I illustrates a decision tree for the cocktail party problem. This tree is a different way of displaying the same information shown in the payoff table. However, as later examples will show, in complex decisions the decision tree is frequently a much more lucid means of presenting the relevant information than is a payoff table.

The tree is made up of a series of nodes and branches. At the first node on the left, the host has the choice of having the party inside or outside. Each branch represents an alternative course of action or decision. At the end of each branch or alternative course is another node representing a chance event—whether or not it will rain. Each subsequent alternative course to the right represents an alternative outcome of this chance event. Associated with each complete alternative course through the tree is a payoff, shown at the end of the rightmost or terminal branch of the course.

When I am drawing decision trees, I like to indicate the action or decision forks with square nodes and the chance-event forks with round ones. Other symbols may be used instead, such as single-line and double-line branches, special letters, or colors. It does not matter so much which method of distinguishing you use so long as you do employ one or another. A decision tree of any size will always combine (a) action choices with (b) different possible events or results of action which are partially affected by chance or other uncontrollable circumstances.

Decision-event chains

The previous example, though involving only a single stage of decision, illustrates the elementary principles on which larger, more complex decision trees are built. Let us take a slightly more complicated situation:

You are trying to decide whether to approve a development budget for an improved product. You are urged to do so on the grounds that the development, if successful, will give you a competitive edge, but if you do not develop the product, your competitor may—and may seriously damage your market share. You sketch out a decision tree that looks something like the one in Exhibit II.

Your initial decision is shown at the left. Following a decision to proceed with the project, if development is successful, is a second stage of decision at Point A. Assuming no important change in the situation between now and the time of Point A, you decide now what alternatives will be important to you at that time. At the right of the tree are the outcomes of different sequences of decisions and events. These outcomes, too, are based on your present information. In effect you say, “If what I know now is true then, this is what will happen.”

Of course, you do not try to identify all the events that can happen or all the decisions you will have to make on a subject under analysis. In the decision tree you lay out only those decisions and events or results that are important to you and have consequences you wish to compare. (For more illustrations, see the Appendix.)

Decision trees for decision making. (1964, July 1). Harvard Business Review. https://hbr.org/1964/07/decision-trees-for-decision-making