PDF SUPPLEMENTARY CHAPTER E Decision Analysis

Chapter Outline

Applying Decision Analysis Tools Structuring Decision Problems Selecting Decision Alternatives One-Time Decisions Without Event

Probabilities Repeated Decisions With Event

Probabilities Expected Value of Perfect

Information Decision Trees OM Spotlight: How Computers

Play Chess OM Spotlight: Collegiate Athletic

Drug Testing

Solved Problems Key Terms and Concepts Questions for Review and

Discussion Problems and Activities Cases

Trendy's Pies Service Guarantee Decisions

for McCord Hotels Endnotes

Decision Analysis SUPPLEMENTARY

CHAPTER E

Learning Objectives

? To identify characteristics of management decisions where decision analysis techniques are used and to define the elements of a decision problem.

? To evaluate risk in making decisions and apply decision criteria to select an appropriate decision alternative.

? To construct simple decision trees and use them to select optimal expected value decisions.

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? "What do you think we should do? We're down by 10 with 5 minutes left-- plenty of time to get the ball back," pondered Ken Kendall, head coach of West High in talking to offensive coach Craig Russell. West was facing fourth down and short yardage for another first down from their opponent's 9-yard line. "Should we try for the first down or go for the field goal?" Craig noted that statistically a run is better than a field goal attempt inside the 10-yard line. Ken wasn't so sure, trying to weigh the risk of not getting the first down or a touchdown instead of an almost sure field goal.

? Electric utilities face decisions that can have important impacts on the environment. The impacts stem from the by-products of combustion and other chemicals, equipment, and processes that utilities use to produce electricity. For example, utilities use large boilers to boil water and make steam to generate electricity. The cleaning process results in a waste solution that may be hazardous. Whether or not the waste stream will be hazardous is uncertain, as are the costs and effects of the various management strategies. Several courses of action--choice of cleaning agent, whether or not to include a prerinse stage, treatment and disposal method, and cleaning frequency--are available. Using techniques of decision analysis, the consulting firm Decision Focus Incorporated developed a strategy that would save a utility $119,000 for one boiler over a 20-year horizon.1

Decision analysis is the formal study of how people make decisions, particularly when faced with uncertain information, as well as a collection of techniques to support the analysis of decision problems.

Decision analysis is the formal study of how people make decisions, particularly when faced with uncertain information, as well as a collection of techniques to support the analysis of decision problems. For example, the manufacturer of a new style or line of seasonal clothing would like to manufacture large quantities of the product if consumer acceptance and, consequently, demand for the product are going to be high. Unfortunately, the seasonal clothing items require the manufacturer to make a production-quantity decision before the actual demand is known. Most decisions that we face in business and in our personal lives require a choice in the face of an uncertain future.

Decision analysis has many applications in product selection, facility capacity expansion and location, inventory analysis, technology and process selection, and other areas of operations management. The two opening episodes are some examples. In fact, Virgil Carter, a former NFL quarterback, and Robert Machol applied decision analysis to evaluate football strategies. They found, for example, that the expected value of having the ball with first down and 10 yards to go varies by field position. If the ball is close to one's own goal line, then the team's expected scoring value is 1.64, indicating that their opponent is more likely to score as a result of getting the ball back in good field position. As field position moves closer to the opponent's goal line, the expected value becomes positive and increases. A further analysis of field goal attempts showed that inside the 30-yard line, the run is preferred to the field goal attempt if there are 1 or 2 yards to go, and possibly with 3. Inside the 10-yard line, the run is preferred to the field goal attempt with up to 5 yards to go. These results were contrary to practice, but many coaches continued to employ the field goal far more than the analysis indicated.2

Supplementary Chapter E: Decision Analysis

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APPLYING DECISION ANALYSIS TOOLS

Decision analysis tools should not be used in every decision situation. Characteristics of management decisions where decision analysis techniques apply are summarized as follows:3

1. They must be important. Decision analysis techniques would not be appropriate for minor decisions where the consequences of a mistake are so small that it is not worth our time to study the situation carefully. The consequences of many decisions, such as building a major facility, are not felt immediately but may cover a long time period.

2. They are probably unique. Decisions that recur can be programmed and then delegated. But the ones that are unusual and perhaps occur only one time cannot be handled this way.

3. They allow some time for study. For example, decision analysis techniques would not be useful in making a decision in the emergency room or when a jet fighter flames out during takeoff.

4. They are complex. Practical decision problems involve multiple objectives, requiring the evaluation of trade-offs among the objectives. For example, in evaluating routes for proposed pipelines, a decision maker would want to minimize environmental impact, minimize health and safety hazards, maximize economic benefit, and maximize social impact. Decisions involve many intangibles, such as the goodwill of a client, employee morale, and governmental regulations, and may involve several stakeholders. For instance, to build a plant in a new area, corporate management may require approval from stockholders, regulatory agencies, community zoning boards, and perhaps even the courts. Finally, most decisions are closely allied to other decisions. Choices today affect both the alternatives available in the future and the desirability of those alternatives. Thus, a sequence of decisions must often be made.

5. They involve uncertainty and risk. Uncertainty refers to not knowing what will happen in the future. An advertising campaign may fail, a reservoir may break, or a new product may be a complete failure. Uncertainty is further complicated when little or no data are available, or some data are very expensive or timeconsuming to obtain. Faced with such uncertainties, different people view the same set of information in different ways. Risk is the uncertainty associated with an undesirable outcome, such as financial loss. To appreciate the importance of risk, consider the fact that it takes hundreds of millions of dollars and about 10 years for a pharmaceutical company to bring a drug to market. Once there, seven of ten products fail to return the company's cost of capital. Decisions involving capital investment and continuation of research over the long development cycle do not lend themselves to traditional financial analysis.4

Learning Objective

To identify characteristics of management decisions where decision analysis techniques are used and to define the elements of a decision problem.

Uncertainty refers to not knowing what will happen in the future. Risk is the uncertainty associated with an undesirable outcome, such as financial loss.

Structuring Decision Problems

To illustrate the process of defining a decision problem, we present an example of a medium-size producer of industrial chemical products, Commonwealth Chemicals Company, that is facing a decision about capacity expansion. The company has recently developed a new synthetic industrial lubricant that will increase tool life for machining operations in metal-fabrication industries. A new factory would be necessary to produce the lubricant on a large scale, but expanding the existing facilities would allow production on a smaller scale.

Managers are uncertain which decision to choose. Clearly, the best decision depends on future demand. If the demand for the product is high, the expansion

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Supplementary Chapter E: Decision Analysis

Decision alternatives represent the choices that a decision maker can make.

Events represent the future outcomes that can occur after a decision is made and that are not under the control of the decision maker.

A numerical value associated with a decision coupled with some event is called a payoff.

alternative will not provide enough capacity to meet all the demand and profits will be lost. If demand is low, and a new factory is built, the excess capacity will substantially reduce the return on investment. With an unstable economy, it is difficult to predict actual demand for the product.

The first step in structuring a decision problem is to define the decision alternatives. Decision alternatives represent the choices that a decision maker can make. In this case, the alternatives are whether to expand the existing plant or to build a new factory. Let

d1 decision to expand the existing plant d2 decision to build a new plant

The second step is to define the events that might occur after a decision is made. Events represent the future outcomes that can occur after a decision is made and that are not under the control of the decision maker. For each combination of production-volume decision and subsequent event, a payoff can be computed. For instance, if the manufacturer decides to produce 10,000 units, but demand is low, the manufacturer will incur the cost of producing the 10,000 units but will receive revenue for sales of only 5,000; the remaining units will have to be disposed of at a loss. On the other hand, if sales are medium or high, all 10,000 units will be sold, and the net profit can be computed. The payoff would be the net profit.

For instance, in deciding to expand an existing plant or build a new one, Commonwealth Chemicals needs to consider the future demand for the product. Different possible levels of demand represent the events. Demand might be expressed quantitatively in sales units or dollars. In this example, events might be designated as "high demand," "medium demand," and "low demand." Alternatively, they might be quantified as "demand estimated as 15,000 units," "demand estimated as 10,000 units," and "demand estimated as 5,000 units." If you are planning a spring break vacation to Florida in January, you might define events as the weather that you might encounter. Uncertain weather-related outcomes might be defined qualitatively, for example, sunny and warm, sunny and cold, rainy and warm, or rainy and cold. For the Commonwealth Chemicals decision problem, we will define the events as

s1 low product demand s2 high product demand

Next, we need well-defined decision criteria on which to evaluate potential options. Decision criteria might be net profit, customer service, cost, social benefits, or any other measure of output that may be appropriate for the particular situation being analyzed. A numerical value associated with a decision coupled with some event is called a payoff. Using the best information available, the managers of Commonwealth Chemicals have estimated the payoffs, expressed as profits, shown in Exhibit E.1. A table of this form is referred to as a payoff table. The notation we use for the entries in the payoff table is V(di, sj), which denotes the payoff, V, associated with decision alternative di and event sj. Using this notation, we see that V(d2, s1) $100,000.

Exhibit E.1

Payoff Table for Commonwealth Chemicals

Decision Alternative

Expand existing plant (d1) Build new plant (d2)

Possible Future Events

Low Product Demand (s1)

$200,000 $100,000

High Product Demand (s2)

$300,000 $450,000

Supplementary Chapter E: Decision Analysis

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In many decision problems, the probabilities of events can be estimated, either from historical data or managerial judgment. Knowing the likelihood of the occurrence of events helps to assess risk when making a decision. In some cases, however, event probabilities may not be available or appropriate to try to assess. We will provide examples of both situations in the following sections.

In summary, the elements of a decision problem are (1) decision alternatives, (2) events, (3) estimated payoffs for each combination of decision alternatives and events, and possibly (4) probabilities of the events.

SELECTING DECISION ALTERNATIVES

Making decisions with uncertain future consequences is often quite frustrating and a source of anxiety for individuals and managers alike. We run the risk that any decision we choose may result in undesirable consequences once we see what the future holds in store. There are two principal ways of viewing a decision strategy, and these depend on the frequency with which the decision will be made. For onetime decisions, managers must take into account the risk associated with making the wrong decision. However, for decisions that are repeated over and over, managers can choose decisions based on the expected payoffs that might occur.

Learning Objective

To evaluate risk in making decisions and apply decision criteria to select an appropriate decision alternative.

One-Time Decisions Without Event Probabilities

The Commonwealth Chemicals decision is clearly a one-time decision. So how should the choice be made? Different criteria can be used to reflect different attitudes toward risk, and they may result in different decision recommendations. For a problem in which the payoff is profit, as it is in the Commonwealth Chemicals problem, three common criteria are

1. Maximax--choose the decision that will maximize the maximum possible profit among all events. This is an aggressive, or risk-taking, approach.

2. Maximin--choose the decision that will maximize the minimum possible profit among all events. This is a conservative, or risk-averse, approach.

3. Minimax regret--choose the decision that will minimize the maximum opportunity loss associated with the events. Opportunity loss represents the regret, or ill-feeling, that people often have after making a nonoptimal decision ("I should have bought that stock years ago . . ."). This approach is neither aggressive nor conservative, but focuses on not erring too much in either direction.

We will apply these criteria for the Commonwealth Chemicals problem. For the maximax criterion, we see that if d1 is selected, the maximum payoff is $300,000, and it occurs for s2. If d2 is selected, the maximum payoff is $450,000, also for s2. The decision maker should choose d2, build a new plant, since it results in the largest possible payoff.

For the maximin criterion, we see that if d1 is chosen, the minimum payoff is $200,000, whereas if d2 is selected, the minimum payoff is $100,000. Thus, to maximize the minimum payoff, the decision maker should choose d1, expand the existing plant.

To apply the minimax-regret criterion, we must first construct a regret or opportunity-loss matrix. The opportunity loss associated with a particular decision, di, and state of nature, sj, is the difference between the best payoff that the decision maker can receive by making the optimal decision d* corresponding to sj, V(d*, sj), and the payoff for choosing any arbitrary decision di and having sj occur, V(di, sj). For example, if we know that s1 will occur, the best decision is to choose

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