The monitoring of a agency that I shall call Stygian Chemical Industries, Ltd., have to decide whether to build a little plant or a huge one to manufacture a new product with an expected sector life of ten years. The decision hinges on what size the sector for the product will be. Possibly demand also will certainly be <…>

The management of a company that I shall call Stygian Chemical Industries, Ltd., should decide whether to develop a little plant or a large one to manufacture a brand-new product through an intended market life of ten years. The decision hinges on what size the industry for the product will be. Possibly demand also will be <…>


The administration of a company that I shall call Stygian Chemical Industries, Ltd., have to decide whether to build a small plant or a big one to manufacture a brand-new product via an expected sector life of ten years. The decision hinges on what size the sector for the product will be. Possibly demand will certainly be <…>


The administration of a company that I shall speak to Stygian Chemical Industries, Ltd., must decide whether to build a tiny plant or a huge one to manufacture a new product with an supposed sector life of ten years. The decision hinges on what dimension the industry for the product will be.

You are watching: Whether to use a decision table or a decision tree often is a matter of personal preference.

Possibly demand also will be high in the time of the initial 2 years but, if many type of initial customers discover the product unsatismanufacturing facility, will certainly loss to a low level thereafter. Or high initial demand might indicate the opportunity of a continual high-volume sector. If demand also is high and the company does not expand also within the first two years, competitive assets will certainly sudepend be presented.

If the firm builds a big plant, it need to live via it whatever before the size of market demand. If it builds a little plant, administration has the choice of expanding the plant in two years in the event that demand also is high throughout the introductory period; while in the event that demand also is low in the time of the introductory duration, the firm will preserve operations in the little plant and make a tidy profit on the low volume.

Management is uncertain what to execute. The firm thrived swiftly during the 1950’s; it kept pace with the chemical sector mainly. The brand-new product, if the industry turns out to be huge, provides the existing administration a possibility to press the agency into a brand-new duration of profitable expansion. The development department, especially the development job engineer, is pushing to construct the massive plant to make use of the first major product advance the department has actually produced in some years.

The chairman, a primary stockholder, is wary of the possibility of large unrequired plant capacity. He favors a smaller sized plant commitment, but recognizes that later expansion to accomplish high-volume demand would certainly require more investment and be much less reliable to run. The chairguy likewise recognizes that unmuch less the agency moves promptly to fill the demand which establishes, competitors will certainly be tempted to relocate in with indistinguishable products.

The Stygian Chemical difficulty, oversimplified as it is, illustprices the unpredictabilities and problems that organization management must fix in making investment decisions. (I usage the term “investment” in a wide sense, referring to outlays not only for new plants and tools yet likewise for big, risky orders, unique marketing infrastructure, study programs, and various other functions.) These decisions are growing even more necessary at the exact same time that they are raising in complexity. Countmuch less executives desire to make them better—but how?

In this short article I shall current one freshly occurred concept called the “decision tree,” which has actually significant potential as a decision-making tool. The decision tree have the right to clarify for monitoring, as have the right to no various other analytical tool that I understand of, the options, risks, objectives, financial gains, and also information demands connected in an investment difficulty. We shall be hearing a good deal about decision trees in the years ahead. Although a novelty to many businessguys this particular day, they will certainly sucount be in widespread administration parlance prior to many kind of more years have passed.

Later in this post we shall go back to the problem encountering Stygian Chemical and check out how monitoring deserve to proceed to fix it by using decision trees. First, however, a simpler instance will certainly highlight some qualities of the decision-tree approach.

Displaying Alternatives

Let us mean it is a quite overactors Saturday morning, and also you have 75 people coming for cocktails in the afternoon. You have actually a pleasant garden and also your residence is not also large; so if the weather permits, you would certainly prefer to erected the refreshments in the garden and have actually the party tbelow. It would be even more pleasant, and your guests would certainly be even more comfortable. On the various other hand also, if you set up the party for the garden and also after all the guests are assembled it begins to rain, the refreshments will certainly be damaged, your guests will get damp, and also you will certainly heartily wish you had actually determined to have actually the party in the home. (We might complicate this difficulty by considering the opportunity of a partial commitment to one course or one more and methods to change approximates of the weather as the day goes on, but the easy difficulty is all we need.)

This specific decision have the right to be stood for in the create of a “payoff” table:


Much more facility decision questions deserve to be depicted in payoff table create. However, specifically for complex investment decisions, a various depiction of the information pertinent to the problem—the decision tree—is advantageous to display the paths through which the various possible outcomes are accomplished. Pierre Massé, Commissioner General of the National Agency for Productivity and also Equipment Planning in France, notes:

“The decision difficulty is not posed in terms of an isolated decision (bereason today’s decision relies on the one we shall make tomorrow) nor yet in terms of a sequence of decisions (bereason under uncertainty, decisions taken later on will certainly be affected by what we have actually learned in the meanwhile). The difficulty is posed in regards to a tree of decisions.”1

Exhilittle bit I illustprices a decision tree for the cocktail party trouble. This tree is a different method of displaying the exact same indevelopment presented in the payoff table. However, as later examples will certainly display, in complex decisions the decision tree is typically a more lucid means of presenting the appropriate information than is a payoff table.


Exhilittle bit I. Decision Tree for Cocktail Party

The tree is comprised of a collection of nodes and branches. At the first node on the left, the hold has the alternative of having the party inside or outside. Each branch represents an alternate course of activity or decision. At the finish of each branch or alternate course is an additional node representing a possibility event—whether or not it will rain. Each succeeding alternate course to the appropriate represents an alternate outcome of this opportunity occasion. Associated via each finish alternate course with the tree is a payoff, presented at the finish of the rightmany or terminal branch of the course.

When I am illustration decision trees, I favor to suggest the activity or decision forks with square nodes and also the chance-occasion forks with round ones. Other icons might be provided instead, such as single-line and also double-line branches, unique letters, or colors. It does not issue so a lot which method of distinguishing you use so lengthy as you carry out employ one or another. A decision tree of any type of size will certainly constantly integrate (a) action options through (b) various feasible events or results of activity which are partially influenced by possibility or various other uncontrolled scenarios.

Decision-occasion chains

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

You are trying to decide whether to give a development budgain for an boosted product. You are urged to execute so on the grounds that the advance, if successful, will offer you a competitive edge, but if you execute not construct the product, your competitor may—and might seriously damages your sector share. You sketch out a decision tree that looks something like the one in Exhilittle II.


Exhilittle II. Decision Tree with Chains of Actions and Events

Your initial decision is presented at the left. Following a decision to continue via the task, if advance is successful, is a second phase of decision at Point A. Assuming no important readjust in the case in between currently and also the time of Point A, you decide now what options will certainly be essential to you at that time. At the right of the tree are the outcomes of different sequences of decisions and also occasions. These outcomes, also, are based on your current indevelopment. In effect you say, “If what I know currently is true then, this is what will take place.”

Of course, you do not attempt to identify all the events that can happen or all the decisions you will certainly need to make on a subject under evaluation. In the decision tree you lay out only those decisions and also events or results that are important to you and have actually after-effects you wish to compare. (For even more illustrations, view the Appendix.)


For readers interested in even more examples of decision-tree structure, I shall explain in this appendix 2 representative cases through which I am acquainted and show the trees that could be drawn to analyze management’s decision-making options. We shall not problem ourselves here through prices, yields, probabilities, or supposed worths.

New Facility

The option of options in building a plant counts upon industry forecasts. The alternative liked will, consequently, impact the sector outcome. For example, the armed forces products department of a diversified firm, after some period of low earnings because of intense competition, has actually won a contract to develop a new kind of armed forces engine suitable for Military deliver vehicles. The department has actually a contract to construct fertile capacity and also to produce at a mentioned contract level over a duration of three years.

Figure A illustrates the situation. The dotted line mirrors the contract price. The solid line mirrors the proposed buildup of production for the military. Some various other possibilities are depicted by damelted lines. The agency is not certain whether the contract will certainly be ongoing at a fairly high price after the third year, as shown by Line A, or whether the armed forces will certainly rotate to another more recent advancement, as shown by Line B. The firm has no guarantee of compensation after the 3rd year. There is also the opportunity, indicated by Line C, of a huge extra commercial sector for the product, this possibility being rather dependent on the expense at which the product have the right to be made and sold.


If this commercial market could be tapped, it would certainly represent a significant brand-new business for the agency and also a comprehensive advancement in the profitcapability of the division and its importance to the agency.

Management desires to discover 3 methods of creating the product as follows:

1. It could subcontract all fabrication and erected an easy assembly through restricted require for investment in plant and equipment; the costs would certainly tend to be relatively high and also the company’s investment and also profit possibility would certainly be restricted, yet the company assets which are at hazard would certainly additionally be limited.

2. It can undertake the major component of the fabrication itself yet usage general-function machine tools in a plant of general-function construction. The department would have a opportunity to retain even more of the most profitable operations itself, exploiting some technical advancements it has made (on the basis of which it got the contract). While the expense of manufacturing would certainly still be fairly high, the nature of the investment in plant and devices would certainly be such that it could most likely be turned to other provides or liquidated if the service disappeared.

3. The agency can build a extremely mechanized plant through specialized fabrication and also assembly equipment, entailing the biggest investment yet yielding a dramatically reduced unit production cost if manufacturing volume were sufficient. Following this arrangement would boost the chances for a extension of the army contract and also penetration into the commercial sector and would boost the profitability of whatever before organization can be acquired in these sectors. Faitempt to sustain either the military or the commercial industry, but, would reason considerable financial loss.

Either of the first two options would certainly be much better adapted to low-volume manufacturing than would the third.

Some major uncertainties are: the cost-volume relationships under the alternative production methods; the size and framework of the future market—this relies in part on expense, but the level and also level of dependence are unknown; and also the possibilities of competitive advances which would render the product competitively or technologically obsolete.

How would this instance be displayed in decision-tree form? (Before going better you might want to draw a tree for the trouble yourself.) Figure B mirrors my version of a tree. Note that in this instance the opportunity choices are rather influenced by the decision made. A decision, for example, to construct a much more effective plant will certainly open up possibilities for an increased industry.


Plant Modernization

A company monitoring is confronted with a decision on a proposal by its design staff which, after three years of study, desires to install a computer-based manage device in the company’s major plant. The intended cost of the manage mechanism is some $30 million. The declared advantages of the system will certainly be a reduction in labor price and also an improved product yield. These benefits depfinish on the level of product throughput, which is likely to increase over the next decade. It is believed that the installation regimen will certainly take around 2 years and also will certainly price a substantial amount over and also over the expense of equipment. The engineers calculate that the automation job will certainly yield a 20% return on investment, after taxes; the estimate is based upon a ten-year foreactors of product demand by the market research department, and an assumption of an eight-year life for the process regulate mechanism.

What would certainly this investment yield? Will actual product sales be greater or reduced than forecast? Will the process work? Will it achieve the economic climates expected? Will rivals follow if the company is successful? Are they going to mechanize anyway? Will brand-new commodities or processes make the standard plant obsolete before the investment deserve to be recovered? Will the controls last eight years? Will somepoint better come along sooner?

The initial decision alternatives are (a) to install the proposed manage mechanism, (b) postpone action till trends in the market and/or competition come to be clearer, or (c) initiate even more examination or an independent testimonial. Each alternate will be followed by resolution of some uncertain aspect, in component dependent on the action taken. This resolution will certainly lead in turn to a new decision. The dotted lines at the ideal of Figure C show that the decision tree proceeds inabsolutely, though the decision choices carry out tend to come to be repeated. In the situation of postponement or better research, the decisions are to install, postpone, or restudy; in the situation of installation, the decisions are to proceed operation or abandon.

An instant decision is regularly among a sequence. It may be among a number of sequences. The affect of the current decision in narrowing dvery own future options and the effect of future options in affecting the value of the current choice must both be thought about.

Adding Financial File

Now we have the right to return to the troubles confronted by the Stygian Chemical monitoring. A decision tree characterizing the investment trouble as outlined in the introduction is shown in Exhibit III. At Decision #1 the firm must decide in between a huge and a little plant. This is all that have to be determined now. But if the firm chooses to construct a small plant and also then finds demand also high in the time of the initial duration, it have the right to in two years—at Decision #2—pick to expand its plant.

But let us go past a bare outline of choices. In making decisions, executives should take account of the probabilities, prices, and returns which appear likely. On the basis of the information currently available to them, and also assuming no essential readjust in the company’s instance, they factor as follows:

Marketing estimates suggest a 60% opportunity of a large sector in the long run and a 40% opportunity of a low demand, occurring initially as follows:
Because of this, the chance that demand also initially will certainly be high is 70% (60 + 10). If demand also is high initially, the agency estimates that the chance it will proceed at a high level is 86% (60 ÷ 70). Comparing 86% to 60%, it is noticeable that a high initial level of sales alters the approximated possibility of high sales in the succeeding periods. Similarly, if sales in the initial period are low, the possibilities are 100% (30 ÷ 30) that sales in the succeeding durations will be low. Thus the level of sales in the initial duration is intended to be a quite exact indicator of the level of sales in the succeeding periods. Price quotes of annual income are made under the presumption of each different outcome:

1. A huge plant via high volume would certainly yield $1,000,000 every year in cash flow.

2. A large plant via low volume would certainly yield just $100,000 because of high resolved expenses and also inefficiencies.

3. A little plant with low demand also would be economical and also would certainly yield yearly cash income of $400,000.

4. A little plant, throughout an initial duration of high demand also, would certainly yield $450,000 per year, but this would certainly drop to $300,000 yearly in the long run bereason of competition. (The sector would be larger than under Alternative 3, however would certainly be separated up among more rivals.)

5. If the tiny plant were increased to meet sustained high demand also, it would certainly yield $700,000 cash flow annually, and also so would be much less effective than a large plant constructed initially.

6. If the little plant were increased but high demand also were not sustained, estimated annual cash flow would be $50,000.

It is estimated additionally that a huge plant would price $3 million to put into operation, a tiny plant would certainly expense $1.3 million, and also the expansion of the small plant would certainly expense an additional $2.2 million.

When the foregoing data are incorporated, we have actually the decision tree presented in Exhibit IV. Bear in mind that nothing is shown below which Stygian Chemical’s executives did not understand before; no numbers have actually been pulled out of hats. However before, we are beginning to see dramatic proof of the worth of decision trees in laying out what management knows in a means that allows even more systematic evaluation and also leads to much better decisions. To amount up the requirements of making a decision tree, monitoring must:

1. Identify the points of decision and also alternatives obtainable at each point.

2. Identify the points of uncertainty and the form or selection of different outcomes at each allude.

3. Estimate the values necessary to make the analysis, especially the probabilities of various events or outcomes of action and the expenses and also gains of assorted events and also actions.

4. Analyze the alternative worths to choose a course.

Choosing Course of Action

We are now prepared for the following action in the analysis—to compare the consequences of various courses of action. A decision tree does not offer monitoring the answer to an investment problem; fairly, it helps administration recognize which alternative at any type of certain alternative allude will certainly yield the greatest expected financial get, given the information and options pertinent to the decision.

Of course, the gains need to be perceived through the dangers. At Stygian Chemical, as at many type of corporations, supervisors have actually different points of watch towards risk; for this reason they will certainly draw different conclusions in the situations described by the decision tree presented in Exhilittle bit IV. The many civilization participating in a decision—those providing funding, ideas, data, or decisions, and having various values at risk—will watch the uncertainty bordering the decision in various means. Unless these distinctions are recognized and also faced, those who should make the decision, pay for it, supply data and analyses to it, and live with it will judge the issue, relevance of information, require for evaluation, and also criterion of success in different and conflicting ways.

For example, firm stockholders might treat a particular investment as one of a series of possibilities, some of which will certainly job-related out, others of which will certainly fail. A major investment might pose dangers to a middle manager—to his project and also career—no issue what decision is made. Another participant might have a lot to obtain from success, yet little bit to shed from faitempt of the task. The nature of the risk—as each individual sees it—will influence not just the assumptions he is willing to make however likewise the strategy he will follow in managing the threat.

The presence of multiple, unproclaimed, and conflicting objectives will absolutely add to the “politics” of Stygian Chemical’s decision, and one have the right to be certain that the political element exists whenever the resides and ambitions of human being are affected. Here, as in equivalent instances, it is not a bad exercise to think through who the parties to an investment decision are and to try to make these assessments:

What is at risk? Is it profit or equity value, survival of the service, maintenance of a project, opportunity for a major career?

Who is bearing the risk? The stockholder is typically bearing risk in one develop. Management, employees, the community—all might be bearing different threats. What is the character of the risk that each perkid bears? Is it, in his terms, distinct, once-in-a-life time, sequential, insurable? Does it influence the economic climate, the market, the firm, or a part of the company?

Considerations such as the foregoing will certainly sudepend enter right into top management’s reasoning, and also the decision tree in Exhilittle bit IV will certainly not remove them. But the tree will show administration what decision this day will certainly add most to its permanent purposes. The tool for this following step in the evaluation is the idea of “rollearlier.”

“Rollback” idea

Here is just how rollearlier functions in the situation explained. At the time of making Decision #1 (watch Exhilittle IV), monitoring does not need to make Decision #2 and also does not even understand if it will have the occasion to perform so. But if it were to have the choice at Decision #2, the firm would expand the plant, in watch of its current knowledge. The evaluation is displayed in Exhibit V. (I shall disregard for the minute the question of discounting future profits; that is introduced later on.) We watch that the complete supposed value of the expansion different is $160,000 higher than the no-development alternative, over the eight-year life continuing to be. Hence that is the alternate monitoring would pick if faced through Decision #2 with its existing indevelopment (and also thinking just of monetary get as a conventional of choice).

Readers might wonder why we started with Decision #2 once today’s problem is Decision #1. The reason is the following: We must be able to put a monetary worth on Decision #2 in order to “roll back” to Decision #1 and compare the acquire from taking the reduced branch (“Build Small Plant”) with the get from taking the upper branch (“Build Big Plant”). Let us contact that monetary value for Decision #2 its position value. The place worth of a decision is the expected worth of the wanted branch (in this situation, the plant-expansion fork). The meant value is ssuggest a kind of average of the results you would intend if you were to repeat the situation over and over—getting a $5,600 thousand yield 86% of the time and also a $400 thousand yield 14% of the time.

Stated in an additional means, it is worth $2,672 thousand to Stygian Chemical to acquire to the position wright here it deserve to make Decision #2. The question is: Given this value and also the other information presented in Exhilittle IV, what currently shows up to be the ideal activity at Decision #1?

Turn now to Exhilittle VI. At the right of the branches in the height half we see the yields for miscellaneous events if a huge plant is constructed (these are sindicate the numbers in Exhilittle bit IV multiplied out). In the bottom half we see the tiny plant numbers, including Decision #2 position value plus the yield for the 2 years before Decision #2. If we alleviate all these returns by their probabilities, we obtain the following comparison:

Build huge plant: ($10 × .60) + ($2.8 × .10) + ($1 × .30) – $3 = $3,600 thousand also

Build little plant: ($3.6 × .70) + ($4 × .30) – $1.3 = $2,400 thousand

The option which maximizes expected complete cash yield at Decision #1, therefore, is to develop the substantial plant initially.

Accounting for Time

What around taking distinctions in the time of future income into account? The time in between successive decision stperiods on a decision tree might be comprehensive. At any phase, we may need to weigh differences in instant expense or revenue against differences in value at the next stage. Whatever before traditional of alternative is applied, we can put the two alternatives on a equivalent basis if we discount the worth assigned to the following stage by an correct percent. The discount percent is, in impact, an allowance for the price of capital and also is comparable to the usage of a discount rate in the existing value or discounted cash flow techniques currently renowned to businessmen.

When decision trees are offered, the discounting procedure can be applied one phase at a time. Both cash flows and also position worths are discounted.

For simplicity, let us assume that a discount price of 10% per year for all stperiods is decided on by Stygian Chemical’s monitoring. Applying the rollago principle, we aacquire begin via Decision #2. Taking the very same numbers used in previous exhibits and discounting the cash flows at 10%, we acquire the data shown in Part A of Exhilittle bit VII. Note especially that these are the current worths as of the moment Decision #2 is made.


Exhilittle VII. Analysis of Decision #2 with Discounting Note: For simplicity, the first year cash circulation is not discounted, the second year cash circulation is discounted one year, and also so on.

Now we want to go via the same procedure offered in Exhilittle V as soon as we acquired supposed worths, only this time using the discounted yield numbers and obtaining a discounted intended worth. The results are presented in Part B of Exhilittle VII. Because the discounted intended worth of the no-growth alternative is greater, that number becomes the place worth of Decision #2 this time.

Having done this, we go earlier to occupational via Decision #1 aacquire, repeating the exact same analytical procedure as before only with discounting. The calculations are presented in Exhibit VIII. Keep in mind that the Decision #2 place value is treated at the time of Decision #1 as if it were a lump sum got at the end of the 2 years.

The large-plant different is again the preferred one on the basis of discounted meant cash circulation. But the margin of difference over the small-plant alternative ($290 thousand) is smaller sized than it was without discounting.

Uncertainty Alternatives

In depicting the decision-tree concept, I have treated uncertainty choices as if they were discrete, well-identified possibilities. For my examples I have actually made usage of uncertain instances depending basically on a single variable, such as the level of demand also or the success or faientice of a development job. I have actually smust protect against unessential complication while placing focus on the vital interrelationships among the existing decision, future options, and also the intervening unpredictabilities.

In many instances, the unparticular elements execute take the develop of discrete, single-variable options. In others, but, the possibilities for cash circulation in the time of a stage may range with a totality spectrum and might depfinish on a variety of independent or partially related variables topic to possibility influences—expense, demand also, yield, economic climate, and so forth. In these situations, we have uncovered that the array of varicapability or the likelihood of the cash flow falling in a given selection throughout a stage can be calculated readily from expertise of the crucial variables and also the uncertainties bordering them. Then the selection of cash-circulation possibilities throughout the phase deserve to be broken down into 2, three, or even more “subsets,” which have the right to be offered as discrete opportunity options.


Peter F. Drucker has actually succinctly expressed the relation in between present planning and future events: “Long-selection planning does not resolve future decisions. It deals with the futurity of present decisions.”2 Today’s decision need to be made in light of the anticipated impact it and the outcome of uncertain occasions will certainly have on future worths and decisions. Since today’s decision sets the stage for tomorrow’s decision, today’s decision must balance economic climate with flexibility; it must balance the must capitalize on profit avenues that may exist via the capacity to react to future scenarios and requirements.

The unique feature of the decision tree is that it allows management to incorporate analytical methods such as discounted cash circulation and present worth methods with a clear portrayal of the influence of future decision choices and occasions. Using the decision tree, monitoring can take into consideration various courses of activity with greater ease and clarity. The interactions between existing decision choices, uncertain occasions, and also future options and also their outcomes end up being more visible.

Of course, there are many kind of valuable elements of decision trees in addition to those that might be extended in the area of just one article. When these other elements are disputed in subsequent short articles,3 the totality selection of feasible gains for management will be viewed in greater information.

Sudepend the decision-tree concept does not market last answers to managements making investment decisions in the challenge of uncertainty. We have not got to that phase, and also possibly we never before will certainly. Nevertheless, the idea is helpful for portraying the structure of investment decisions, and also it can likewise provide fantastic aid in the review of capital investment opportunities.

1. Optimal Investment Decisions: Rules for Action and also Criteria for Choice (Englelumber Cliffs, New Jersey, Prentice-Hall, Inc., 1962), p. 250.

See more: September 25Th: The Phrase, Cuius Regio, Eius Religio, Means

2. “Long-Range Planning,” Management Science, April 1959, p. 239.

3. We are expecting one more short article by Mr. Magee in a forthcoming concern.—The Editors