Sample Final. DSc 3120 Departmental Final Examination

Transcription

1 Instructor's Name Sample Final Your Name All Class Hour / DSc 3120 Departmental Final Examination Sample Questions You may take the full examination period for this final exam, but may also leave early if you finish early. To avoid possible accusations of academic dishonesty, attempt to sit where there is an empty seat between yourself and any other student. As always, we expect you to present only your own work. You may have a calculator, one 8½X 11 sheet of notes, and one sheet of scratch paper. We recommend that you use pencils and erasers so that you may correct errors. Do not disassemble this exam. Put your name on this page only, so that your instructor can grade papers, not people. Your instructor may announce additional conditions. On problems, do your best to make your reasoning clear to your instructor. This may make it possible to award you partial credit when your numeric answer is incorrect. Be sure to read each question carefully, so that your answer addresses the issue presented (which might not be the one you expected). We do not require you to answer the questions on this exam in any particular order. A strategy that many "A" students use is to scan the entire exam, then answer questions in the order from easiest to most difficult. This holds down the chance of getting "stuck" on a tough problem and wasting time that could otherwise harvest relatively easy points. Your instructor will announce how the questions will be scored 2

2 Shirley Ujest and her longtime friend Sal Monella have developed a hot new product. It is a color fax board for use in PC s. They see two fundamentally different ways they could manufacture it. The conventional way would be to use existing chips currently available on the open market. The alternative is to use ASIC s (Application Specific Integrated Circuits). The costs they have been able to estimate, with the help of their bookkeeper, are: ASIC Based Conventional ASIC Setup $200,000 $0 Board Setup $10,000 $10,000 Plant Operations $200,000 $200,000 Marketing $250,000 $250,000 Software/Unit $5 $5 Manual/Unit $1 $1 Packaging/Unit $1 $1 Board/Unit $1 $2 Labor/Unit $2 $8 Chips/Unit $2 $5 Overhead/Unit $6.60 $4.60 Shirley and Sal are not willing to count on more than a two year life for the product in this fast moving industry. The bookkeeper allocated fixed costs for those two years on the assumption that 100,000 color fax modems would be sold in those two years. 1. Calculate below, showing your work, the break-even point (in units) of a color fax modem (ready to ship) for each of the two manufacturing methods assuming that they plan to sell the units for $59 each. 2. Compute, showing your work, the number of units at which Shirley and Sal should be indifferent between the two methods. Which method is best at volumes greater than that number? 3

3 3. Write out a) The general form of the multiplicative Time Series Decomposition model and b) The form of the model that we actually use. Briefly explain why they are different. 4. Monte Carlo Simulation tends to be difficult, expensive, and time consuming to use. State one good reason for using it, in light of these obstacles. 5. Principles for intelligent design of spreadsheet models include issues of organization, avoiding embedded parameters, cell protection, labeling, formatting, and such. What motive or motives might be behind these principles? 4

4 6. Sam Dilligaf is trying to forecast sales for his store, Sam s Sporting Supermart. Sam's first try was with Simple Exponential Smoothing, using α = Unfortunately, his dog chewed his worksheet. (Even adults have trouble with dogs.) Please help him by filling in the cells indicated by a with a label, correct values, or correct Excel formulas. If you use copyable formulas, you may indicate copying where appropriate. Darkly shaded cells should remain empty; others require a number, a formula, or a label as appropriate. (For Bias and MAD, use formulas only.) A B C D E F 1 Year Quarter Enroll Forecast Abs(error) Bias = 16 Alpha = 0.75 MAD = 7. If Sam had used a Naï ve forecast, what would his forecast for Quarter 1, 2000 have been? 5

5 8. Looking at the results, Sam wasn t convinced that Simple Exponential Smoothing was the best was to forecast his sales. He decided to try Time Series Decomposition in another spreadsheet. He began by trying to measure seasonality. Unfortunately, though he tied up his dog, this time his cat shredded the worksheet, and you are needed again. Please fill in the appropriate missing cells with either correct actual calculations or correct Excel formulas. (Mean Ratios and Seasonal Indices to 4 decimals, all other to two decimals.) A B C D E F 1 Year Quarter Actual Sales 1 year M.A. CMA Ratios Mean Seasonal 16 Ratios Indices Avg =

6 Using the Seasonal Indices you repaired for him, Elmer deseasonalized the data and took it to another spreadsheet that was capable of computing trend functions for him. This spreadsheet assumed that the first Quarter of 1994 was Period 1. His results are in the following table: Trend Results Linear Exponential Power Parabola A = B = C = R^2 = MSE = BIAS = -9.47E E-15 Trend Formulas Linear Exponential Power Parabola Y=a+b*X Y=a*EXP(b*X) Y=a*X^b Y=a+b*X+c*X^2 9. Given the information above, which of these curve forms would you recommend that he use, and why? 10. Using the curve that you selected, compute the Time Series Decomposition Forecast for the third Quarter of Do no rounding of coefficients or trend value (though you should round your final forecast appropriately). Be sure to show your work. 7

7 The all Washed Up Car Wash has found a tremendous bargain on a new car waxing machine imported from the newly independent Republic of Lowenbrau. The only weak point is the special wax pump, which can be expected to fail relatively frequently and cannot be repaired. AWUCW can order up to five replacement pumps at a time, which would be delivered with the annual end of year shipment from Lowenbrau. They are available at no other time, and are expensive. If the wax pump fails and they have no replacement, they must stop using the machine until the next shipment arrives. Breakdowns per year Probability Sum 1.00 The probabilities of breakdowns during any given year are shown to the right. 11. In an average year, how many pumps can they expect to fail? Compute to two decimal places based on the above table. 12. Since a simple expected value can hide as much information as it reveals, AWUCW has asked you to simulate pump failures over the ten year useful life of the machine. Use the table below, in which we provide random numbers for your use. You may find it convenient to set up your own probability table on this page. Year Random Number Number of Failures 8

8 13. AWUCW management is considering a policy of ordering enough spare pumps each year to bring their stock of spares up to two pumps. Comment on this policy. 14. You have become a loan officer in a small bank. It is the bank s policy to make loans to people who seem to have a better than 50% chance of being a good credit risk. Further, the bank has determined that 90% of the people with steady jobs are good credit risks, but only 25% of the people with no steady job are good credit risks. In probability notation, this translates to: P(G S) = 0.9 P(G N) = 0.25 [G = Good credit risk, B = Bad risk] P(B S) = 0.1 P(B N) = 0.75 [S = Steady job, N = No steady job] A seedy character (looking a lot like your DSc 3120 instructor) comes to your desk seeking a loan. You immediately assess the probability of his having a steady job as P(S) = 0.25 [and thus P(N) = 0.75], but you permit him, as a courtesy, to complete an application. Checking his credit rating, you learn that he is indeed a good credit risk. Using Bayes Theorem, revise your probability that he has a steady job. In other words, find P(S G). 15. Having grown wealthy, your portfolio of properties now includes the NoTell Motel. You have noticed, not to your surprise, that when you reduce your room rates, you rent more rooms and sell more meals in your coffee shop. The incremental cost per meal is approximately constant at all volumes, and it takes the same personnel to run the coffee shop whether it is empty or there is a line waiting for meals. On the other hand, as the occupancy of the motel goes up, you need more personnel for cleaning the rooms each day. Sketch (clearly) an influence diagram showing a reasonable path of influences from a room rate decision to a level of profitability. Do not attempt to write or calculate any formulas. 9

9 16. A re-heat blow-molding machine makes 12 two-liter bottles per cycle. The machine completes a cycle every 6 seconds for 60 minutes per hour in a normal eight-hour day. Peachtree Bottling Co. operates one of these machines at a daily cost of $1245, including labor but excluding allocated costs. Each bottle weighs 20 grams. The recycled plastic pellets used in the machine cost material cost $1.50/kg. There are no other incremental costs. Dustin Thyme, a cost analyst for Peachtree Bottling, has developed this equation for unit cost: 20 * * 30 * 60 * Use Dimensional Analysis to demonstrate either that this equation does or that it does not make sense. You need not calculate the unit cost numerically. 8 [ ] Makes sense [ ] Does not make sense 17. As Marketing V.P. of the Rusty s Muffler chain, you have long used a sophisticated forecasting model involving location, demographics, etc. with great success. For the past three years, one of your locations has consistently sold about 15% above projections, while another was about 25% below. What will you investigate. 10

10 Susan s Surprise Catering operates a sandwich truck in the downtown district, selling coffee, soft drinks, sandwiches, and desert snacks. Based on experience, the owner feels that during a Monday lunch hour, sandwich demand and its probability are correctly described in the table below. The The Payout Table for various levels of demand and production choices is given below. Sandwiches Sandwiches Demanded Made Answer questions showing as much as practical of your work above. 18 a) How many sandwiches would Susan make using the Maximax criterion? b) How many sandwiches would Susan make using the Maximin criterion? c) How many sandwiches would Susan make using the LaPlace criterion? 19. If Susan learned that P(S1) =.1 and P(S2) =.5, then she could apply the expected return (or EMV) criterion. a) What choice would Susan make using the expected return (or EMV) criterion? b) What payoff will Susan receive for this decision? c) What is the minimum expected regret? d) What decision would you make using this decision criterion? 20. a) Calculate the Expected Value of Perfect Information (EVPI) in this case. b) Briefly but clearly explain the meaning of EVPI. 11

11 DSc 3120 Final Exam Topics An analysis and summary of all Final Exam questions areas from six recent final exams BASIC Modeling Counts Break-even point(s) 6 Spreadsheet principles 5 Influence diagram 1 Crossover point 4 Incremental Cost 4 Dimensional analysis 3 Relevant Factors 2 Critical Thinking (generally) 2 Construct profit function (as separate issue) 1 Nature of Fixed Cost 1 When break-even 1 Cumulative break-even 1 Forecasting Some of Naï ve, Exponential Smooting, Bias, and/or MAD 9 Select and/or compute Trend 9 Some of MA, CMA, Raw Ratios, Seasonal Index 6 Stable time series assumption 3 Identify meaningless SI s as such 2 TSD model form 1 Meaning of MAD 1 Purpose of Naï ve 1 Decision Analysis Bayes Theorem 6 Payoff table 6 EVUC and/or EVPI 6 Maximax, maximin, and/or LaPlace-Bayes 5 Compute ER (EMV) 5 Decision Tree 5 Conclusions from ER (EMV) 3 Risk and ER (EMV) 3 Marginal probabilities 2 Simulation Manual simulation 5 Why (or when) use Monte Carlo simulation 5 Uniform distribution 2 Expected # failures 4 Conclusions from simulation 4 12