The monitoring of a agency that ns shall speak to Stygian chemical Industries, Ltd., need to decide even if it is to develop a small plant or a big one come manufacture a new product v an expected market life the ten years. The decision hinges top top what dimension the industry for the product will be. Possibly demand will it is in <…>

The management of a agency that i shall speak to Stygian chemical Industries, Ltd., have to decide whether to develop a little plant or a large one to manufacture a new product v an expected industry life the ten years. The decision hinges top top what dimension the sector for the product will be. Possibly demand will be <…>


The management of a agency that i shall contact Stygian chemical Industries, Ltd., have to decide even if it is to develop a tiny plant or a large one come manufacture a new product through an expected market life the ten years. The decision hinges ~ above what size the industry for the product will certainly be. Possibly need will be <…>


The management of a firm that ns shall call Stygian chemistry Industries, Ltd., must decide whether to build a tiny plant or a big one come manufacture a brand-new product with an expected sector life the ten years. The decision hinges top top what dimension the industry for the product will be.

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Possibly demand will it is in high throughout the initial 2 years but, if numerous initial users uncover the product unsatisfactory, will autumn to a short level thereafter. Or high early demand can indicate the possibility of a continual high-volume market. If need is high and the firm does not expand within the first two years, competitive products will surely it is in introduced.

If the company builds a huge plant, it should live through it everything the size of sector demand. If it build a tiny plant, management has actually the option of expanding the plant in 2 years in the occasion that demand is high during the introduce period; if in the occasion that demand is low during the introduce period, the firm will preserve operations in the small plant and make a tidy benefit on the low volume.

Management is unsure what to do. The company grew rapidly during the 1950’s; it retained pace v the chemical market generally. The brand-new product, if the sector turns the end to be large, provides the present management a opportunity to press the company into a new period of rewarding growth. The development department, particularly the advance project engineer, is pushing to build the massive plant to make use of the an initial major product advance the room has produced in some years.

The chairman, a major stockholder, is wary of the possibility of big unneeded plant capacity. The favors a smaller sized plant commitment, however recognizes that later growth to fulfill high-volume need would require much more investment and also be less reliable to operate. The chairman also recognizes that unless the firm moves timeless to fill the demand which develops, competitors will be tempted to relocate in with indistinguishable products.

The Stygian chemistry problem, oversimplified together it is, illustrates the uncertainties and issues that organization management have to resolve in making invest decisions. (I usage the ax “investment” in a wide sense, introduce to outlays not only for new plants and also equipment but also for large, risky orders, special marketing facilities, study programs, and also other purposes.) this decisions room growing more important at the exact same time that they are increasing in complexity. Many executives want to do them better—but how?

In this short article I shall existing one recently occurred concept called the “decision tree,” which has tremendous potential together a decision-making tool. The decision tree have the right to clarify for management, as have the right to no other analytical device that I know of, the choices, risks, objectives, monetary gains, and also information needs affiliated in an invest problem. Us shall be hearing a great deal about decision tree in the years ahead. Although a new to many businessmen today, they will certainly surely it is in in usual management parlance prior to many an ext years have actually passed.

Later in this short article we shall return to the problem facing Stygian Chemical and see how management can proceed to deal with it by utilizing decision trees. First, however, a easier example will illustrate some qualities of the decision-tree approach.

Displaying choices

Let us mean it is a quite overcast Saturday morning, and you have 75 world coming for cocktails in the afternoon. You have a satisfied garden and your residence is not as well large; therefore if the weather permits, friend would prefer to set up the refreshments in the garden and have the party there. It would be more pleasant, and also your guests would certainly be more comfortable. Top top the various other hand, if you collection up the party for the garden and after every the guests space assembled it begins to rain, the refreshments will certainly be ruined, her guests will acquire damp, and also you will heartily wish you had decided to have the party in the house. (We might complicate this trouble by considering the opportunity of a partial commitment to one course or another and also opportunities to adjust estimates of the weather together the day goes on, yet the an easy problem is all we need.)

This specific decision can be represented in the kind of a “payoff” table:


Much more complex decision questions can be shown in payoff table form. However, an especially for facility investment decisions, a different representation of the info pertinent come the problem—the decision tree—is beneficial to present the routes whereby the various feasible outcomes space achieved. Pierre Massé, Commissioner general of the National company for Productivity and Equipment plan in France, notes:

“The decision problem is not posed in regards to an isolated decision (because today’s decision depends on the one us shall do tomorrow) nor yet in terms of a succession of decision (because under uncertainty, decision taken later on will be affected by what we have learned in the meanwhile). The trouble is make in regards to a tree that decisions.”1

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


Exhibit I. Decision Tree for Cocktail Party

The tree is consisted of of a collection of nodes and also branches. At the first node ~ above the left, the host has the choice of having the party inside or outside. Every branch represents an alternate course of action or decision. In ~ the end of every branch or alternate course is an additional node representing a chance event—whether or not it will rain. Every subsequent different course come the right represents an alternative outcome the this chance event. Connected with each complete alternative course with the tree is a payoff, presented at the end of the rightmost or terminal branch the the course.

When i am illustration decision trees, I prefer to show the action or decision forks through square nodes and also the chance-event forks v round ones. Other symbols may be offered instead, such as single-line and double-line branches, unique letters, or colors. It does not issue so much which technique of distinguishing you use so long as you execute employ one or another. A decision tree of any type of size will always combine (a) action options with (b) different possible events or results of activity which are partially affected by possibility or other uncontrollable circumstances.

Decision-event chain

The vault example, though entailing only a solitary stage the decision, illustrates the elementary values on i beg your pardon larger, more facility decision trees space built. Let united state take a contempt more facility situation:

You room trying to decision whether to grant a advance budget for an enhanced product. You are urged to do so ~ above the grounds that the development, if successful, will give you a vain edge, yet if you carry out not develop the product, your contender may—and may seriously damage your sector share. You sketch out a decision tree that looks something choose the one in exhibition II.


Exhibit II. Decision Tree v Chains the Actions and Events

Your early stage decision is shown at the left. Adhering to a decision to proceed with the project, if advance is successful, is a second stage of decision at allude A. Assuming no important readjust in the situation between now and the time of allude A, girlfriend decide currently what options will be vital to friend at that time. At the right of the tree space the outcomes of various sequences the decisions and events. This outcomes, too, are based upon your current information. In impact you say, “If what I recognize now is true then, this is what will certainly happen.”

Of course, you execute not try to determine all the events that can occur or every the decisions you will have to make on a subject under analysis. In the decision tree friend lay out just those decisions and also events or outcomes that are necessary to you and have aftermath you wish to compare. (For an ext illustrations, see the Appendix.)


For reader interested in further instances of decision-tree structure, ns shall explain in this appendix two representative cases with which ns am familiar and also show the trees that could be drawn to analysis management’s decision-making alternatives. We shall not worry ourselves below with costs, yields, probabilities, or meant values.

New facility

The selection of options in structure a plant counts upon sector forecasts. The alternate chosen will, in turn, affect the market outcome. Because that example, the army products department of a diversity firm, ~ some duration of short profits due to intense competition, has actually won a contract to develop a new kind of army engine perfect for army transport vehicles. The division has a contract to construct productive capacity and to develop at a stated contract level over a period of three years.

Figure A illustrates the situation. The dotted line mirrors the contract rate. The heavy line shows the proposed buildup of manufacturing for the military. Some various other possibilities are portrayed by dashed lines. The firm is not sure whether the contract will certainly be continued at a relatively high price after the 3rd year, as shown by heat A, or whether the military will rotate to an additional newer development, as indicated by heat B. The firm has no guarantee of compensation ~ the third year. Over there is additionally the possibility, suggested by heat C, of a large additional commercial industry for the product, this possibility being rather dependent on the expense at which the product deserve to be made and sold.


If this advertising market could be tapped, the would stand for a significant new organization for the company and a substantial improvement in the profitability of the division and its prominence to the company.

Management wants to discover three methods of producing the product together follows:

1. It could subcontract every fabrication and set up a straightforward assembly with minimal need for investment in plant and also equipment; the costs would often tend to be relatively high and also the this firm investment and profit opportunity would it is in limited, but the agency assets which room at threat would additionally be limited.

2. It could undertake the significant part of the fabrication itself but use general-purpose an equipment tools in a plant of general-purpose construction. The division would have a possibility to retain more of the most financially rewarding operations itself, exploiting some technical developments it has made (on the basis of i m sorry it acquired the contract). While the expense of production would still be reasonably high, the nature that the investment in plant and equipment would certainly be such the it might probably it is in turned come other offers or liquidated if the service disappeared.

3. The agency could build a extremely mechanized plant with devoted fabrication and also assembly equipment, entailing the biggest investment yet yielding a substantially lower unit manufacturing cost if production volume were adequate. Complying with this arrangement would improve the opportunities for a extension of the armed forces contract and also penetration into the commercial market and also would boost the profitability of whatever business might be acquired in this markets. Failure to sustain either the armed forces or the advertising market, however, would cause substantial financial loss.

Either that the very first two options would be far better adapted come low-volume manufacturing than would the third.

Some significant uncertainties are: the cost-volume relationships under the different manufacturing methods; the size and also structure the the future market—this depends in component on cost, yet the degree and also extent the dependence room unknown; and also the possibilities of competitive developments which would certainly render the product competitively or technologically obsolete.

How would this case be displayed in decision-tree form? (Before going additional you could want to draw a tree for the trouble yourself.) figure B reflects my variation of a tree. Note that in this instance the chance options are somewhat influenced by the decision made. A decision, for example, to construct a much more efficient plant will open up possibilities for an broadened market.


Plant Modernization

A firm management is confronted with a decision on a proposal through its engineering staff which, after three years that study, desires to install a computer-based manage system in the company’s significant plant. The expected cost of the control system is some $30 million. The claimed advantages of the system will it is in a palliation in labor cost and an improved product yield. These benefits rely on the level of product throughput, which is likely to climb over the following decade. The is assumed that the installation routine will take around two years and will expense a substantial amount end and over the expense of equipment. The engineers calculate that the automation job will yield a 20% return ~ above investment, after taxes; the forecast is based on a ten-year projection of product need by the market research department, and also an assumption of an eight-year life for the procedure control system.

What would certainly this invest yield? will certainly actual product sales be greater or lower than forecast? will certainly the process work? will certainly it achieve the economies expected? Will rivals follow if the firm is successful? space they going to mechanize anyway? Will new products or processes make the basic plant obsolete before the investment have the right to be recovered? will certainly the controls last eight years? will something better come along sooner?

The initial decision options are (a) to install the proposed regulate system, (b) postpone activity until patterns in the industry and/or competition come to be clearer, or (c) initiate much more investigation or an live independence evaluation. Each alternate will be followed by resolution of some uncertain aspect, in component dependent ~ above the activity taken. This resolution will lead consequently to a new decision. The dotted lines at the right of number C suggest that the decision tree proceeds indefinitely, though the decision choices do often tend to end up being repetitive. In the instance of postponement or additional study, the decisions are to install, postpone, or restudy; in the case of installation, the decisions are to proceed operation or abandon.

An immediate decision is often one that a sequence. It may be one of a number of sequences. The affect of the present decision in narrowing under future alternatives and the effect of future alternatives in affect the worth of the present selection must both it is in considered.

Adding jae won Data

Now we have the right to return come the problems challenged by the Stygian chemistry management. A decision tree characterizing the investment difficulty as outlined in the development is shown in exhibit III. In ~ Decision #1 the firm must decide in between a large and a tiny plant. This is every that should be decided now. However if the firm chooses to build a tiny plant and then finds need high during the early period, it can in 2 years—at Decision #2—choose to increase its plant.

But let us go past a bare rundown of alternatives. In making decisions, executives need to take account that the probabilities, costs, and returns which appear likely. On the communication of the data now obtainable to them, and also assuming no important readjust in the that company situation, they factor as follows:

Marketing approximates indicate a 60% opportunity of a huge market in the long run and also a 40% opportunity of a low demand, arising initially together follows:
Therefore, the chance that demand initially will be high is 70% (60 + 10). If need is high initially, the company estimates the the chance it will proceed at a high level is 86% (60 ÷ 70). Comparing 86% come 60%, the is noticeable that a high early level that sales alters the estimated chance of high sales in the succeeding periods. Similarly, if sales in the initial duration are low, the chances are 100% (30 ÷ 30) the sales in the subsequent periods will be low. Therefore the level the sales in the initial duration is intended to it is in a rather exact indicator of the level the sales in the subsequent periods. estimates of annual income space made under the assumption of each different outcome:

1. A big plant through high volume would certainly yield $1,000,000 annually in cash flow.

2. A large plant v low volume would certainly yield just $100,000 since of high solved costs and also inefficiencies.

3. A tiny plant v low demand would be economical and would yield annual cash revenue of $400,000.

4. A small plant, during an initial duration of high demand, would yield $450,000 every year, however this would drop come $300,000 yearly in the lengthy run since of competition. (The sector would be larger than under alternate 3, however would be divided up among more competitors.)

5. If the small plant were broadened to meet sustained high demand, it would yield $700,000 cash circulation annually, and so would certainly be less efficient than a large plant developed initially.

6. If the small plant to be expanded yet high demand were no sustained, estimated yearly cash flow would it is in $50,000.

it is estimated further the a huge plant would expense $3 million come put right into operation, a small plant would price $1.3 million, and the expansion of the tiny plant would certainly cost second $2.2 million.

When the foregoing data room incorporated, we have actually the decision tree presented in exhibition IV. Bear in mind the nothing is displayed here i beg your pardon Stygian Chemical’s executives walk not recognize before; no numbers have actually been pulled out of hats. However, us are beginning to watch dramatic proof of the value of decision trees in laying out what management knows in a way that enables more systematic analysis and leader to far better decisions. To sum up the needs of do a decision tree, management must:

1. Recognize the points of decision and also alternatives easily accessible at every point.

2. Recognize the clues of uncertainty and also the form or range of alternate outcomes at every point.

3. Calculation the values needed to make the analysis, particularly the probabilities of different events or results of action and the costs and also gains of various events and actions.

4. Analysis the different values to pick a course.

Choosing food of action

We are currently ready because that the following step in the analysis—to compare the results of different courses of action. A decision tree does not give management the answer to an invest problem; rather, it helps management recognize which alternative at any kind of particular selection point will certainly yield the biggest expected financial gain, offered the info and choices pertinent to the decision.

Of course, the gains must be regarded with the risks. In ~ Stygian Chemical, together at plenty of corporations, managers have different points the view towards risk; for this reason they will draw different conclusions in the circumstances explained by the decision tree presented in exhibition IV. The many people participating in a decision—those providing capital, ideas, data, or decisions, and having various values in ~ risk—will watch the uncertainty neighboring the decision in various ways. Unless these distinctions are recognized and also dealt with, those who need to make the decision, pay because that it, it is provided data and analyses to it, and live with it will judge the issue, relationship of data, require for analysis, and criterion that success in different and also conflicting ways.

For example, agency stockholders might treat a details investment as among a collection of possibilities, some of which will job-related out, rather of which will certainly fail. A significant investment may pose threats to a center manager—to his job and also career—no matter what decision is made. One more participant may have a lot of to get from success, but little to shed from fail of the project. The nature the the risk—as each individual look at it—will impact not just the assumptions he is willing to do but additionally the strategy he will certainly follow in dealing with the risk.

The presence of multiple, unstated, and also conflicting objectives will definitely contribute to the “politics” of Stygian Chemical’s decision, and one deserve to be details that the political aspect exists at any time the lives and ambitions of civilization are affected. Here, as in similar cases, it is no a bad exercise to think with who the next to an invest decision are and to shot to make these assessments:

What is at risk? Is it profit or equity value, survive of the business, maintain of a job, opportunity for a major career?

Who is bearing the risk? The stockholder is normally bearing danger in one form. Management, employees, the community—all might be bearing various risks. What is the character of the hazard that each human being bears? Is it, in his terms, unique, once-in-a-lifetime, sequential, insurable? go it impact the economy, the industry, the company, or a section of the company?

Considerations such together the foregoing will certainly surely enter into top management’s thinking, and also the decision tree in exhibition IV will certainly not remove them. Yet the tree will present management what decision this particular day will contribute most to its long-term goals. The tool for this following step in the analysis is the concept of “rollback.”

“Rollback” concept

Here is how rollback functions in the case described. At the moment of making Decision #1 (see exhibit IV), administration does not need to make Decision #2 and does not even know if the will have the occasion to perform so. But if the were to have actually the choice at Decision #2, the firm would broaden the plant, in watch of its present knowledge. The analysis is shown in exhibit V. (I shall neglect for the minute the inquiry of discounting future profits; that is presented later.) We see that the full expected worth of the expansion alternate is $160,000 greater than the no-expansion alternative, end the eight-year life remaining. Therefore that is the alternate management would pick if faced with Decision #2 with its existing information (and thinking only of monetary gain as a conventional of choice).

Readers may wonder why we started with Decision #2 as soon as today’s trouble is Decision #1. The factor is the following: We require to have the ability to put a financial value on Decision #2 in order come “roll back” to Decision #1 and compare the obtain from taking the lower branch (“Build small Plant”) v the acquire from acquisition the top branch (“Build big Plant”). Allow us contact that monetary value because that Decision #2 its position value. The position value of a decision is the meant value the the preferred branch (in this case, the plant-expansion fork). The meant value is just a type of mean of the results you would mean if you were to repeat the case over and over—getting a $5,600 thousand productivity 86% of the time and a $400 thousand productivity 14% that the time.

Stated in one more way, that is precious $2,672 thousand to Stygian chemistry to acquire to the place where it can make Decision #2. The inquiry is: provided this value and the various other data presented in exhibition IV, what now shows up to be the best action at Decision #1?

Turn now to exhibition VI. In ~ the right of the branches in the top fifty percent we watch the yields for various occasions if a huge plant is constructed (these are merely the numbers in exhibition IV multiplied out). In the bottom half we watch the small plant figures, consisting of Decision #2 position value to add the yield for the 2 years before Decision #2. If we alleviate all these yields by your probabilities, we gain the complying with comparison:

Build large plant: ($10 × .60) + ($2.8 × .10) + ($1 × .30) – $3 = $3,600 thousands

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

The selection which maximizes expected complete cash productivity at Decision #1, therefore, is to construct the big plant initially.

Accounting because that Time

What around taking differences in the time that future income into account? The time between successive decision step on a decision tree may be substantial. At any stage, we may need to weigh distinctions in immediate cost or revenue against differences in value at the next stage. Everything standard of selection is applied, we can put the two options on a comparable basis if we discount the worth assigned come the next stage by an suitable percentage. The discount percent is, in effect, an allowance for the expense of capital and is comparable to the usage of a discount price in the present value or discounted cash circulation techniques currently well known to businessmen.

When decision trees space used, the discounting procedure can be applied one phase at a time. Both cash flows and also position values room discounted.

For simplicity, let united state assume the a discount rate of 10% per year for every stages is decided on by Stygian Chemical’s management. Applying the rollback principle, we again begin with Decision #2. Taking the same numbers used in vault exhibits and also discounting the cash operation at 10%, we gain the data shown in part A of exhibition VII. Note an especially that these space the existing values as of the time Decision #2 is made.


Exhibit VII. Evaluation of Decision #2 with Discounting Note: because that simplicity, the an initial year cash flow is not discounted, the 2nd year cash circulation is discounted one year, and also so on.

Now we want to go with the exact same procedure offered in exhibit V as soon as we acquired expected values, only this time using the discounted yield figures and also obtaining a discounted expected value. The outcomes are displayed in component B of exhibition VII. Due to the fact that the discounted expected value that the no-expansion alternative is higher, that figure becomes the position value of Decision #2 this time.

Having done this, we go earlier to work-related through Decision #1 again, repeating the exact same analytical procedure as prior to only v discounting. The calculations are presented in exhibition VIII. Keep in mind that the Decision #2 position value is cure at the time of Decision #1 together if it were a bump sum received at the finish of the two years.

The large-plant alternative is again the preferred one top top the communication of discounted expected cash flow. Yet the margin of distinction over the small-plant alternative ($290 thousand) is smaller sized than it was without discounting.

Uncertainty choices

In depicting the decision-tree concept, I have treated uncertainty options as if they to be discrete, well-defined possibilities. For my instances I have actually made usage of uncertain cases depending usually on a solitary variable, such as the level of demand or the success or fail of a breakthrough project. I have sought to prevent unnecessary complication if putting emphasis on the key interrelationships among the present decision, future choices, and also the intervening uncertainties.

In many cases, the uncertain elements do take it the type of discrete, single-variable alternatives. In others, however, the possibilities because that cash flow throughout a phase may selection through a totality spectrum and also may depend on a variety of independent or partly related variables subject to chance influences—cost, demand, yield, economic climate, and also so forth. In this cases, us have discovered that the variety of variability or the likelihood that the cash flow falling in a given selection during a stage have the right to be calculated readily from knowledge of the vital variables and also the uncertainties surrounding them. Then the range of cash-flow possibilities throughout the stage can be broken down into two, three, or more “subsets,” which can be provided as discrete possibility alternatives.


Peter F. Drucker has actually succinctly express the relation in between present planning and future events: “Long-range planning does not address future decisions. It encounters the futurity of present decisions.”2 Today’s decision must be do in light of the anticipated impact it and the outcome of uncertain occasions will have on future values and decisions. Because today’s decision to adjust the stage for tomorrow’s decision, today’s decision must balance economic situation with flexibility; it have to balance the have to capitalize on profit methods that might exist v the capacity to reaction to future circumstances and also needs.

The distinctive feature the the decision tree is that it enables management to integrate analytical approaches such as discounted cash flow and also present value approaches with a clear portrayal the the impact of future decision alternatives and events. Utilizing the decision tree, administration can think about various courses of activity with greater ease and clarity. The interactions between present decision alternatives, uncertain events, and also future choices and their results become much more visible.

Of course, there are numerous practical facets of decision tree in addition to those that could be spanned in the room of just one article. Once these other elements are questioned in succeeding articles,3 the whole selection of possible gains for management will be watched in higher detail.

Surely the decision-tree concept does not offer final answers come managements making investment decisions in the confront of uncertainty. We have actually not got to that stage, and also perhaps we never will. Nevertheless, the principle is an important for showing the structure of investment decisions, and also it can an in similar way provide excellent assist in the testimonial of funding investment opportunities.

1. Optimal invest Decisions: rule for action and Criteria because that Choice (Englewood Cliffs, brand-new Jersey, Prentice-Hall, Inc., 1962), p. 250.

See more: A Line Graph Shows The Relationship Between Three Variables ?

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

3. We are expecting another article through Mr. Magee in a forthcoming issue.—The Editors