Reference no: EM132463727

Question 1.

In their efforts to improve services to the community, Blue Band Company Ltd is considering the purchase of a new ambulance. The decision will rest partly on the anticipated distance to be driven next year. The kilometres driven during the past five years are as follows:

Year              Distance (km)

1                      3000

2                      4000

3                     3400

4                     3800

5                     3700

Problem a) Forecast the number of kilometres for next year using a two-year moving average.

Problem b) Find the MAD based on the two-year moving average forecast in part (a). (Hint: You will have only three years of matched data.)

Problem c) Use a weighted two-year moving average with weights of 0.4 and 0.6 to forecast next year's mileage. (The weight of 0.6 is for the most recent year.) What MAD results from using this approach to forecasting? (Hint: You will have only three years of matched data.)

Problem d) Compute the forecast for year 6 using exponential smoothing, an initial forecast for year 1 of 3000 kilometres and α = 0.5.

Question 2: Sales of vegetable dehydrators at Bud Banis's discount department store in Gander over the past year are shown below. Management prepared a forecast using a combination of exponential smoothing and its collective judgment for the four months March, April, May, and June of 2016:

Month 2015-2016           Unit Sales        Management's Forecast

July                                    100                       -

Aug                                      93                       -

Sept                                     96                      -

Oct                                     110                      -

Nov                                      124                     -

Dec                                       119                    -

Jan                                         92                     -

Feb                                         83                     -

Mar                                         101                 120

Apr                                            96                112

May                                           89                110

June                                          108                108

Problem a) Compute MAD and MAPE for management's technique.

Problem b) Do management's results outperform (i.e., have smaller MAD and MAPE than) a naive forecast?

Problem c) Which forecast do you recommend, based on lower forecast error?

Question 3: K-Motors produced several transistors (in millions) during the past five years follows:

Year                   Transistors

1                          140

2                          160

3                          190

4                          200

5                          210

Problem a) Forecast the number of transistors to be made next year, using linear regression.

Problem b) Compute the mean squared error (MSE) when using linear regression.

Problem c) Compute the mean absolute percent error (MAPE)

Question 4. Kamloops residents have fond memories of ice skating at a local park. An artist has captured the experience in a drawing and is hoping to reproduce it and sell framed copies to current and former residents. He thinks that if the market is good, he can sell 400 copies of the elegant version at $125 each. If the market is not good, he will sell only 300 at $90 each. He can make a deluxe version of the same drawing instead. He feels that if the market is good, he can sell 500 copies of the deluxe version at $100 each. If the market is not good, he will sell only 400 copies at $70 each. In either case, production costs will be approximately $35 000. He can also choose to do nothing. If he believes there is a 50% probability of a good market, what should he do? Why?

Question 5. Chrystab Consulting designs and constructs air conditioning and heating systems for hospitals and clinics. Currently, the company's staff is overloaded with design work. There is a major design project due in eight weeks. The penalty for completing the design late is $14 000 per week, since any delay will cause the facility to open later than anticipated and cost the client significant revenue. If the company uses its inside engineers to complete the design, it will have to pay them overtime for all work. Chrystab has estimated that it will cost $12 000 per week (wages and overhead), including late weeks, to have company engineers complete the design. Chrystab is also considering having an outside engineering firm do the design. A bid of $92 000 has been received for the completed design. Yet another option for completing the design is to conduct a joint design by having a third engineering company complete all electromechanical components of the design at a cost of $56 000. Chrystab would then complete the rest of the design and control systems at an estimated cost of $30 000. Chrystab has estimated the following probabilities of completing the project within various time frames when using each of the three options. Those estimates are shown in the following table:

Option                                    Probability of Completing the Design

                                   On time                   1 week late               2 weeks late                     3 weeks late

Internal Engineers            0.4                          0.5                                  0.1             -

External Engineer             0.2                         0.4                                    0.3              0.1

Joint Design                    0.1                         0.3                                    0.4               0.2

Problem 1: What is the best decision based on an expected monetary value criterion? (Note: You want the lowest EMV because we are dealing with costs in this problem.)

Question 6: McBeth Ent., wants to redesign its kitchens to improve productivity and quality. Three designs, called designs K1, K2, and K3, are under consideration. No matter which design is used, daily demand for sandwiches at a typical Macbeth restaurant is for 500 sandwiches. A sandwich costs $1.30 to produce. Non-defective sandwiches sell, on the average, for $2.50 per sandwich. Defective sandwiches cannot be sold and are scrapped. The goal is to choose a design that maximizes the expected profit at a typical restaurant over a 300-day period. Designs K1, K2, and K3 cost $100 000, $130 000, and $180 000 respectively. Under design K1, there is a 0.80 chance that 90 out of each 100 sandwiches are non-defective and a 0.20 chance that 70 out of each 100 sandwiches are non-defective. Under design K2, there is a 0.85 chance that 90 out of each 100 sandwiches are non-defective and a 0.15 chance that 75 out of each 100 sandwiches are non-defective. Under design K3, there is a 0.90 chance that 95 out of each 100 sandwiches are non-defective and a 0.10 chance that 80 out of each 100 sandwiches are non-defective. What is the expected profit level of the design that achieves the maximum expected 300-day profit level?