FORECASTING DEMAND
SOLUTION We have:
Week 3/19: Ft = ∝At–1 + (1 – ∝) (Ft–1+ Tt–1)
= 0.1(700) + 0.9(650 + 0) = 655.00 Tt = β (Ft – Ft–1) + (1 – β) Tt–1 Ft+1 = Ft + Tt = 655 + 1 = 656.000 The 656.00 is the adjusted forecast for week 3/26.
Week 3/26: Ft = 0.1(685) + 0.9(655 + 1.0) = 658.90
Tt = 0.2(658.9-655) + 0.8(1.0) = 1.58 Therefore Ft+1 = 658.9 + 1.58 = 660.48
The remainder of the calculations is in Table 5.15. The trend-adjusted forecast for the week of 5/14 is 711.89 = 712 units
Table 5.15
(1) (2) (3) (4) (5) (6)
Week Previous Actual Smoothed Smoothed
Next-average demand average trendTt period projection
Fˆt –1 At–1 ˆ
Ft Tt ˆ–1
Ft
Mar19 650.00 700 655.00 1.00 656.00
26 655.00 685 658.90 1.58 660.48
Apr. 2 658.90 648 659.23 1.33 660.56
9 659.23 717 666.20 2.46 669.06
16 660.20 713 673.09 3.35 676.44
23 673.09 728 681.60 4.39 685.99
30 681.60 754 691. 79 5.74 698.53
May 7 692.79 762 704.88 7.01 711.89
14 770
EXERCISE
1. What are forecasts?
2. What are the costs associated with forecasting–or not forecasting?
3. Summarize the key features of the more commonly used forecasting method.
4. What is a time series, and what are the components of a time series?
5. Explain the (a) trend, (b) seasonal, (c) cyclical, and (d) random components of a series.
6. What steps are involved in using time series data to make a forecast?
7. What is exponential smoothing?
8. Distinguish between, (a) simple regression, and (b) simple correlation.
9. Forecast demand for March was 950 units, but actual demand turned out to be only 820. If the firm is using a simple exponential smoothing technique with a = 0.2, what is the forecast for April?
[Ans. 924 units]
10. Using the results from Problem 1, assume the April demand was actually 980 units. Now what is the
forecast for May? [Ans. 935 units]
11. A forecaster is using an exponential smoothing model with a = 0.4 and wishes to convert to a moving average. What length of moving average is approximately equivalent? [Ans. 4 periods]
12. A university registrar has adopted a simple exponential smoothing model ( a = 0.4) to forecast enrollments during the three regular terms (excluding summer). The results are shown in Table 5.16 (a) Use the data to develop an enrollment forecast for the third quarter of year 2. (b) What would be the effect of increasing the smoothing constant to 1.0?
Table 5.16
Year Quarter Actual Old Forecast New
Enrollment Forecast Error Correction Forecast
(000) (000) (000) (000) (000)
1 1st 20.50 20.00 0.5 0.20 20.20
2nd 21.00
3rd 19.12
2 1st 20.06
2nd 22.00
3rd
[Ans. (a) 20,800, (b) Forecast would reflect the total amount of variation of previous demand from previous forecast—therefore, no smoothing.]
13. A firm producing photochemical has a weekly demand pattern as shown in Table 5.17. Using a smoothing constant of = 0.5 for both original data and trend, and beginning with week I, (a) compute the simple exponentially smoothed forecast and (b) compute the trend-adjusted exponentially smoothed forecast for the first five periods.
Table 5.17
Week 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Demand 30 34 22 16 10 10 14 20 30 36 30 10 12 20 30
14. Find the regression equation resulting from the values
∑ X
= 70,∑Y
= 90,∑ XY
= 660,∑ X2 = 514, n = 10. [Ans. Yc = 0.25 + 1.25X]
15. A producer of roofing materials has collected data relating interest rates to sales of asphalt shingles and found that the unexplained variation = 680, and explained variation = 2840.
(a) Find the correlation coefficient. (b) Explain its meaning.
[Ans. (a) r = 0.90 (b) 81 per cent of the variation in shingle sales is associated with interest-rate levels.]
16. The Carpet Cleaner Co. is attempting to do a better job of inventory management by predicting the number of vacuums the company will sell per week on the basis of the number of customers who respond to magazine advertisements in an earlier week. On the basis of a sample of n = 102 weeks, the following data were obtained:
a = 25
∑ (
Y –Yc)
2 = 22,500b = 0.10
∑ (
Y –Yc)
2 = 45,000(a) Provide a point estimate of the number of vacuums sold per week when 80 inquiries were received in the earlier week. (b) Estimate (at the 95.5 per cent level) the number of vacuums sold per week when 80 inquiries were received the week earlier. (c) State the value of the coefficient of determination. (d) Explain the meaning of your r2 value.
[Ans. (a) 33, (b) Using the large-sample approximation, the interval is 3 to 63 because Sy–x=15 (c) 0.5 (d) 50 per cent of the variation in number of vacuums sold is explained by the magazine advertisements.]
17. A recreation operations planner has had data collected on automobile traffic at a selected location Y on an interstate highway in hopes that the information can be used to predict weekday demand for state: operated camposites 200 miles away. Random samples of 32 weekdays during the camping season resulted in data from which the following expression was developed:
Yc = 18 + 0.02X.
where X is the number of automobiles passing the location and Y is the number of camposites demanded that day. In addition, the unexplained variation is
∑ (
Y–Yc)
2 = 1,470, and the total variation is(
–)
2∑
Y Y = 4,080. (a). What is the value of the coefficient of determination?(b) Explain, in words; the meaning of the coefficient of determination. (c) What is the value of the coefficient of correlation?
[Ans.(a) 0.64 (b) It tells the percentage of variation in camposites demanded that is associated with automobile traffic at the selected site. (c) 0.80.]
18. Allan’s Underground Systems installs septic systems for new houses constructed outside the city limits. To help forecast his demand, Mr. Allan has collected the data shown in Table on the number of country building permits issued per month, along with the corresponding number of bid requests he has received over a 15-month period.
Table 5.18
Month 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
No. Building permits 8 20 48 60 55 58 50 45 34 38 10 5 12 29 50
No. Bid requests 20 7 8 4 18 40 48 54 47 42 30 22 10 4 3
(a) Compute the simple correlation coefficient r between the number of building permits issued and the number of bid requests received in that month. Use all 15 periods of data.
(b) Use the first 12 months of data for building permits, and compute r between the number of building permits issued in a month and the number of bid requests received 2 months later (i.e., a 2-month lag).
(c) Repeat (b), but use a 3-month lag. (d) Which type of regression model would be best to forecast bid requests: a same-month model, a 2-month lag model, or a 3-month lag model?
[Ans. (a) 0.08 (b) 0.84 (c) 0.96 (d) A 3-month lag model is best. It permits Allan to explain 93 per cent of the variation in number of bid requests.]
19. Two experienced managers have resisted the introduction of a computerized exponential smoothing system, claiming that there judgmental forecast are “much better than any impersonal computer could do.” There past record of prediction is as shown in Table 5.19.
Table 5.19
Week Actual Demand Forecast
1 4,000 4500
2 4,200 5,000
3 4,200 4,000
4 3,000 3,800
5 3,800 3,600
6 5,000 4,000
7 5,600 5,000
8 4,400 4,800
9 5,000 4,000
10 4,800 5,000
(a) Compute the MAD. (b) Compute the tracking signal. (c) On the basis of your calculations, is the judgmental system performing satisfactorily?
[Ans. (a) 570 (b) 0.53 (c) yes]
REFERENCES
1. Joseph, G. Monks, Theory and Problems of Operations Management, Tata McGraw-Hill Publishing Company Limited, 2nd Edition, 2004.
2. Joseph, G. Monks, Operations Management, McGraw-Hill International Edition, 3rd Edition.
3. S. Anil Kumar, N. Suresh, Production and Operations Management, New Age International (P) Limited Publishers, 2nd Edition, 2008.
6.1 INTRODUCTION
Product design is the mother of all operations processes in an organisation. The processes for manufacture, the planning of production, the processes and checks for quality depend upon the nature of the product. One may say that it all starts with the design of the product. Even the logistics or plain shipment of the product depends upon how or what the product has been designed for.
Design gives the blueprint. When the design engineer keys in the computer aided design or when a product design artist draws lines on a sheet of paper, it starts a train of activities.
6.2 PURPOSE OF A PRODUCT DESIGN
Is product design a creative designer’s fancy? In popular perception, the term designer conjures up images of a maverick yet highly creative artist who in his fits of imagination comes up with a hitherto not seen product. What is design without creativity in it? Indeed, designs are ‘creative’ in nature and they should be so. However, in an organisational context, the design should serve the organisational objectives while being creative. Since an organisation has a purpose, the product design should help to serve that larger purpose.
Design starts with conceptualisation which has to have a basis. Providing value to the customer, the return on investment to the company and the competitiveness of the company should form the basis of the product design effort. What separates a product designer from a freelance artist is the former’s orientation towards these organisational objectives.
A product’s design has tremendours impact on what materials and components would be used, which suppliers will be included, what machines or what type of processes will be used to manufacture it, where it will be stored, how it will be transported. Since a customer does not necessarily imply an already tied-up customer, but also a potential one, what and how will the general yet target customer community be informed depends upon what the design of the product is. For instance, a simple