Howard College Investment Alternatives Economic Probabilities Calculations

Howard College

Question Description

I’m studying for my Economics class and don’t understand how to answer this. Can you help me study?

5-6 You are considering three investment alternatives for some spare cash: Old Reliable

Corporation stock (A1), Fly-By-Nite Air Cargo Company stock (A2), and a federally insured

savings certificate (A3). You expect the economy will either “boom” (N1) or “bust” (N2), and

you estimate that a boom is more likely (p1 = 0.6) than a bust (p2 = 0.4). Outcomes for

the three alternatives are expected to be (1) $2,000 in boom or $500 in bust for Old Reliable

Corporation; (2) $6,000 in boom, but –$5,000 (loss) in bust for Fly-By-Nite; and (3) $1,200


5.7 If you have no idea of the economic probabilities pj in Question 5-6, what would be your

decision based on uncertainty using (a) maximax, (b) maximin, (c) equally likely, and (d)

minimax regret assumptions? DO THIS QUESTION IN EXCEL FILE and if there are some calculations please show me your math when I click on the cells

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5 Decision Making Preview Decision making is an essential part of planning. Decision making and problem solving are used in all management functions, although usually they are considered a part of the planning phase. This chapter presents information on decision making and how it relates to the first management func-tion of planning. A discussion of the origins of management science leads into one on modeling, the five-step process of management science, and the process of engineering problem solving. Different types of decisions are examined in this chapter. They are classified under conditions of certainty, using linear programming; risk, using expected value and decision trees; or uncertainty, depending on the degree with which the future environment determining the outcomes of these decisions is known. The chapter continues with brief discussions of integrated databases, management information and decision support systems, and expert systems, and closes with a comment on the need for effective implementation of decisions. Management Functions Leading Planning Decision Making Organizing Controlling 127 128 Chapter 5 Decision Making Learning Objectives When you have finished studying this chapter, you should be able to do the following: • • • • • Discuss how decision making relates to planning. Explain the process of engineering problem solving. Solve problems using three types of decision-making tools. Discuss the differences between decision making under certainty, risk, and uncertainty. Describe the basics of other decision-making techniques. Nature of Decision Making Relation to Planning Managerial decision making is the process of making a conscious choice between two or more rational alternatives in order to select the one that will produce the most desirable consequences (benefits) relative to unwanted consequences (costs). If there is only one alternative, there is nothing to decide. The overall planning/decision-making process has already been described at the beginning of Chapter 4, and there we discussed the key first steps of setting objectives and establishing premises (assumptions). In this chapter, we consider the process of developing and evaluating alternatives and selecting from among them the best alternative, and we review briefly some of the tools of management science available to help us in this evaluation and selection. If planning is truly “deciding in advance what to do, how to do it, when to do it, and who is to do it” (as proposed by Amos and Sarchet), then decision making is an essential part of planning. Decision making is also required in designing and staffing an organization, developing methods of motivating subordinates, and identifying corrective actions in the control process. However, it is conventionally studied as part of the planning function, and it is discussed here. Occasions for Decision Chester Barnard wrote his classic book The Functions of the Executive from his experience as president of the New Jersey Bell Telephone Company and of the Rockefeller Foundation, and in it he pursued the nature of managerial decision making at some length. He concluded that the occasions for decision originate in three distinct fields: (a) from authoritative communications from superiors; (b) from cases referred for decision by subordinates; and (c) from cases originating in the initiative of the executive concerned. Barnard points out that occasions for decisions stemming from the “requirements of superior authority . . . cannot be avoided,” although portions of it may be delegated further to subordinates. Nature of Decision Making 129 Appellate cases (referred to the executive by subordinates) should not always be decided by the executive. Barnard explains that “the test of executive action is to make these decisions when they are important, or when they cannot be delegated reasonably, and to decline the others.” Barnard concludes that “occasions of decision arising from the initiative of the executive are the most important test of the executive.” These are occasions where no one has asked for a decision, and the executive usually cannot be criticized for not making one. The effective executive takes the initiative to think through the problems and opportunities facing the organization, conceives programs to make the necessary changes, and implements them. Only in this way does the executive fulfill the obligation to make a difference because he or she is in that chair rather than someone else. Types of Decisions Routine and Nonroutine Decisions. Pringle et al. classify decisions on a continuum ranging from routine to nonroutine, depending on the extent to which they are structured. They describe routine decisions as focusing on well-structured situations that recur frequently, involve standard decision procedures, and entail a minimum of uncertainty. Common examples include payroll processing, reordering standard inventory items, paying suppliers,- and so on. The decision maker can usually rely on policies, rules, past precedents, standardized methods of processing, or computational techniques. Probably 90 percent of -management decisions are largely routine. Indeed, routine decisions usually can be delegated to lower levels to be made within established policy limits, and increasingly they can be programmed for computer decision if they can be structured simply enough. Nonroutine decisions, on the other hand, deal with unstructured situations of a novel, nonrecurring nature, often involving incomplete knowledge, high uncertainty, and the use of subjective judgment or even intuition, where no alternative can be proved to be the best possible solution to the particular problem. Such decisions become more and more common the higher one goes in management and the longer the future period influenced by the decision is. Unfortunately, almost the entire educational process of the engineer is based on the solution of highly structured problems for which there is a single textbook solution. Engineers often find themselves unable to rise in management unless they can develop the tolerance for ambiguity that is needed to tackle unstructured problems. Objective versus Bounded Rationality. Simon defines a decision as being objectively rational if in fact it is the correct behavior for maximizing given values in a given situation. Such -rational decisions are made “(a) by viewing the behavior alternatives prior to decision in panoramic [exhaustive] fashion, (b) by considering the whole complex of consequences that would follow on each choice, and (c) with the system of values as criterion singling out one from the whole set of alternatives.” Rational decision making, therefore, consists of optimizing, or maximizing, the out-come by choosing the single best alternative from among all possible ones, which is the approach suggested in the planning/decisionmaking model at the beginning of Chapter 4. However, Simon believes that actual behavior falls short of objective rationality in at least three ways. 130 Chapter 5 Decision Making 1. Rationality requires a complete knowledge and anticipation of the consequences that will follow on each choice. In fact, knowledge of consequences is always fragmentary. 2. Since these consequences lie in the future, imagination must supply the lack of experienced feeling in attaching value to them. But values can be only imperfectly anticipated. 3. Rationality requires a choice among all possible alternative behaviors. In actual behavior, only a few of these possible alternatives ever come to mind. Managers, under pressure to reach a decision, have neither the time nor other resources to consider all alternatives or all the facts about any alternative. A manager “must operate under conditions of bounded rationality, taking into account only those few factors of which he or she is aware, understands, and regards as relevant.” Administrators must satisfice by accepting a course of action that is satisfactory or “good enough,” and get on with the job rather than searching forever for the “one best way.” Managers of engineers and scientists, in particular, must learn to insist that their subordinates go on to other problems when they reach a solution that satisfices, rather than pursuing their research or design beyond the point at which incremental benefits no longer match the costs to achieve them. Level of Certainty. Decisions may also be classified as being made under conditions of certainty,- risk, or uncertainty, depending on the degree with which the future environment determining the outcome of these decisions is known. These three categories are compared later in this chapter. Management Science Origins Quantitative techniques have been used in business for many years in applications such as return on investment, inventory turnover, and statistical sampling theory. However, today’s emphasis on the quantitative solution of complex problems in operations and management, known initially as operations research and more commonly today as management science, began at the Bawdsey Research Station in England at the beginning of World War II. Hicks puts it as follows: In August 1940, a research group was organized under the direction of P. M. S. Blackett of the University of Manchester to study the use of a new radar-controlled antiaircraft system. The research group came to be known as “Blackett’s circus.” The name does not seem unlikely in the light of their diverse backgrounds. The group was composed of three physiologists, two mathematical physicists, one astrophysicist, one Army officer, one surveyor, one general physicist, and two mathematicians. The formation of this group seems to be commonly accepted as the beginning of operations research. Some of the problems this group (and several that grew from it) studied were the optimum depth at which antisubmarine bombs should be exploded for greatest effectiveness (20 to 25 feet) and the relative merits of large versus small convoys (large convoys led to fewer total ship losses). Soon after the United States entered the war, similar activities were initiated by the U.S. Navy and the Army Air Force. With the immediacy of the military threat, these studies involved research 131 Management Science on the operations of existing systems. After the war, these techniques were applied to longer-range -military problems and to problems of industrial organizations. With the development of more and more powerful electronic computers, it became possible to model large systems as a part of the design process, and the terms systems engineering and management science came into use. Management science has been defined as having the following “primary distinguishing characteristics”: 1. A systems view of the problem—a viewpoint is taken that includes all of the significant interrelated variables contained in the problem. 2. The team approach—personnel with heterogeneous backgrounds and training work together on specific problems. 3. An emphasis on the use of formal mathematical models and statistical and quantitative techniques. What Is Systems Engineering? Systems engineering is an interdisciplinary approach and means to enable the realization of successful systems. It focuses on defining customer needs and required functionality early in the development cycle, documenting requirements, then proceeding with design synthesis and system validation while considering the complete problem. Models and Their Analysis A model is an abstraction or simplification of reality, designed to include only the essential features that determine the behavior of a real system. For example, a three-dimensional physical model of a chemical processing plant might include scale models of major equipment and large-diameter pipes, but it would not normally include small pipings or electrical wirings. The conceptual model of the planning/decisionmaking process in Chapter 4 certainly does not illustrate all the steps and feedback loops present in a real situation; it is only indicative of the major ones. Most of the models of management science are mathematical models. These can be as simple as the common equation representing the financial operations of a company: net income = revenue - expenses - taxes On the other hand, they may involve a very complex set of equations. As an example, the Urban Dynamics model was created by Jay Forrester to simulate the growth and decay of cities. This model consisted of 154 equations representing relationships between the factors that he believed were essential: three economic classes of workers (managerial/professional, skilled, and “underem-ployed”), three corresponding classes of housing, three types of industry (new, mature, and declin-ing), taxation, and land use. The values of these factors evolved through 250 simulated years to model the changing characteristics of a city. Even these 154 relationships still proved too simplistic to provide any reliable guide to urban development policies (see Babcock for a discussion.). 132 Chapter 5 Decision Making Management science uses a five-step process that begins in the real world, moves into the model world to solve the problem, and then returns to the real world for implementation. The -following explanation is, in itself, a conceptional model of a more complex process: Real World Simulated (Model) World 1. Formulate the problem (defining objectives, variables, and constraints). 2. Construct a mathematical model (a simplified yet realistic representation of the system). 3. Test the model’s ability to predict the present from the past, and revise until you are satisfied. 4. Derive a solution from the model. 5. Apply the model’s solution to the real system, document its effectiveness, and revise further as required. The scientific method or scientific process is fundamental to scientific investigation and to the acquisition of new knowledge based upon physical evidence by the scientific community. Scientists use observations and reasoning to propose tentative explanations for natural phenomena, termed hypotheses. Engineering problem solving is more applied and is different to some extent from the scientific method. Scientific Method Engineering Problem Solving Approach • • • • • • • • • • • Define the problem. Collect data. Develop hypotheses. Test hypotheses. Analyze results. Draw conclusion. Define the problem. Collect and analyze the data. Search for solutions. Evaluate alternatives. Select solution and evaluate the impact. The Analyst and the Manager To be effective, the management science analyst cannot just create models in an ivory tower. The problem-solving team must include managers and others from the department or system being studied—to establish objectives, explain system operation, review the model as it develops from an operating perspective, and help test the model. The user who has been part of model development, has developed some understanding of it and confidence in it, and feels a sense of ownership of it is most likely to use it effectively. 133 Tools for Decision Making The manager is not likely to have a detailed knowledge of management science techniques or the time for model development. Today’s manager should, however, understand the nature of management science tools and the types of management situations in which they might be useful. Increasingly, management positions are being filled with graduates of management (or engineer-ing management) programs that have included an introduction to the fundamentals of management science- and statistics. Regrettably, all too few operations research or management science programs require the introduction to organization and behavioral theory that would help close the manager– analyst gap from the opposite direction. There is considerable discussion today of the effect of computers and their applications (management science, decision support systems, expert systems, etc.) on managers and organizations. Certainly, workers and managers whose jobs are so routine that their decisions can be reduced to mathematical equations have reason to worry about being replaced by computers. For most manag-ers, however, modern methods offer the chance to reduce the time one must spend on more trivial matters, freeing up time for the types of work and decisions that only people can accomplish. Tools for Decision Making Categories of Decision Making Decision making can be discussed conveniently in three categories: decision making under -certainty, under risk, and under uncertainty. The payoff table, or decision matrix, shown in Table 5-1 will help in this discussion. Our decision will be made among some number m of alternatives, identified as A1, A2, g, Am. There may be more than one future “state of nature” N. (The model allows for n different futures.) These future states of nature may not be equally likely, but each state Nj will have some (known or unknown) probability of occurrence pj. Since the future must take on one of the n values of Nj, the sum of the n values of pj must be 1.0. The outcome (or payoff, or benefit gained) will depend on both the alternative chosen and the future state of nature that occurs. For example, if you choose alternative Ai and state of nature Nj takes place (as it will with probability pj), the payoff will be outcome Oij. A full payoff table will contain m times n possible outcomes. Table 5-1 Payoff Table State of Nature/Probability N 1 p N 2 p A O O A2 O21 O22 g Ai g g Oi1 g Oi2 g g Alternative 1 Am 1 11 O m1 2 12 O m2 g N j p g g O1j g O2j g g g Oij g g g Omj j g N n p g g O1n g O2n g g g Oin g g g Omn n 134 Chapter 5 Decision Making Let us consider what this model implies and the analytical tools we might choose to use under each of our three classes of decision making. Decision Making Under Certainty Decision making under certainty implies that we are certain of the future state of nature (or we assume that we are). (In our model, this means that the probability p1 of future N1 is 1.0, and all other futures have zero probability.) The solution, naturally, is to choose the alternative Ai, which gives us the most favorable outcome Oij. Although this may seem like a trivial exercise, there are many problems that are so complex that sophisticated mathematical techniques are needed to find the best solution. Linear Programming. One common technique for decision making under certainty is called linear programming. In this method, a desired benefit (such as profit) can be expressed as a mathematical function (the value model or objective function) of several variables. The solution is the set of values for the independent variables (decision variables) that serves to maximize the benefit (or, in many problems, to minimize the cost), subject to certain limits (constraints). Steps include: • • • • State the problem. What are the decision variables? Objective function Constraints Example Consider a factory producing two products, product X and product Y. The problem is this: If you can realize $10.00 profit per unit of product X and $14.00 per unit of product Y, what is the production level of x units of product X and y units of product Y that maximizes the profit P each day? Your production, and therefore your profit, is subject to resource limitations, or constraints. Assume in this example that you employ five workers—three machinists and two assemblers— and that each works only 40 hours a week. • Product X requires three hours of machining and one hour of assembly per unit. • Product Y requires two hours of machining and two hours of assembly per unit. State the problem: How many of product X and product Y to produce to maximize profit? Decision variables: Let x = number of product X to pro ...
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Expected Values
Expected Value of A1
Expected Value of A2
Expected value of A3
(a) Maximax Approach (choosing...

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