Fluent Essays

please read the regulations carefully and I have been attached chapter 5 from the textbook to know the context and the rubric to follow to exceed expectations. MGT-530: – Module 06/CT 03 Regulations:  · GRADING EXPECTATIONS : 1. I recommend that you use the grading rubric to shape your work product (Attached).   2. With respect to grading, The instructor really looks for 2 things:  citations and substance . I encourage you to include cites and information from scholarly and/or peer-reviewed sources in addition to the course text (Stevenson, W. (2018). Operations management (13th ed.). New York, NY: McGraw-Hill Irwin. ISBN-13:9781259667473) Otherwise, my potential for points is reduced. It  indicates you have read the course materials and searched far and wide for theories, statistics, and facts to address the issue at hand. I encourage you to paraphrase these sources. Convert the content into your own words rather than using direct quotes. This improves the synthesis of information, and it makes the writing more closely resemble your own style.  In addition to scholarly citations, a substantive assignment is one that not only answers the question but advances the discussion. Please, do more than is expected. · The writer must apply APA style guidelines.   Avoid plagiarism · Support your submission with: 1. Course material concepts, principles, and theories from the textbook and Use it in the references (Stevenson, W. (2018). Operations management (13th ed.). New York, NY: McGraw-Hill Irwin. ISBN-13:9781259667473) 2.  At least Four scholarly, peer-reviewed journal articles such as: 2.1 Anh, N. L. H., & Linh, H. M. (2021). Sensitivity analysis for set-valued equilibrium problems. Positivity, 25(1), 31–48. https://doi.org/10.1007/s11117-020-00748-8 2.2 Nor, S. H. S., Ismail, S., & Yap, B. W. (2019). Personal bankruptcy prediction using decision tree model. Journal of Economics, Finance & Administrative Science, 24(47), 157–172. 3. Use one resource from YouTube. · Be not more than 5 pages in length, does not include the title page, abstract, conclusion and required reference page, which are never a part of the minimum content requirements.  Decision Tree The supplement to Chapter 5 in your textbook describes and develops several decision trees. Case for consideration—an operations manager for a cereal producer is faced with a choice of: A large-scale investment (A) to purchase a new cooker which could produce a substantial pay-off in terms of increased revenue net of costs but requires an investment of 3,750,000 Saudi Riyal. After extensive market research it is thought that there is a 40\% chance that a pay-off of 9,375,000 Saudi Riyal will be realized, but there is a 60\% chance that it will be only 3,000,000 Saudi Riyal. A smaller scale project (B) to refurbish an existing cooker. At 1,875,000 Saudi Riyal, this option is less costly but produces a lower pay-off. Again, extensive research data suggests a 30\% chance of a gain of 3,750,000 Saudi Riyal but a 70\% chance of it being only 1,875,000 Saudi Riyal. Continuing the present operation without change (C) which cost nothing, but produces no pay-off. Address the following requirements: · Develop a decision tree for the case described. · Explain the process of developing a decision tree, draw the decision tree (include the decision tree in an appendix showing chance nodes, probabilities, outcomes, expected values, and net expected value). · Defend your final decision based on your decision tree. Thank you for your support MGT - 5 30 : – Module 0 6 /CT 0 3 Regulations : · GRADING EXPECTATIONS   : 1. I recommend that you use the grading rubric to shape your work product ( Attached ).    2. With respect to   grading, The instructor really looks for 2 things:   citations   and substance . I encourage you to include cites and information from   scholarly and/or peer - re viewed sources in addition to the course text ( Stevenson , W. (2018). Operations management (13th ed.). New York, NY: McGraw - Hill Irwin. ISBN - 13:9781259667473) Otherwise , my potential for points is reduced. It   indicates you have read the course materials and searched far and wide for theories, statistics, and facts   to address the issue at hand.   I encourage you to paraphrase these sources. Convert the content into your own words rather than using direct quotes . This improves the synthesis of information, a nd it makes the writing more closely resemble your own style.   In addition to   scholarly citations, a substantive assignment is one that not only answers the question but advances the discussion. Please, do more than is expected. · The writer must apply AP A style guidelines . Avoid plagiarism · Support your submission with: 1. Course material concepts, principles, and theories from the textbook and Use it in the references (Stevenson, W. (2018). Operations management (13th ed.). New York, NY: McGraw - Hill Irwin. ISBN - 13:9781259667473) 2.   At least Four scholarly, peer - reviewed journal articles such as: 2.1 Anh, N. L. H., & Linh, H. M. (2021). Sensitivity analysis for set - valued equilibrium problems. Positivity, 25(1), 31 – 48. https://doi.org/10.1007/s11117 - 020 - 00748 - 8 2.2 Nor, S. H. S., Ismail, S., & Yap, B. W. (2019). Personal bankruptcy prediction using decision tree model. Journal of Economics, Finance & Administrative Science, 24(47), 157 – 172. 3. U se one resource from YouTube . · Be not more than 5 pages in length, does not include the title page, abstract, conclusion and required reference page, which are never a part of the minimum content requirements. MGT-530: – Module 06/CT 03 Regulations:  GRADING EXPECTATIONS : 1. I recommend that you use the grading rubric to shape your work product (Attached).   2. With respect to grading, The instructor really looks for 2 things: citations and substance. I encourage you to include cites and information from scholarly and/or peer-reviewed sources in addition to the course text (Stevenson, W. (2018). Operations management (13th ed.). New York, NY: McGraw-Hill Irwin. ISBN-13:9781259667473) Otherwise, my potential for points is reduced. It  indicates you have read the course materials and searched far and wide for theories, statistics, and facts to address the issue at hand. I encourage you to paraphrase these sources. Convert the content into your own words rather than using direct quotes. This improves the synthesis of information, and it makes the writing more closely resemble your own style.  In addition to scholarly citations, a substantive assignment is one that not only answers the question but advances the discussion. Please, do more than is expected.  The writer must apply APA style guidelines. Avoid plagiarism  Support your submission with: 1. Course material concepts, principles, and theories from the textbook and Use it in the references (Stevenson, W. (2018). Operations management (13th ed.). New York, NY: McGraw-Hill Irwin. ISBN-13:9781259667473) 2.  At least Four scholarly, peer-reviewed journal articles such as: 2.1 Anh, N. L. H., & Linh, H. M. (2021). Sensitivity analysis for set-valued equilibrium problems. Positivity, 25(1), 31–48. https://doi.org/10.1007/s11117-020-00748-8 2.2 Nor, S. H. S., Ismail, S., & Yap, B. W. (2019). Personal bankruptcy prediction using decision tree model. Journal of Economics, Finance & Administrative Science, 24(47), 157–172. 3. Use one resource from YouTube.  Be not more than 5 pages in length, does not include the title page, abstract, conclusion and required reference page, which are never a part of the minimum content requirements. MGT530 Critical Thinking Writing Rubric - Module 2 Exceeds Expectation Meets Expectation Below Expectation Limited Evidence Content, Research, and Analysis 21-25 Points 16-20 Points 11-15 Points 6-10 Points Requirements Includes all of the required components, as specified in the assignment. Includes most of the required components, as specified in the assignment. Includes some of the required components, as specified in the assignment. Includes few of the required components, as specified in the assignment. 21-25 Points 16-20 Points 11-15 Points 6-10 Points Content Demonstrates substantial and extensive knowledge of the materials, with no errors or major omissions. Demonstrates adequate knowledge of the materials; may include some minor errors or omissions. Demonstrates fair knowledge of the materials and/or includes some major errors or omissions. Fails to demonstrate knowledge of the materials and/or includes many major errors or omissions. 25-30 Points 19-24 Points 13-18 Points 7-12 Points Analysis Provides strong thought, insight, and analysis of concepts and applications. Provides adequate thought, insight, and analysis of concepts and applications. Provides poor though, insight, and analysis of concepts and applications. Provides little or no thought, insight, and analysis of concepts and applications. 13-15 Points 10-12 Points 7-9 Points 4-6 Points Sources Sources go above and beyond required criteria and are well chosen to provide effective substance and perspectives on the issue under examination. Sources meet required criteria and are adequately chosen to provide substance and perspectives on the issue under examination. Sources meet required criteria but are poorly chosen to provide substance and perspectives on the issue under examination. Source selection and integration of knowledge from the course is clearly deficient. Mechanics and Writing 5 Points 4 Points 3 Points 1-2 Points Demonstrates college-level proficiency in organization, grammar and style. Project is clearly organized, well written, and in proper format as outlined in the assignment. Strong sentence and paragraph structure, contains no errors in grammar, spelling, Project is fairly well organized and written and is in proper format as outlined in the assignment. Reasonably good sentence and paragraph structure, may include a few Project is poorly organized and written and may not follow proper format as outlined in the assignment. Inconsistent to inadequate sentence and paragraph development, Project is not organized or well written and is not in proper format as outlined in the assignment. Poor quality work; unacceptable in terms of grammar, spelling, APA style, MGT530 Critical Thinking Writing Rubric - Module 2 APA style, or APA citations and references. minor errors in grammar, spelling, APA style, or APA citations and references. and/or includes numerous or major errors in grammar, spelling, APA style or APA citations and references. and APA citations and references. Total points possible = 100 ste67472_ch05s_220-241.indd 220 01/06/17 07:28 PM 220 S U P P L E M E N T O U T L I N E 5 5S.1 Introduction, 220 5S.2 The Decision Process and Causes of Poor Decisions, 221 5S.3 Decision Environments, 222 5S.4 Decision Making under Certainty, 222 5S.5 Decision Making under Uncertainty, 223 5S.6 Decision Making under Risk, 225 5S.7 Decision Trees, 225 5S.8 Expected Value of Perfect Information, 227 5S.9 Sensitivity Analysis, 228 Decision Theory L E A R N I N G O B J E C T I V E S After completing this supplement, you should be able to: LO5S.1 Outline the steps in the decision process. LO5S.2 Name some causes of poor decisions. LO5S.3 Describe and use techniques that apply to decision making under uncertainty. LO5S.4 Describe and use the expected-value approach. LO5S.5 Construct a decision tree and use it to analyze a problem. LO5S.6 Compute the expected value of perfect information. LO5S.7 Conduct sensitivity analysis on a simple decision problem. 5S.1 INTRODUCTION Decision theory represents a general approach to decision making. It is suitable for a wide range of operations management decisions. Among them are capacity planning, product and service design, equipment selection, and location planning. Decisions that lend themselves to a decision theory approach tend to be characterized by the following elements: 1. A set of possible future conditions that will have a bearing on the results of the decision. 2. A list of alternatives for the manager to choose from. 3. A known payoff for each alternative under each possible future condition. To use this approach, a decision maker would employ this process: 1. Identify the possible future conditions (e.g., demand will be low, medium, or high; the competitor will or will not introduce a new product). These are called states of nature. 2. Develop a list of possible alternatives, one of which may be to do nothing. 3. Determine or estimate the payoff associated with each alternative for every possible future condition. 4. If possible, estimate the likelihood of each possible future condition. 5. Evaluate alternatives according to some decision criterion (e.g., maximize expected profit), and select the best alternative. S U P P L E M E N T Final PDF to printer Supplement to Chapter Five Decision Theory 221 ste67472_ch05s_220-241.indd 221 01/06/17 07:28 PM The information for a decision is often summarized in a payoff table, which shows the expected payoffs for each alternative under the various possible states of nature. These tables are helpful in choosing among alternatives because they facilitate comparison of alternatives. Consider the following payoff table, which illustrates a capacity planning problem. Payoff table Table showing the expected payoffs for each alternative in every possible state of nature. POSSIBLE FUTURE DEMAND Alternatives Low Moderate High Small facility $10*  $10  $10 Medium facility     7      12    12 Large facility   (4)      2    16 *Present value in $ millions. The payoffs are shown in the body of the table. In this instance, the payoffs are in terms of present values, which represent equivalent current dollar values of expected future income less costs. This is a convenient measure because it places all alternatives on a comparable basis. If a small facility is built, the payoff will be the same for all three possible states of nature- rightFor a medium facility, low demand will have a present value of $7 million, whereas both moderate and high demand will have present values of $12 million. A large facility will have a loss of $4 million if demand is low, a present value of $2 million if demand is moderate, and a present value of $16 million if demand is high. The problem for the decision maker is to select one of the alternatives, taking the present value into account. Evaluation of the alternatives differs according to the degree of certainty associated with the possible future conditions. 5S.2 THE DECISION PROCESS AND CAUSES OF POOR DECISIONS Despite the best efforts of a manager, a decision occasionally turns out poorly due to unfore- seeable circumstances. Luckily, such occurrences are not common. Often, failures can be traced to a combination of mistakes in the decision process, to bounded rationality, or to suboptimization. The decision process consists of these steps: 1. Identify the problem. 2. Specify objectives and criteria for a solution. 3. Develop suitable alternatives. 4. Analyze and compare alternatives. 5. Select the best alternative. 6. Implement the solution. 7. Monitor to see that desired result is achieved. In many cases, managers fail to appreciate the importance of each step in the decision- making process. They may skip a step or not devote enough effort to completing it before jumping to the next step. Sometimes this happens owing to a manager’s style of making quick decisions or a failure to recognize the consequences of a poor decision. The manager’s ego can be a factor. This sometimes happens when the manager has experienced a series of successes— important decisions that turned out right. Some managers then get the impression that they can do no wrong. But they soon run into trouble, which is usually enough to bring them back down to earth. Other managers seem oblivious to negative results and continue the process they associate with their previous successes, not recognizing that some of that success may have LO5S.1 Outline the steps in the decision process. LO5S.2 Name some causes of poor decisions. Final PDF to printer 222 Supplement to Chapter Five Decision Theory ste67472_ch05s_220-241.indd 222 01/06/17 07:28 PM been due more to luck than to any special abilities of their own. A part of the problem may be the manager’s unwillingness to admit a mistake. Yet other managers demonstrate an inability to make a decision; they stall long past the time when the decision should have been rendered. Of course, not all managers fall into these traps—it seems safe to say that the majority do not. Even so, this does not necessarily mean that every decision works out as expected. Another factor with which managers must contend is bounded rationality, or the limits imposed on decision making by costs, human abilities, time, technology, and the availability of information. Because of these limitations, managers cannot always expect to reach deci- sions that are optimal in the sense of providing the best possible outcome (e.g., highest profit, least cost). Instead, they must often resort to achieving a satisfactory solution. Still another cause of poor decisions is that organizations typically departmentalize deci- sions. Naturally, there is a great deal of justification for the use of departments in terms of overcoming span-of-control problems and human limitations. However, suboptimization can occur. This is a result of different departments’ attempts to reach a solution that is optimum for each. Unfortunately, what is optimal for one department may not be optimal for the orga- nization as a whole. If you are familiar with the theory of constraints (see Chapter 16), subop- timization and local optima are conceptually the same, with the same negative consequences. 5S.3 DECISION ENVIRONMENTS Operations management decision environments are classified according to the degree of certainty present. There are three basic categories: certainty, risk, and uncertainty. Certainty means that relevant parameters such as costs, capacity, and demand have known values. Risk means that certain parameters have probabilistic outcomes. Uncertainty means that it is impossible to assess the likelihood of various possible future events. Consider these situations: 1. Profit per unit is $5. You have an order for 200 units. How much profit will you make? (This is an example of certainty since unit profits and total demand are known.) 2. Profit is $5 per unit. Based on previous experience, there is a 50 percent chance of an order for 100 units and a 50 percent chance of an order for 200 units. What is expected profit? (This is an example of risk since demand outcomes are probabilistic.) 3. Profit is $5 per unit. The probabilities of potential demands are unknown. (This is an example of uncertainty.) The importance of these different decision environments is that they require different anal- ysis techniques. Some techniques are better suited for one category than for others. 5S.4 DECISION MAKING UNDER CERTAINTY When it is known for certain which of the possible future conditions will actually happen, the decision is usually relatively straightforward: Simply choose the alternative that has the best payoff under that state of nature. Example 5S–1 illustrates this. Bounded rationality The limitations on decision mak- ing caused by costs, human abilities, time, technology, and availability of information. Suboptimization The result of different departments each attempting to reach a solu- tion that is optimum for that department. Certainty Environment in which relevant parameters have known values. Risk Environment in which certain future events have probable outcomes. Uncertainty Environment in which it is impossible to assess the likelihood of vari- ous future events. Choosing an Alternative Under Certainty Determine the best alternative in the payoff table on the previous page for each of the cases: It is known with certainty that demand will be (a) low, (b) moderate, (c) high. E X A M P L E 5 S – 1 Final PDF to printer Supplement to Chapter Five Decision Theory 223 ste67472_ch05s_220-241.indd 223 01/06/17 07:28 PM 5S.5 DECISION MAKING UNDER UNCERTAINTY At the opposite extreme is complete uncertainty: No information is available on how likely the various states of nature are. Under those conditions, four possible decision criteria are maxi- min, maximax, Laplace, and minimax regret. These approaches can be defined as follows: Maximin—Determine the worst possible payoff for each alternative, and choose the alternative that has the “best worst.” The maximin approach is essentially a pessimistic one because it takes into account only the worst possible outcome for each alternative. The actual outcome may not be as bad as that, but this approach establishes a “guaranteed minimum.” Maximax—Determine the best possible payoff, and choose the alternative with that pay- off. The maximax approach is an optimistic, “go for it” strategy; it does not take into account any payoff other than the best. Laplace—Determine the average payoff for each alternative, and choose the alternative with the best average. The Laplace approach treats the states of nature as equally likely. Minimax regret—Determine the worst regret for each alternative, and choose the alter- native with the “best worst.” This approach seeks to minimize the difference between the payoff that is realized and the best payoff for each state of nature. The next two examples illustrate these decision criteria. LO5S.3 Describe and use techniques that apply to decision making under uncertainty. Maximin Choose the alterna- tive with the best of the worst possible payoffs. Maximax Choose the alter- native with the best possible payoff. Laplace Choose the alter- native with the best aver- age payoff of any of the alternatives. Minimax regret Choose the alternative that has the least of the worst regrets. Choose the alternative with the highest payoff. Thus, if we know demand will be low, we would elect to build the small facility and realize a payoff of $10 million. If we know demand will be moderate, a medium factory would yield the highest payoff ($12 million versus either $10 million or $2 million). For high demand, a large facility would provide the highest payoff. Although complete certainty is rare in such situations, this kind of exercise provides some perspective on the analysis. Moreover, in some instances, there may be an opportunity to consider allocation of funds to research efforts, which may reduce or remove some of the uncertainty surrounding the states of nature, converting uncertainty to risk or to certainty. S O L U T I O N S O L U T I O N Choosing an Alternative Using Maximax, Maximin, and Laplace Referring to the payoff table in the Introduction, determine which alternative would be chosen under each of these strategies: a. Maximin b. Maximax c. Laplace E X A M P L E 5 S – 2 a. Using maximin, the worst payoffs for the alternatives are as follows: Small facility: $10 million Medium facility:     7 million Large facility:   –4 million Hence, since $10 million is the best, choose to build the small facility using the maxi- min strategy. mhhe.com/stevenson13e Final PDF to printer 224 Supplement to Chapter Five Decision Theory ste67472_ch05s_220-241.indd 224 01/06/17 07:28 PM b. Using maximax, the best payoffs are as follows: Small facility: $10 million Medium facility:   12 million Large facility:   16 million The best overall payoff is the $16 million in the third row. Hence, the maximax crite- rion leads to building a large facility. c. For the Laplace criterion, first find the row totals, and then divide each of those amounts by the number of states of nature (three in this case). Thus, we have   Row Total (in $ millions) Row Average (in $ millions) Small facility $30 $10.00  Medium facility 31 10.33  Large facility 14 4.67  Because the medium facility has the highest average, it would be chosen under the Laplace criterion. S O L U T I O N Choosing an Alternative Using Minimax Regret Determine which alternative would be chosen using a minimax regret approach to the capacity planning program. E X A M P L E 5 S – 3 The first step in this approach is to prepare a table of regrets (opportunity loss). To do this, subtract every payoff in each column from the best payoff in that column. For instance, in the first column, the best payoff is 10, so each of the three numbers in that column must be subtracted from 10. Going down the column, the regrets will be 10 – 10 = 0, 10 – 7 = 3, and 10 – (–4) = 14. In the second column, the best payoff is 12. Subtracting each payoff from 12 yields 2, 0, and 10. In the third column, 16 is the best payoff. The regrets are 6, 4, and 0. These results are summarized in a regret table:   REGRETS (IN $ MILLIONS)   Alternatives Low Moderate High Worst Small facility $0 $2 $6 $6 Medium facility 3 0 4 4 Large facility 14 10 0 14 The second step is to identify the worst regret for each alternative. For the first alterna- tive, the worst is 6; for the second, the worst is 4; and for the third, the worst is 14. The best of these worst regrets would be chosen using minimax regret. The lowest regret is 4, which is for a medium facility. Hence, that alternative would be chosen. Regret (opportunity loss) The difference between a given payoff and the best payoff for a state of nature. Solved Problem 6 at the end of this supplement illustrates decision making under uncer- tainty when the payoffs represent costs. The main weakness of these approaches (except for Laplace) is that they do not take into account all of the payoffs. Instead, they focus on the worst or best, and so they lose some information. Still, for a given set of circumstances, each has certain merits that can be helpful to a decision maker. Final PDF to printer Supplement to Chapter Five Decision Theory 225 ste67472_ch05s_220-241.indd 225 01/06/17 07:28 PM 5S.6 DECISION MAKING UNDER RISK Between the two extremes of certainty and uncertainty lies the case of risk: The probability of occurrence for each state of nature is known. (Note that because the states are mutually exclusive and collectively exhaustive, these probabilities must add to 1.00.) A widely used approach under such circumstances is the expected monetary value criterion. The expected value is computed for each alternative, and the one with the best expected value is selected. The expected value is the sum of the payoffs for an alternative where each payoff is weighted by the probability for the relevant state of nature. Thus, the approach is Expected monetary value (EMV) criterion—Determine the expected payoff of each alternative, and choose the alternative that has the best expected payoff. LO5S.4 Describe and use the expected-value approach. Expected monetary value (EMV) criterion The best expected value among the alternatives. S O L U T I O N Choosing an Alternative Using Expected Value Using the expected monetary value criterion, identify the best alternative for the previous payoff table for these probabilities: low = .30, moderate = .50, and high = .20. E X A M P L E 5 S – 4 Find the expected value of each alternative by multiplying the probability of occurrence for each state of nature by the payoff for that state of nature and summing them: EVsmall = .30($10) + .50($10) + .20($10) = $10 EVmedium = .30($7) + .50($12) + .20($12) = $10.5 EVlarge = .30($ −4) + .50($2) + .20($16) = $3 Hence, choose the medium facility because it has the highest expected value. The expected monetary value approach is most appropriate when a decision maker is nei- ther risk averse nor risk seeking, but is risk neutral. Typically, well-established organizations with numerous decisions of this nature tend to use expected value because it provides an indi- cation of the long-run, average payoff. That is, the expected-value amount (e.g., $10.5 million in the last example) is not an actual payoff but an expected or average amount that would be approximated if a large number of identical decisions were to be made. Hence, if a decision maker applies this criterion to a large number of similar decisions, the expected payoff for the total will approximate the sum of the individual expected payoffs. 5S.7 DECISION TREES In health care the array of treatment options and medical costs makes tools such as decision trees particularly valuable in diagnosing and prescribing treatment plans. For example, if a 20-year-old and a 50-year-old both are brought into an emergency room complaining of chest pains, the attending physician, after asking each some questions on family history, patient his- tory, general health, and recent events and activities, will use a decision tree to sort through the options to arrive at the appropriate decision for each patient. Decision trees are tools that have many practical applications, not only in health care but also in legal cases and a wide array of management decision making, including credit card fraud; loan, credit, and insurance risk analysis; decisions on new product or service develop- ment; and location analysis. A decision tree is a schematic representation of the alternatives available to a decision maker and their possible consequences. The term gets its name from the treelike appearance LO5S.5 Construct a decision tree and use it to analyze a problem. Decision tree A schematic representation of the available alternatives and their possible consequences. mhhe.com/stevenson13e Final PDF to printer 226 Supplement to Chapter Five Decision Theory ste67472_ch05s_220-241.indd 226 01/06/17 07:28 PM of the diagram (see Figure 5S.1). Although tree diagrams can be used in place of a payoff table, they are particularly useful for analyzing situations that involve sequential decisions. For instance, a manager may initially decide to build a small facility only to discover that demand is much higher than anticipated. In this case, the manager may then be called upon to make a subsequent decision on whether to expand or build an additional facility. A decision tree is composed of a number of nodes that have branches emanating from them (see Figure 5S.1). Square nodes denote decision points, and circular nodes denote chance events. Read the tree from left to right. Branches leaving square nodes represent alternatives; branches leaving circular nodes represent chance events (i.e., the possible states of nature). After the tree has been drawn, it is analyzed from right to left; that is, starting with the last decision that might be made. For each decision, choose the alternative that will yield the greatest return (or the lowest cost). If chance events follow a decision, choose the alterna- tive that has the highest expected monetary value (or lowest expected cost). FIGURE 5S.1 Format of a decision tree State of na ture 1 State of nature 2 State of na ture 1 State of nature 2 Payo� 1 Payo� 2 Payo� 3 Payo� 4 Payo� 5 Payo� 6 2 2 Choos e A 1 Choose A2 1 Ch oo se A 1 Choose A 2 Initial decision Possible second decisions Choos e A 3 Choose A 4 Decision point Chance event Low dem and (.4) High demand (.6) $40 Do no thin g Expand Bu ild sm all Build large Overtime Do no thin g Reduce prices Low dem and (.4) High demand (.6) $50 $55 ($10) $50 $40 $70 Choosing an Alternative Using Expected Value with a Decision Tree A manager must decide on the size of a video arcade to construct. The manager has narrowed the choices to two: large or small. Information has been collected on payoffs, and a decision tree has been constructed. Analyze the decision tree and determine which initial alternative (build small or build large) should be chosen in order to maximize expected monetary value. E X A M P L E 5 S – 5 mhhe.com/stevenson13e Final PDF to printer Supplement to Chapter Five Decision Theory 227 ste67472_ch05s_220-241.indd 227 01/06/17 07:28 PM 5S.8 EXPECTED VALUE OF PERFECT INFORMATION In certain situations, it is possible to ascertain which state of nature will actually occur in the future. For instance, the choice of location for a restaurant may weigh heavily on whether a new highway will be constructed or whether a zoning permit will be issued. A decision maker may have probabilities for these states of nature; however, it may be possible to delay a deci- sion until it is clear which state of nature will occur. This might involve taking an option to buy the land. If the state of nature is favorable, the option can be exercised; if it is unfavorable, the option can be allowed to expire. The question to consider is whether the cost of the option will be less than the expected gain due to delaying the decision (i.e., the expected payoff above the expected value). The expected gain is the expected value of perfect information (EVPI) Other possible ways of obtaining perfect information depend somewhat on the nature of the decision being made. Information about consumer preferences might come from market research, additional information about a product could come from product testing, or legal experts might be called on. There are two ways to determine the EVPI. One is to compute the expected payoff under certainty and subtract the expected payoff under risk. That is, Expected value of perfect information = Expected payoff under certainty − Expected payoff under risk (5S-1) LO5S.6 Compute the expected value of perfect information. Expected value of perfect information (EVPI) The differ- ence between the expected payoff with perfect informa- tion and the expected payoff under risk. The dollar amounts at the branch ends indicate the estimated payoffs if the sequence of chance events and decisions that is traced back to the initial decision occurs. For example, if the initial decision is to build a small facility and it turns out that demand is low, the payoff will be $40 (thousand). Similarly, if a small facility is built, demand turns out high, and a later decision is made to expand, the payoff will be $55 (thousand). The figures in parentheses on branches leaving the chance nodes indicate the probabilities of those states of nature. Hence, the probability of low demand is .4, and the probability of high demand is .6. Payoffs in parentheses indicate losses. Analyze the decisions from right to left: 1. Determine which alternative would be selected for each possible second decision. For a small facility with high demand, there are three choices: do nothing, work overtime, and expand. Because expand has the highest payoff, you would choose it. Indicate this by placing a double slash through each of the other alternatives. Similarly, for a large facility with low demand, there are two choices: do nothing and reduce prices. You would choose reduce prices because it has the higher expected value, so a double slash is placed on the other branch. 2. Determine the product of the chance probabilities and their respective payoffs for the remaining branches: Build small     Low demand .4($40) = $16 High demand .6($55) = $33 $49 Build large   Low demand .4($50) = $20 High demand .6($70) = $42 $62 3. Hence, the choice should be to build the large facility because it has a larger expected value than the small facility. S O L U T I O N Final PDF to printer 228 Supplement to Chapter Five Decision Theory ste67472_ch05s_220-241.indd 228 01/06/17 07:28 PM Computing the Expected Value of Perfect Information Using Formula 5S-1 Using the information from Example 5S–4, determine the expected value of perfect infor- mation using Formula 5S–1. E X A M P L E 5 S – 6 S O L U T I O N First, compute the expected payoff under certainty. To do this, identify the best payoff under each state of nature. Then combine these by weighting each payoff by the probability of that state of nature and adding the amounts. Thus, the best payoff under low demand is $10, the best under moderate demand is $12, and the best under high demand is $16. The expected payoff under certainty is, then, .30($10) + .50($12) + .20($16) = $12.2 The expected payoff under risk, as computed in Example 5S–4, is $10.5. The EVPI is the difference between these: EVPI = $12.2 − $10.5 = $1.7 This figure indicates the upper limit on the amount the decision maker should be willing to spend to obtain perfect information in this case. Thus, if the cost equals or exceeds this amount, the decision maker would be better off not spending additional money and simply going with the alternative that has the highest expected payoff. A second approach is to use the regret table to compute the EVPI. To do this, find the expected regret for each alternative. The minimum expected regret is equal to the EVPI. S O L U T I O N Computing the Expected Value of Perfect Information Using Expected Regret Determine the expected value of perfect information for the capacity-planning problem using the expected regret approach. E X A M P L E 5 S – 7 Using information from Examples 5S–2, 5S–3, and 5S–4, we can compute the expected regret for each alternative. Thus: Small facility .30(0) + .50(2) + .20(6) = 2.2 Medium facility .30(3) + .50(0) + .20(4) = 1.7 [minimum] Large facility .30(14) + .50(10) + .20(0) = 9.2 The lowest expected regret is 1.7, which is associated with the second alternative. Hence, the EVPI is $1.7 million, which agrees with the previous example using the other approach. 5S.9 SENSITIVITY ANALYSIS Generally speaking, both the payoffs and the probabilities in this kind of a decision problem are estimated values. Consequently, it can be useful for the decision maker to have some indication of how sensitive the choice of an alternative is to changes in one or more of these values. Unfortunately, it is impossible to consider all possible combinations of every variable in a typical problem. Nevertheless, there are certain things a decision maker can do to judge the sensitivity of probability estimates. Sensitivity analysis provides a range of probability over which the choice of alternatives would remain the same. The approach illustrated here is useful when there are two states of LO5S.7 Conduct sensitiv- ity analysis on a simple decision problem. Sensitivity analysis Deter- mining the range of probabil- ity for which an alternative has the best expected payoff. mhhe.com/stevenson13e Final PDF to printer Supplement to Chapter Five Decision Theory 229 ste67472_ch05s_220-241.indd 229 01/06/17 07:28 PM nature. It involves constructing a graph and then using algebra to determine a range of prob- abilities for which a given solution is best. In effect, the graph provides a visual indication of the range of probability over which the various alternatives are optimal, and the algebra provides exact values of the endpoints of the ranges. Example 5S–8 illustrates the procedure. S O L U T I O N Finding Optimal Probability Ranges for the Expected Value Approach Given the following table, determine the range of probability for state of nature #2, that is, P(2), for which each alternative is optimal under the expected-value approach.     STATE OF NATURE     #1 #2   A   4 12 Alternative B 16   2   C 12   8 E X A M P L E 5 S – 8 First, plot each alternative relative to P(2). To do this, plot the #1 value on the left side of the graph and the #2 value on the right side. For instance, for …