Need to solve the questions on the Word document using R. Would also need to provide the R script file with the solutions
BOSTON UNIVERSITY METROPOLITAN COLLEGE DEPARTMENT OF ADMINISTRATIVE SCIENCES AD 616: Enterprise Risk Analytics Assignment 1 What to submit? Please submit (i) a word file explaining in detail your answers to each question (you can use screenshots of the R to explain your answers) AND (ii) an R file with a separation for each question. For each question, make sure you develop the model and present the simulation results – the R file should be self-explanatory. The assessment of your work will include both the accuracy and the clarity of your word file and the R Code. 1. Consider a call center that receives its demand over a set of different travel websites. The weekly demand for each website is normally distributed with a mean and standard deviation given in Table 1. Develop a R script that calculates the average total call center demand and its standard deviation. Table 1: Weekly demand of travel sites (in hours) Travel Site Mean Standard Deviation A 200 20 B 50 10 C 100 15 D 150 30 E 100 30 F 100 10 2. A cell phone manufacturer is considering to offer a refund to its customers whose battery fails before 5 years. The refund is equal to $1 per 1 month short of 5 years. Previous studies show that a battery’ life is normally distributed with a mean of 6 years and standard deviation of 1 year. What is the expected cost per cell phone to the manufacturer of this offer? 3. A convenience store needs to make a decision of how many packages of California rolls prepare for tomorrow. A package of California rolls cost the store $2.00 and it sells for $6.00. Daily demand is normally distributed with a mean of 100 packages of California rolls and a standard deviation of 40 packages of California rolls. If there are leftovers at the end of the day, the store donates them. Develop a R model that simulates the daily profit resulting from the preparation of 50, 75, 100, 120, 140, 160 packages of California rolls in a day (run them one at a time). Of these 6 options, which option maximizes the expected profit? 5/18/2021 Module 1 https://learn.bu.edu/bbcswebdav/pid-9009296-dt-content-rid-54138273_1/courses/21sum1metad616so1/course/module1/allpages.htm 1/27 Module 1 This is a single, concatenated file, suitable for printing or saving as a PDF for offline viewing. Please note that some animations or images may not work. Module 1 Study Guide and Deliverables May 11 - 17 Topics: Lecture 1: Introduction to Enterprise Risk Analytics Lecture 2: Analyzing Risk in the Enterprise Readings: Lectures 1 and 2 online content Discussions: Module 1 Discussion: Introduce Yourself (non- graded) Postings end on Monday, May 17 at 11:59 PM ET Assignments: Assignment 1: Individual Assignment covering Lecture 1 and Lecture 2. Due on Monday, May 17 at 11:59 PM ET Tutorial: Tutorial 1 for solving Assignment 1 Assessments: Quiz 1 opens on on Saturday, May 15 at 9:00 AM ET, closes on Monday, May 17 at 11:59 PM ET Live Classrooms: Tuesday, May 11 from 6:00-8:00 PM ET Lecture 1 Learning Objectives After you complete this lecture, you will be familiar with: Definition of uncertainty and risk Risk analysis and risk analytics Methods of risk analysis 5/18/2021 Module 1 https://learn.bu.edu/bbcswebdav/pid-9009296-dt-content-rid-54138273_1/courses/21sum1metad616so1/course/module1/allpages.htm 2/27 Simulation as a risk analysis tool Advantages and disadvantages of simulation Past, present, and future of simulation Types of simulation software Components of a simulation study and steps of conducting a simulation study What is Uncertainty and Risk? In AD 571 Business Analytics Foundations, in many applications you have assumed that the world is certain and that there is no uncertainty in the decision-making process. However, uncertainty is at the heart of many business problems, and a key aspect of solving business problems is to deal with uncertainty appropriately. Uncertainty is defined as the imperfect knowledge of what will happen in the future. There are many sources of uncertainty that may appear in various business situations: Demands for products Times between arrivals to a bank/store Stock price returns Changes in interest rates Changes in exchange rates A company's market share for a particular product At times, uncertainty can be reduced or eliminated. For instance, standardization of work process can reduce the variation of the output. Similarly, mistake proofing can be utilized to eliminate the chance of a defect in a process. Once uncertainty is determined to exist at a certain level, companies should take action to determine its potential effect on the organization. "By failing to consider uncertainty explicitly in their decision- making process, companies run the risk of improperly valuing the (economic) consequences of a course of action exposing themselves to unacceptable risk missing opportunities for better solutions”1 Therefore, decisions made on the basis of uncertain information involve risk. In this course, we define risk as "the likelihood of an undesirable outcome."2 Hence, "risk implies a potential for loss"3 and it is in the interest of companies to analyze and manage risk so as to have full control over their decision-making process. It is important to note that by analyzing risk, companies not only avoid loss but also discover opportunities and increase their competitiveness in the marketplace. "To try to eliminate risk in business enterprise is futile. Risk is inherent in the commitment of present resources to future expectations. Indeed, economic progress can be defined as the ability to take greater risks. Attempts to eliminate risks, even the attempt to minimize them, can only make them irrational and unbearabe. It can only result in the greatest risk of all: rigidity." Peter Drucker 5/18/2021 Module 1 https://learn.bu.edu/bbcswebdav/pid-9009296-dt-content-rid-54138273_1/courses/21sum1metad616so1/course/module1/allpages.htm 3/27 As Peter Drucker, who has been described as the founder of modern management, notes, it is impossible to eliminate risk in a business environment. Risk is inherent in business processes. Therefore, the best we can do is to try to analyze and manage the risk. The more information we gain about how much we are exposed to risk, the more informed decisions we take in the management of the enterprise. Our goal in this class is to learn how to properly analyze risk and make better decisions for the future of the enterprise. “Risk is usually assessed by evaluating the probability that the outcome will occur along with the severity of the outcome. For instance, an investment that has a high probability of losing money is riskier than an investment with a lower probability of losing money. Along the same lines, an investment that may result in $10 million loss is riskier than one that might result in only a $10,000 loss."4 “In assessing risk, we answer the following questions: What is the probability that we will incur a financial loss? What is the probability that the net present value of our project will turn out negative? What is the probability that we will run out of inventory?”5 Risk Analysis and Risk Analytics "Risk Analysis is an approach for developing a comprehensive understanding and awareness of risk associated with a particular variable of interest."6 The following scenario illustrates the concept of risk analysis: Example: The executives of a food company must decide whether to launch a new packaged cereal. They have come to the conclusion that five factors are determining variables: advertising and promotion expense, total cereal market, share of market for this product, operating costs, and new capital investment. On the basis of the "most likely" estimate for each of these variables, the picture looks very bright — a healthy 30% return, indicating a significantly positive expected net present value. This future, however, depends on each of the "most likely" estimates coming true in the actual case. If each of these "educated guesses" has, for example, a 60% chance of being correct, there is only an 8% chance that all five will be correct (0.60 × 0.60 × 0 .60 × 0.60 × 0.60) if the factors are assumed to be independent. So, the "expected" return, or present value measure, is actually dependent on a rather unlikely coincidence. The decision maker needs to know a great deal more about the other values used to make each of the five estimates and about what he stands to gain or lose from various combinations of these values. Source: Hertz, D. B., & Thomas, H. (1983). Risk analysis and its applications. John Wiley & Sons, Ltd. "Thus, risk analysis seeks to examine the impact of uncertainty on the estimates and their potential interaction with one another on the output variable of interest."7 In this course, we will learn about risk analysis in the presence of (big) data — hence the phrase "risk analytics." It is tempting to use the most likely value (or expected value) to model an uncertain quantity (as illustrated in the cereal example above). However, using the expected values for uncertain variables tells us nothing about the variability of the performance measure that we base our decisions on. 5/18/2021 Module 1 https://learn.bu.edu/bbcswebdav/pid-9009296-dt-content-rid-54138273_1/courses/21sum1metad616so1/course/module1/allpages.htm 4/27 Example8: Suppose a $1,000 investment is expected to return $10,000 in two years. Would you invest if the equiprobable outcomes could range from $9,000 to $11,000? the equiprobable outcomes could range from -$30,000 to $50,000? Although these two alternatives produce the same expected return ((9,000 +11,000)/2 = $10,000 and (-$30,000 + $50,000)/2 = $10,000) in the end, they carry different levels of risk. Apparently, the second alternative is riskier than the first alternative as it involves losing money (in the amount of $30,000!). "Therefore, even if we can determine the expected outcome of a decision, it is equally important if not more so to consider the risk involved in the decision."9 By proactively analyzing and managing risk, companies can make better decisions that add value. Methods of Risk Analysis10 We will examine the impact of uncertainty in the decision-making process of various enterprises. We will see several examples where uncertainty is inherent and hence risk analysis is crucial: Outsourcing New product development Single-period purchase decision Exchange-rate risk Marketing a new product There are three common methods used to analyze risk in a corporate environment: Best Case/Worst Case Analysis What-If Analysis Simulation Best Case/Worst Case Analysis: Best-case analysis uses the most optimistic value for each uncertain input in the model. Worst- case analysis, on the other hand, uses the most pessimistic value for each uncertain input in the model. There is a middle-way in between which is called base-case analysis. Base-case analysis uses the most likely value for each uncertain input. It is the most widely used approach by managers; however, it leads to a pitfall called flaw of averages. Figure 1.1 illustrates this approach. Flaw of Averages: Using the best-case analysis for uncertain inputs 5/18/2021 Module 1 https://learn.bu.edu/bbcswebdav/pid-9009296-dt-content-rid-54138273_1/courses/21sum1metad616so1/course/module1/allpages.htm 5/27 Source: Albright, S. C., & Winston, W. L. (2015). Business analytics: Data analysis and decision making (5th Edition). Cengage Learning. Best case/worst case analysis is easy to do but it does