CHAPTER 3
Solution
2. HISTORICAL DEMAND
Month / DemandJan / 12
Feb / 11
Mar / 15
Apr / 12
May / 16
Jun / 15
a. Weighted moving average forecast
Weights are .60, .30, .10
WMAFJuly = .60 * 15 +.3 *16 + .10 * 12 = 15
b. 3-period moving average forecast
MAFJuly = (15 + 16 + 12)/3 = 43/3 = 14.33
c. Exponential smoothing forecast α = .20, ESFJune = 13
ESFJuly = .20 * 15 + (1-.20) * 13 = 13.4
d. Simple linear regression
Month / x / y / xy / x2Jan / 1 / 12 / 12 / 1
Feb / 2 / 11 / 22 / 4
Mar / 3 / 15 / 45 / 9
Apr / 4 / 12 / 48 / 16
May / 5 / 16 / 80 / 25
Jun / 6 / 15 / 90 / 36
21 / 81 / 297 / 91
e. Regression forecast x = 7
Y7 = 10.8 + .7714 * 7 = 16.2
4. ZEUS COMPUTER CHIPS
Deseasonalize the data
Year / Quarter / Period (x) / Actual Demand (y) / Average of the same quartereach year / Seasonal Factor / Deseasonalized Demand (Yd) / x2 / x * Yd
2007 / I / 1 / 4800 / 3833.3 / 1.23 / 3902.4 / 1 / 3902.4
II / 2 / 3500 / 2766.7 / 0.89 / 3932.6 / 4 / 7865.2
III / 3 / 4300 / 3500.0 / 1.12 / 3839.3 / 9 / 11517.9
IV / 4 / 3000 / 2366.7 / 0.76 / 3947.4 / 16 / 15789.6
2008 / I / 5 / 3500 / 1.23 / 2845.5 / 25 / 14227.5
II / 6 / 2700 / 0.89 / 3033.7 / 36 / 18202.2
III / 7 / 3500 / 1.12 / 3125.0 / 49 / 21875
IV / 8 / 2400 / 0.76 / 3157.9 / 64 / 25263.2
2009 / I / 9 / 3200 / 1.23 / 2601.6 / 81 / 23414.4
II / 10 / 2100 / 0.89 / 2359.6 / 100 / 23596
III / 11 / 2700 / 1.12 / 2410.7 / 121 / 26517.7
IV / 12 / 1700 / 0.76 / 2236.8 / 144 / 26841.6
78 / 37400 / 12.00 / 37392.5 / 650 / 219013
Calculate the seasonal factors and then determine the regression trend line
Calculate the forecast for 2010
Year / Quarter / Period / Y from Regression Line / Seasonal Factor / Forecast (Y * seasonal factor)2010 / I / 13 / 2023.4 / 1.23 / 2488.78
II / 14 / 1855.3 / 0.89 / 1651.22
III / 15 / 1687.2 / 1.12 / 1889.66
IV / 16 / 1519.1 / 0.76 / 1154.52
5. BI-MONTHLY SALES DATA
a. Plot the data
b. Fit simple linear regression model to the data
Month / x / y / xy / x2January–February / 1 / 109 / 109 / 1
March–April / 2 / 104 / 208 / 4
May–June / 3 / 150 / 450 / 9
July–August / 4 / 170 / 680 / 16
September–October / 5 / 120 / 600 / 25
November–December / 6 / 100 / 600 / 36
January–February / 7 / 115 / 805 / 49
March–April / 8 / 112 / 896 / 64
May–June / 9 / 159 / 1,431 / 81
July–August / 10 / 182 / 1,820 / 100
September–October / 11 / 126 / 1,386 / 121
November–December / 12 / 106 / 1,272 / 144
78 / 1,553 / 10,257 / 650
c. Determine seasonal factors using the regression model
Month / y / Y / Seasonal Factor (yi/Yi) / Average Seasonal FactorJanuary–February / 109 / 123 / 0.89 / 0.89
March–April / 104 / 124 / 0.84 / 0.85
May–June / 150 / 125 / 1.2 / 1.2
July–August / 170 / 127 / 1.34 / 1.36
September–October / 120 / 128 / 0.94 / 0.94
November–December / 100 / 129 / 0.78 / 0.78
January–February / 115 / 130 / 0.88
March–April / 112 / 131 / 0.85
May–June / 159 / 132 / 1.2
July–August / 182 / 133 / 1.37
September–October / 126 / 135 / 0.93
November–December / 106 / 136 / 0.78
d. Prepare the seasonalized forecast for next year
Month / x / Y / Seasonal Factor / Seasonalized ForecastJanuary–February / 13 / 136.85 / 0.89 / 121.8
March–April / 14 / 138 / 0.85 / 117.3
May–June / 15 / 139.15 / 1.2 / 166.98
July–August / 16 / 140.3 / 1.36 / 190.81
September–October / 17 / 141.45 / 0.94 / 132.96
November–December / 18 / 142.6 / 0.78 / 111.23
6. MAVERICK
a.
Month / Demand / Forecast / Error / AbsoluteError
1 / 20
2 / 18
3 / 21
4 / 25 / 20 / 5 / 5
5 / 24 / 21 / 3 / 3
6 / 27 / 23 / 4 / 4
7 / 22 / 25 / -3 / 3
8 / 30 / 24 / 6 / 6
9 / 23 / 26 / -3 / 3
10 / 20 / 25 / -5 / 5
11 / 29 / 24 / 5 / 5
12 / 22 / 24 / -2 / 2
1 / 24
SUM / 10 / 36
MEAN / 1.11 / 4
b.
Month / Demand / Forecast / Error / AbsoluteError
1 / 20
2 / 18
3 / 21
4 / 25 / 20 / 5 / 5
5 / 24 / 20 / 4 / 4
6 / 27 / 23 / 4 / 4
7 / 22 / 25 / -3 / 3
8 / 30 / 25 / 5 / 5
9 / 23 / 26 / -3 / 3
10 / 20 / 25 / -5 / 5
11 / 29 / 27 / 2 / 2
12 / 22 / 23 / -1 / 1
1 / 23
SUM / 8 / 32
MEAN / 0.9 / 3.6
c. The three month weighted moving average performed better than the three month moving average on both measures of forecast error. Sometimes there can be contradictions in these two measures , but in this case the weighted moving average is the best on both measures.
Bias / MAD3-month moving avg. / 1.11 / 4
Weighted 3-mo. MA / 0.9 / 3.6
7. MAVERICK (CONTINUED)
a. .
Month / Demand / Forecast / Error / Absolute / Forecast / Error / Absolute / Forecast / Error / Absolute0.2 / Error / 0.5 / Error / 0.8 / Error
1 / 20
2 / 18
3 / 21
4 / 25 / 20 / 5 / 5 / 20 / 5 / 5 / 20 / 5 / 5
5 / 24 / 21 / 3 / 3 / 22.5 / 1.5 / 1.5 / 24 / 0 / 0
6 / 27 / 21.6 / 5.4 / 5.4 / 23.3 / 3.7 / 3.7 / 24 / 3 / 3
7 / 22 / 22.7 / -0.7 / 0.7 / 25.2 / -3.2 / 3.2 / 26.4 / -4.4 / 4.4
8 / 30 / 22.6 / 7.4 / 7.4 / 23.6 / 6.4 / 6.4 / 22.9 / 7.1 / 7.1
9 / 23 / 24.1 / -1.1 / 1.1 / 26.8 / -3.8 / 3.8 / 28.6 / -5.6 / 5.6
10 / 20 / 23.9 / -3.9 / 3.9 / 24.9 / -4.9 / 4.9 / 24.1 / -4.1 / 4.1
11 / 29 / 23.1 / 5.9 / 5.9 / 22.5 / 6.5 / 6.5 / 20.8 / 8.2 / 8.2
12 / 22 / 24.3 / -2.3 / 2.3 / 25.8 / -3.8 / 3.8 / 27.4 / -5.4 / 5.4
1 / 23.8 / 23.9 / 23.1
SUM / 18.7 / 34.7 / 7.4 / 38.8 / 3.8 / 42.8
MEAN / 2.08 / 3.86 / 0.82 / 4.31 / 0.42 / 4.76
b. The MAD values are very much the same for all three smoothing constants. The bias, however, decreases as the Alfa increases. When compared to the weighted average results from problem 6, the MAD values are all about the same. The bias for the weighted moving average is near the values for the higher smoothing constants. That gives some credibility to the argument of weighting the current information more heavily than old information. However, the lowest MAD was created with the lowest smoothing constant, even though the bias was the highest with that forecast.
11. THANSKAVEL
a. Before the initiatives the average demand per week was 200 units and the standard deviation is 22 units for Eggsbar. This means the distribution over the manufacturing lead time had a mean of 1200 (6*200), a variance of 2904 ((222)*6) and a standard deviation of 53.89 (). After the investments, the mean was 800 (4*200), the variance 1936 (4*484) and the standard deviation 44 ().
b. With the company policy of holding 2.5 standard deviations of safety stock and a standard deviation of 53.89, the company was carrying 135 (53.89 * 2.5) units of safety stock. This amounts to $74.07 (10000/135) per unit. After the investments, the amount of safety stock inventory was reduced to 110 (44*2.5) units or $8148 (74.07*110). The savings, therefore, was $1852 (10000 – 8148).
12. CUMBERLAND
a. Yearly distribution of each product:
Average = 1,200/ year
b. Monthly distribution of all products together:
Average = 500/ month
c. Yearly distribution of all products together:
Average = 6,000/year
14. MACRONALD’S
a.
Forecast / ForecastFamily / Product / Of units / $/unit / Of sales
Burgers / Regular / 1200 / $1.00 / $1,200.00
Super / 2700 / $1.50 / $4,050.00
Super-Duper / 2100 / $1.80 / $3,780.00
Chicken / Regular / 1800 / $2.50 / $4,500.00
Cajun / 2700 / $2.75 / $7,425.00
Hoagies / Italian / 2250 / $3.50 / $7,875.00
French / 1650 / $3.00 / $4,950.00
American / 1350 / $3.25 / $4,387.50
Pizza / Cheese / 750 / $1.75 / $1,312.50
Pepperoni / 1200 / $2.25 / $2,700.00
$42,180.00
Family / Manager’s
Forecast / Rolled Up Forecast / Rolled Down Forecast
Burgers / $10,000.00 / $9,030.00 / $13,915.23
Chicken / $15,000.00 / $11,925.00 / $18,376.43
Hoagies / $20,000.00 / $17,212.50 / $26524.46
Pizza / $5,000.00 / $4,012.50 / $6,183.26
$50,000.00 / $42,180.00 / $65,000.00
$13,915.23=$9,030.00 x ($65,000/$42,180)
Rolled Down ForecastFamily / Product / $Sales / units
Burgers / Regular / $1,849.17 / 1849.17
Super / $6,240.95 / 4160.63
Super-Duper / $5,824.88 / 3236.05
Chicken / Regular / $6,934.5 / 2773.8
Cajun / 11441.9 / 4160.7
Hoagies / Italian / 12135.4 / 3467.25
French / 7627.95 / 2542.65
American / 6761.14 / 2080.35
Pizza / Cheese / 2022.56 / 1155.75
Pepperoni / 4160.7 / 1849.2
$65,000.00
Computing units and then dollars:
Burger Regular 1849.17 units= ($13,915/$9,030) x 1,200 units; sales= 1849.17x$1= $1,849.17
Burger Super 4160.63 units= ($13,915/$9,030) x 2,700 units; sales= 4160.63x$1.5=$6,240.94
Chicken Regular 2773.8 units= ($18,376.43/$11,925) x 1,800 units; sales=2773.8x$2.5=$6,934.50
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