Management of the first Syracuse bank is concerned about a less of customers at
ID: 2464116 • Letter: M
Question
Management of the first Syracuse bank is concerned about a less of customers at its main office downtown. One solution that has been proposed is to add one or more drive through teller stations to make it easier for customers in cars to obtain quick service without parking. Chris Carlson, the bank president, thinks the bank should only risk the cost of installing one drive through, he is informed by his staff that the cost (amortized over 20 year period) of bluing a drive through is S12.000 per year. It also costs $16,000 per year in wages and benefits to staff each new teller window. The director of management analysis Beth Shader, believes that the following two factors encourage the immediate construction of two drive through stations however. According to a recent article in banking research magazine, customers Who wait m long Ines for dove-through teller service will cost banks an average of $1 per minute in loss of goodwill. Also, adding a second drive through will cost an additional $16,000 m staffing but amortized construction costs can be out to a total of $20.00 installed together instead o' one at a time, to complete her analysis. Shader collected one month's arrival and service rates at a competing downtown banks drive through stations. This data are shown as observation analyses 1 and 2 in the following tables. Simulate a one hour time period from 1 pm to 2pm for a single teller drive through Simulate a 1 hour time period from 1 pm to 2pm. for a single line of people waiting for next available teller in a two-teller system. Conduct a cost analysis of the two options. Assume that the bank is open 7 hours per day and 200 days per year Observation analysis 1: interarrival times for 1.000 observations Observation analysis 2: customer service time for 1.000 customersExplanation / Answer
a) Simulation of a one-teller drive-through:
Arrivals
Service
Random Number
Time till next arrival
Arrive at time
Random Number
Time need for service
Begin time
End time
Wait time
52
3
1:03
60
3
1:03
1:06
0:00
37
2
1:05
60
3
1:06
1:09
0:01
82
4
1:09
80
5
1:09
1:14
0:00
69
3
1:12
53
3
1:14
1:17
0:02
98
5
1:17
69
4
1:17
1:21
0:00
96
5
1:22
37
3
1:22
1:25
0:00
33
2
1:24
6
1
1:25
1:26
0:01
50
3
1:27
63
4
1:27
1:31
0:00
88
4
1:31
57
3
1:31
1:34
0:00
90
4
1:35
2
1
1:35
1:36
0:00
50
3
1:38
94
6
1:38
1:44
0:00
27
2
1:40
52
3
1:44
1:47
0:04
45
2
1:42
69
4
1:47
1:51
0:05
81
4
1:46
33
3
1:51
1:54
0:05
66
3
1:49
32
3
1:54
1:57
0:05
74
3
1:52
30
3
1:57
2:00
0:05
30
2
1:54
48
3
2:00
2:03
0:06
59
3
1:57
88
5
2:03
2:08
0:06
67
3
2:00
Total wait time
0:40
Total wait time = 40 minutes
Waiting cost = (40 minutes * 7 hours * 200 days) * $1 per minute = $56,000
(b) Simulation of two one-teller drive-through
Arrivals
Service
Teller 1
Teller 1
Random Number
Time till next arrival
Arrive at time
Random Number
Time need for service
Begin time
End time
Begin time
End time
Wait time
52
3
1:03
60
3
1:03
1:06
0:00
37
2
1:05
60
3
1:05
1:08
0:00
82
4
1:09
80
5
1:09
1:14
0:00
69
3
1:12
53
3
1:12
1:15
0:00
98
5
1:17
69
4
1:17
1:21
0:00
96
5
1:22
37
3
1:22
1:25
0:00
33
2
1:24
6
1
1:24
1:25
0:00
50
3
1:27
63
4
1:27
1:31
0:00
88
4
1:31
57
3
1:31
1:34
0:00
90
4
1:35
2
1
1:35
1:36
0:00
50
3
1:38
94
6
1:38
1:44
0:00
27
2
1:40
52
3
1:40
1:43
0:00
45
2
1:42
69
4
1:43
1:47
0:01
81
4
1:46
33
3
1:46
1:49
0:00
66
3
1:49
32
3
1:49
1:52
0:00
74
3
1:52
30
3
1:52
1:55
0:00
30
2
1:54
48
3
1:54
1:57
0:00
59
3
1:57
88
5
1:57
2:02
0:00
67
3
2:00
Total wait time
0:01
Total wait time = 1 minute
Waiting cost = (1 minute * 7 hours * 200 days) * $1 per minute = $1,400
(c)
Total cost per year = Waiting cost + Amortization of drive through + Teller cost
Cost for single one-teller drive-through: = $56,000.00 + $12,000.00 + $16,000.00 = $84,000.00
Cost for two one-teller drive-throughs = $1,400.00 + $20,000.00 +$32,000.00 = $53,400.00
Cost savings achieved by using two booths:
$84,000.00 - $53,400.00 = $30,600.00
Arrivals
Service
Random Number
Time till next arrival
Arrive at time
Random Number
Time need for service
Begin time
End time
Wait time
52
3
1:03
60
3
1:03
1:06
0:00
37
2
1:05
60
3
1:06
1:09
0:01
82
4
1:09
80
5
1:09
1:14
0:00
69
3
1:12
53
3
1:14
1:17
0:02
98
5
1:17
69
4
1:17
1:21
0:00
96
5
1:22
37
3
1:22
1:25
0:00
33
2
1:24
6
1
1:25
1:26
0:01
50
3
1:27
63
4
1:27
1:31
0:00
88
4
1:31
57
3
1:31
1:34
0:00
90
4
1:35
2
1
1:35
1:36
0:00
50
3
1:38
94
6
1:38
1:44
0:00
27
2
1:40
52
3
1:44
1:47
0:04
45
2
1:42
69
4
1:47
1:51
0:05
81
4
1:46
33
3
1:51
1:54
0:05
66
3
1:49
32
3
1:54
1:57
0:05
74
3
1:52
30
3
1:57
2:00
0:05
30
2
1:54
48
3
2:00
2:03
0:06
59
3
1:57
88
5
2:03
2:08
0:06
67
3
2:00
Total wait time
0:40
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