Concept explainers
a)
To construct: A decision tree.
Introduction:
Decision tree:
A decision tree can be termed as map of all the possible outcomes that can arise from the series of related choices. It will allow an individual or an organization to weigh their outcomes in different bases of costs, probabilities and the benefits.
b)
To determine: The best decision using the expected value criterion.
Introduction:
Expected monetary value (EMV):
Expected monetary value is the figure which shows the reasonable returns that can be received from a situation. It can be termed as an average of the best case scenario. It will include both the returns and the likelihood of that particular outcome occurring.
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Operations Management: Sustainability and Supply Chain Management (12th Edition)
- At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.arrow_forwardDilberts Department Store is trying to determine how many Hanson T-shirts to order. Currently the shirts are sold for 21, but at later dates the shirts will be offered at a 10% discount, then a 20% discount, then a 40% discount, then a 50% discount, and finally a 60% discount. Demand at the full price of 21 is believed to be normally distributed with mean 1800 and standard deviation 360. Demand at various discounts is assumed to be a multiple of full-price demand. These multiples, for discounts of 10%, 20%, 40%, 50%, and 60% are, respectively, 0.4, 0.7, 1.1, 2, and 50. For example, if full-price demand is 2500, then at a 10% discount customers would be willing to buy 1000 T-shirts. The unit cost of purchasing T-shirts depends on the number of T-shirts ordered, as shown in the file P10_36.xlsx. Use simulation to determine how many T-shirts the company should order. Model the problem so that the company first orders some quantity of T-shirts, then discounts deeper and deeper, as necessary, to sell all of the shirts.arrow_forwardThe owner of a restaurant in Bloomington, Indiana, has recorded sales data for the past 19 years. He has also recorded data on potentially relevant variables. The data are listed in the file P13_17.xlsx. a. Estimate a simple regression equation involving annual sales (the dependent variable) and the size of the population residing within 10 miles of the restaurant (the explanatory variable). Interpret R-square for this regression. b. Add another explanatory variableannual advertising expendituresto the regression equation in part a. Estimate and interpret this expanded equation. How does the R-square value for this multiple regression equation compare to that of the simple regression equation estimated in part a? Explain any difference between the two R-square values. How can you use the adjusted R-squares for a comparison of the two equations? c. Add one more explanatory variable to the multiple regression equation estimated in part b. In particular, estimate and interpret the coefficients of a multiple regression equation that includes the previous years advertising expenditure. How does the inclusion of this third explanatory variable affect the R-square, compared to the corresponding values for the equation of part b? Explain any changes in this value. What does the adjusted R-square for the new equation tell you?arrow_forward
- The Gorman Manufacturing Company must decide whether to manufacture a component part at its Milan, Michigan, plant or purchase the component part from a supplier. The resulting profit is dependent upon the demand for the product. The following payoff table shows the projected profit (in thousands of dollars): Decision State of Nature Alternative Low Demand (S1) Medium Demand (S2) High Demand )S3) Manufacture, d(1) -20 40 100 Purchase, d(2) 10 45 70 The state-of-nature probabilities are P s1= 0.35, P s2= 0.35, and P s3= 0.30 Use expected value to recommend a decision.arrow_forward.A 45 kW rated solar power system has its power output and the Solar irradiance on the PV system measured during daylight hours over a day. Based on the following data, create a scatter plot of the power output of the PV system vs the solar irradiance and comment on the relationship between the two. Based on the data, can you tell which season this day was in? Solar Irradiance on the PV system (kW/m²) 0 0.079 0.333 0.571 0.751 0.86 0.914 0.93 0.904 0.803 0.606 0.345 0.054 Power output from the PV system (kW) 0 3.098 12.438 20.124 25.703 28.498 29.587 29.69 28.798 26.264 20.434 12.223 2arrow_forwardTucson Machinery, Inc., manufactures numerically controlled machines (NCM), which sell for an average price of $12 million each. Sales for these NCMs for the past two years were as follows: Quantity (units) Quantity (units) Quarter Last year ||| III IV 12 18 20 24 Quarter This year | || ||| IV 20 24 28 32 Find the equation of a simple linear regression line using Excel, in the format of Y=a+bX. Keep two decimals of a and b. Forecast the first quarter sales for next year. Keep two decimals.arrow_forward
- Recently, the owner of a Trader Joe's franchise decided to change how she compensated her top manager. Last year, she paid him a fixed salary of $55,000 and her store made $120,000 in profits (not counting payment to her top manager). She suspected the store could do much better and feared the fixed salary was causing her top manager to shirk on the job. Therefore, this year she decided to offer him a fixed salary of $28,000 plus 15% of the store's profits. Since the change, the store is performing much better, and she forecasts profits this year to be $260,000 (again, not counting the payment to her top manager). Assuming the change in compensation is the reason for the increased profits, and that the forecast is accurate, how much more money will the owner make (net of payment to her top manager) because of this change? $ Does the manager make more money under the new payment scheme? Yesarrow_forwardWhen there are numerous property and equipment transactions during the year, anauditor who plans to assess control risk at a low level usually performs(1) analytical procedures for property and equipment balances at the end of theyear.(2) analytical procedures for current year property and equipment transactions.(3) tests of controls and limited tests of current year property and equipment transactions.(4) tests of controls and extensive tests of property and equipment balances at theend of the yeararrow_forwardThe University of Miami bookstore stocks textbooks in preparation for sales each semester. It normally relies on departmental forecasts and preregistration records to determine how many copies of a text are needed. Preregistration shows 85 operations management students enrolled, but bookstore manager Vaidy Jayaraman has second thoughts, based on his intuition and some historical evidence. Vaidy believes that the distribution of sales may range from 65 to 85 units, according to the following probability model: Demand Probability 65 0.10 Stock 70 0.30 65 This textbook costs the bookstore $82 and sells for $112. Any unsold copies can be returned to the publisher, less a restocking fee and shipping, for a net refund of $30. a) Based on the given information, Vaidy's conditional profits table for the bookstore is: 65 p=0.10 75 0.20 70 p=0.30 80 0.10 Demand 75 p=0.20 80 p = 0.10 85 p=0.30 85 0.30arrow_forward
- The University of Miami bookstore stocks textbooks in preparation for sales each semester. It normally relies on departmental forecasts and preregistration records to determine how many copies of a text are needed. Preregistration shows 85 operations management students enrolled, but bookstore manager Vaidy Jayaraman has second thoughts, based on his intuition and some historical evidence. Vaidy believes that the distribution of sales may range from 65 to 85 units, according to the following probability model: Demand Probability 65 0.05 Stock 65 70 75 80 85 70 0.25 This textbook costs the bookstore $82 and sells for $107. Any unsold copies can be returned to the publisher, less a restocking fee and shipping, for a net refund of $30. a) Based on the given information, Vaidy's conditional profits table for the bookstore is: Demand 75 P=0.30 65 P = 0.05 0000 70 P = 0.25 75 0.30 ☐☐☐☐ 80 0.15 00000 80 85 P = 0.15 P = 0.25 30000 85 0.25 ☐☐☐☐arrow_forward4. A credit rating company recommends granting of credit cards based on several criteria. One is annual income. If the annual income of applicants is normally dis- tributed with mean $22,000 and standard deviation $4,800 and the company recommends no applicant unless his or her income exceeds $15,000, what fraction of the applicants are denied on this basis?arrow_forwardSales of Volkwagen’s popular Beetle have grown steadily at autodealership in Nevada during the past 5 years (see table below).The sales manager had predicted before the new model wasintroduced that first-year sales would be 410 VWs. Usingexponential smoothing with a weight of α= .30, develop forecastfor years 2 through 6.Year Sales Forecast1 450 4102 4953 5184 5635 5846 ? 2. The following data come from regression line projections:Period Forecast Values Actual values1 410 4062 419 4233 428 4234 435 440 Compute the MAD and MSE.arrow_forward
- Practical Management ScienceOperations ManagementISBN:9781337406659Author:WINSTON, Wayne L.Publisher:Cengage,