CHAPTER 3
Solution
2. HISTORICAL DEMAND
Month
Demand
Jan
Feb
Mar
Apr
May
Jun
a.
12
11
15
12
16
15
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
x2
Jan
Feb
Mar
Apr
May
Jun
1
2
3
4
5
6
21
12
11
15
12
16
15
81
12
22
45
48
80
90
297
1
4
9
16
25
36
91
3-1
e.
Regression forecast x = 7
Y7 = 10.8 + .7714 * 7 = 16.2
4. ZEUS COMPUTER CHIPS
Deseasonalize the data
Year
2007
2008
2009
Quarter
I
II
III
IV
I
II
III
IV
I
II
III
IV
Actual
Period Demand
(x)
(y)
1
2
3
4
5
6
7
8
9
10
11
12
78
4800
3500
4300
3000
3500
2700
3500
2400
3200
2100
2700
1700
37400
Average
of the
same
quarter
each year
3833.3
2766.7
3500.0
2366.7
Seasonal
Factor
Deseasonalized
Demand (Yd)
1.23
0.89
1.12
0.76
1.23
0.89
1.12
0.76
1.23
0.89
1.12
0.76
12.00
3902.4
3932.6
3839.3
3947.4
2845.5
3033.7
3125.0
3157.9
2601.6
2359.6
2410.7
2236.8
37392.5
Calculate the seasonal factors and then determine the regression trend line
Calculate the forecast for 2010
3-2
x2
x * Yd
1
4
9
16
25
36
49
64
81
100
121
144
650
3902.4
7865.2
11517.9
15789.6
14227.5
18202.2
21875
25263.2
23414.4
23596
26517.7
26841.6
219013
Year
Quarter
2010 I
II
III
IV
Period
Y from
Regression
Line
13
14
15
16
2023.4
1855.3
1687.2
1519.1
Seasonal
Factor
Forecast (Y *
seasonal factor)
1.23
0.89
1.12
0.76
2488.78
1651.22
1889.66
1154.52
5. BI-MONTHLY SALES DATA
a. Plot the data
b. Fit simple linear regression model to the data
Month
x
January–February
March–April
May–June
July–August
September–October
November–December
January–February
March–April
May–June
July–August
September–October
November–December
y
1
2
3
4
5
6
7
8
9
10
11
12
78
3-3
109
104
150
170
120
100
115
112
159
182
126
106
1,553
xy
109
208
450
680
600
600
805
896
1,431
1,820
1,386
1,272
10,257
x2
1
4
9
16
25
36
49
64
81
100
121
144
650
c. Determine seasonal factors using the regression model
Month
y
January–February
March–April
May–June
July–August
September–October
November–December
January–February
March–April
May–June
July–August
September–October
November–December
Y
109
104
150
170
120
100
115
112
159
182
126
106
123
124
125
127
128
129
130
131
132
133
135
136
Seasonal Average
Factor Seasonal
(yi/Yi)
Factor
0.89
0.84
1.2
1.34
0.94
0.78
0.88
0.85
1.2
1.37
0.93
0.78
0.89
0.85
1.2
1.36
0.94
0.78
d. Prepare the seasonalized forecast for next year
Month
January–February
March–April
May–June
July–August
September–October
November–December
x
Y
13
14
15
16
17
18
136.85
138
139.15
140.3
141.45
142.6
3-4
Seasonal
Factor
0.89
0.85
1.2
1.36
0.94
0.78
Seasonalized
Forecast
121.8
117.3
166.98
190.81
132.96
111.23
6. MAVERICK
a.
Month
1
2
3
4
5
6
7
8
9
10
11
12
1
Demand Forecast
20
18
21
25
24
27
22
30
23
20
29
22
20
21
23
25
24
26
25
24
24
24
SUM
MEAN
Error
Absolute
Error
5
3
4
-3
6
-3
-5
5
-2
5
3
4
3
6
3
5
5
2
10
1.11
36
4
b.
Month
1
2
3
4
5
6
7
8
9
10
11
12
1
Demand Forecast
20
18
21
25
24
27
22
30
23
20
29
22
20
20
23
25
25
26
25
27
23
23
SUM
MEAN
3-5
Error
Absolute
Error
5
4
4
-3
5
-3
-5
2
-1
5
4
4
3
5
3
5
2
1
8
0.9
32
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
MAD
3-month moving
avg.
1.11
4
Weighted 3-mo.
MA
0.9
3.6
7. MAVERICK (CONTINUED)
a. .
Month
1
2
3
4
5
6
7
8
9
10
11
12
1
SUM
MEAN
Demand Forecast Error Absolute Forecast Error Absolute Forecast Error Absolute
0.2
Error
0.5
Error
0.8
Error
20
18
21
25
20
5
5
20
5
5
20
5
5
24
21
3
3
22.5
1.5
1.5
24
0
0
27
21.6
5.4
5.4
23.3
3.7
3.7
24
3
3
22
22.7
-0.7
0.7
25.2 -3.2
3.2
26.4 -4.4
4.4
30
22.6
7.4
7.4
23.6
6.4
6.4
22.9
7.1
7.1
23
24.1
-1.1
1.1
26.8 -3.8
3.8
28.6 -5.6
5.6
20
23.9
-3.9
3.9
24.9 -4.9
4.9
24.1 -4.1
4.1
29
23.1
5.9
5.9
22.5
6.5
6.5
20.8
8.2
8.2
22
24.3
-2.3
2.3
25.8 -3.8
3.8
27.4 -5.4
5.4
23.8
23.9
23.1
18.7
2.08
34.7
3.86
7.4
0.82
3-6
38.8
4.31
3.8
0.42
42.8
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
  12  10 2  34.64
b. Monthly distribution of all products together:
Average = 500/ month
  5  10 2  22.36
c. Yearly distribution of all products together:
Average = 6,000/year
  5  12  10 2  77.46
3-7
14. MACRONALD’S
a.
Family
Burgers
Chicken
Hoagies
Pizza
Family
Burgers
Chicken
Hoagies
Pizza
Product
Regular
Super
Super-Duper
Regular
Cajun
Italian
French
American
Cheese
Pepperoni
Forecast
Forecast
Of units
$/unit Of sales
1200
$1.00
$1,200.00
2700
$1.50
$4,050.00
2100
$1.80
$3,780.00
1800
$2.50
$4,500.00
2700
$2.75
$7,425.00
2250
$3.50
$7,875.00
1650
$3.00
$4,950.00
1350
$3.25
$4,387.50
750
$1.75
$1,312.50
1200
$2.25
$2,700.00
$42,180.00
Manager’s
Rolled Up Forecast Rolled Down Forecast
Forecast
$10,000.00
$9,030.00
$13,915.23
$15,000.00
$11,925.00
$18,376.43
$20,000.00
$17,212.50
$26524.46
$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)
Family
Burgers
Chicken
Hoagies
Pizza
Rolled Down Forecast
Product
$Sales
units
$1,849.17
Regular
$6,240.95
Super
$5,824.88
Super-Duper
$6,934.5
Regular
11441.9
Cajun
12135.4
Italian
7627.95
French
6761.14
American
2022.56
Cheese
4160.7
Pepperoni
$65,000.00
1849.17
4160.63
3236.05
2773.8
4160.7
3467.25
2542.65
2080.35
1155.75
1849.2
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
3-8