Problem 3-14 A tourist center is open on weekends (Friday, Saturday, and Sunday)
ID: 396088 • Letter: P
Question
Problem 3-14
A tourist center is open on weekends (Friday, Saturday, and Sunday). The owner-manager hopes to improve scheduling of part-time employees by determining seasonal relatives for each of these days. Data on recent traffic at the center have been tabulated and are shown in the following table:
a. Develop seasonal relatives for the shop using the centered moving average method. (Round your intermediate calculations and final answers to 2 decimal places.)
b. Develop seasonal relatives for the shop using the SA method. (Round your intermediate calculations and final answers to 4 decimal places.)
Explanation / Answer
Part a:
Seasonal Indices by centered moving average method:
Day
Demand
Centered Moving Averages
Unadjusted Seasonal Factor
Friday
137
Saturday
247
182.00
1.3571
Sunday
157
183.67
0.8548
Friday
147
183.67
0.8004
Saturday
247
183.67
1.3448
Sunday
157
185.33
0.8471
Friday
147
188.67
0.7792
Saturday
257
190.33
1.3503
Sunday
167
190.33
0.8774
Friday
147
190.33
0.7723
Saturday
257
191.17
1.3444
Sunday
167
194.50
0.8586
Friday
152
197.00
0.7716
Saturday
272
197.83
1.3749
Sunday
167
198.67
0.8406
Friday
157
200.33
0.7837
Saturday
272
Sunday
177
CMA for week 1, Saturday = average of (average of (137, 247, 157) and average of (247, 157, 147))
Unadjusted Seasonal factor week 1, Saturday = actual demand/CMA = 247/182 = 1.3571
Adjusted seasonal indices are calculated as follows:
Day/Week
1
2
3
4
5
6
Average
Seasonal Indices (Xbar)
Friday
0.8004
0.7792
0.7723
0.7716
0.7837
0.7814
0.7837
Saturday
1.3571
1.3448
1.3503
1.3444
1.3749
1.3543
1.3582
Sunday
0.8548
0.8471
0.8774
0.8586
0.8406
0.8557
0.8582
Overall average
0.9971
Seasonal Index of Friday = Average of unadjusted seasonal factor for Fridays/overall average.
ANS a:
Day
Seasonal Indices (Xbar)
Friday
0.7837
Saturday
1.3582
Sunday
0.8582
Part b:
Seasonal Index by Seasonal Average method:
Day/Week
1
2
3
4
5
6
Average
Seasonal Indices (Xbar)
Friday
137
147
147
147
152
157
147.8333
0.7756
Saturday
247
247
257
257
272
272
258.6667
1.3570
Sunday
157
157
167
167
167
177
165.3333
0.8674
Overall average
190.6111
ANS b:
Day
Seasonal Indices (SA)
Friday
0.7756
Saturday
1.3570
Sunday
0.8674
Day
Demand
Centered Moving Averages
Unadjusted Seasonal Factor
Friday
137
Saturday
247
182.00
1.3571
Sunday
157
183.67
0.8548
Friday
147
183.67
0.8004
Saturday
247
183.67
1.3448
Sunday
157
185.33
0.8471
Friday
147
188.67
0.7792
Saturday
257
190.33
1.3503
Sunday
167
190.33
0.8774
Friday
147
190.33
0.7723
Saturday
257
191.17
1.3444
Sunday
167
194.50
0.8586
Friday
152
197.00
0.7716
Saturday
272
197.83
1.3749
Sunday
167
198.67
0.8406
Friday
157
200.33
0.7837
Saturday
272
Sunday
177
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