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University_of_California_Los_Angeles_-_BUS_523_An_Introduction_to_Management_Science.pdf
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Page 79
Chapter 14
CP - 76
The complete goal programming model is
Min
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
1
1
1
2
2
3
2
4
3
5
3
6
3
7
3
8
P
d
P
d
P
d
P
d
P
d
P
d
P
d
P
d
−
−
−
−
−
+
−
+
+
+
+
+
+
+
+
s.t.
x
21
–
s
21
–
d
1
+
+
d
1
–
= 800
x
22
+
s
21
–
s
22
–
d
2
+
+
d
2
–
= 1200
x
11
–
s
11
–
d
3
+
+
d
3
–
= 600
x
12
+
s
11
–
s
12
–
d
4
+
+
d
4
–
= 600
4
x
11
+6
x
21
–
d
5
+
+
d
5
–
= 5300
4
x
11
+6
x
21
–
d
6
+
+
d
6
–
= 7300
–4
x
11
+4
x
12
–6
x
21
+6
x
22
–
d
7
+
+
d
7
–
= – 1000
–4
x
11
+4
x
12
–6
x
21
+6
x
22
–
d
8
+
+
d
8
–
= 1000
all variables
≥
0
Information Needed for the Managerial Report
1.
March
April
EZ-190
775
425
EZ-250
800
1200
2.
No changes since the ending inventories for the optimal production schedule are as follows:
March
April
EZ-190
175
0
EZ-250
0
0
3.
The following constraints must be added to the model:
April ending inventory:
s
12
≥
100,
s
22
≥
100
Maximum storage of 300 units in each month:
s
11
≤
300,
s
12
≤
300,
s
21
≤
300,
s
22
≤
300
The new optimal production schedule is as follows:
March
April
EZ-190
900
400
EZ-250
800
1300
The corresponding ending inventories are:
March
April
EZ-190
300
100
EZ-250
0
100
Page 80
Solutions to Case Problems
CP - 77
4.
The new optimal production schedule is:
March
April
EZ-190
625
275
EZ-250
800
1200
The corresponding ending inventories are:
March
April
EZ-190
25
0
EZ-250
0
0
Page 81
CP - 78
Chapter 15
Forecasting
Case Problem 1:
Forecasting Sales
1.
Month 1 corresponds to January for year 1, month 2 corresponds to February for year 1, and so on. A
graph of the time series is shown below:
50
100
150
200
250
300
0
5
10
15
20
25
30
35
40
Month
Sales
2.
Analysis of seasonality:
Month
Seasonal-Irregular
Component Values
Seasonal Index
January
1.445
1.441
1.44
February
1.301
1.297
1.30
March
1.344
1.343
1.34
April
1.047
1.034
1.04
May
1.044
1.054
1.05
June
.779
.801
.80
July
.882
.834
.83
August
.857
.848
.85
September
.618
.638
.63
October
.725
.675
.70
November
.843
.862
.85
December
1.137
1.180
1.16
Page 82
Chapter 15
CP - 79
The deseasonalized time series is shown below:
t
Deseasonalized Sales
t
Deseasonalized Sales
1
168.06
19
189.16
2
180.77
20
189.41
3
173.13
21
193.65
4
171.15
22
185.71
5
175.24
23
196.47
6
175.00
24
198.28
7
174.70
25
195.83
8
178.82
26
196.15
9
174.60
27
197.76
10
185.71
28
197.12
11
178.82
29
200.00
12
177.59
30
200.00
13
182.64
31
200.00
14
183.08
32
204.71
15
184.33
33
200.00
16
185.58
34
211.43
17
183.81
35
203.53
18
186.25
36
202.59
The trend line fitted to the deseasonalized time series is
T
t
=
169.499 + 1.02
t
3.
Sales forecasts
Forecast for Year 4
Using
T
t
=
169.499 + 1.02
t
Month
Trend
Forecast
Seasonal
Index
Monthly
Forecast
January
207.239
1.44
298.424
February
208.259
1.30
270.737
March
209.279
1.34
280.434
April
210.299
1.04
218.711
May
211.319
1.05
221.885
June
212.339
.80
169.871
July
213.359
.83
177.088
August
214.379
.85
182.222
September
215.399
.63
135.701
October
216.419
.70
151.493
November
217.439
.85
184.823
December
218.459
1.16
253.194
4.
Forecast error = $295,000 - $298,424 = -$3,424
The forecast we developed over predicted by $3,424; this represents a very small error.
5.
The analysis can be easily updated each month, especially if a computer software package is
used to perform the analysis.
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