(6) Delicious Sandwich is expecting that the demand per hour will be around 190
ID: 460546 • Letter: #
Question
(6) Delicious Sandwich is expecting that the demand per hour will be around 190 customers. In response to this, they have decided to run 4 cashiers to take and complete orders. Each cashier can handle about 50 customers an hour (yes…they are efficient cashiers!). Based on the analysis given below, what would you recommend for the manager of Delicious Sandwich? Your response will be graded on thoroughness.
Parameter
Value
Parameter
Value
Minutes
Seconds
M/M/s
Arrival rate (lambda)
190
Average server utilization
0.95
Service rate (mu)
50
Average number in the queue (Lq)
16.93695
Number of servers
4
Average number in the system (Ls)
20.73695
Service cost $/time
10
Average time in the queue (Wq)
0.089142
5.348512
320.9107
Waiting cost $/time
12
Average time in the system (Ws)
0.109142
7
392.9107
Cost (Labor + # waiting * wait cost)
243.2435
Cost (Labor + # in system * wait cost)
288.8434
Number of servers
Total Cost Based on Waiting
Total Cost Based on System
1 (insufficient capacity)
n.a.
n.a.
2 (insufficient capacity)
n.a.
n.a.
3 (insufficient capacity)
n.a.
n.a.
4
243.2435
288.8434
5
68.22457
113.8246
6
64.93918
110.5392
7
71.55172
117.1517
8
80.49597
126.096
k
Prob (num in sys = k)
Prob (num in sys <=k)
Prob (num in sys >k)
0
0.00513
0.00513
0.99487
1
0.019495
0.024625
0.975375
2
0.03704
0.061664
0.938336
3
0.046917
0.108581
0.891419
4
0.044571
0.153152
0.846848
5
0.042342
0.195494
0.804506
6
0.040225
0.23572
0.76428
7
0.038214
0.273934
0.726066
8
0.036303
0.310237
0.689763
9
0.034488
0.344725
0.655275
10
0.032764
0.377489
0.622511
11
0.031126
0.408614
0.591386
12
0.029569
0.438184
0.561816
13
0.028091
0.466275
0.533726
14
0.026686
0.492961
0.507039
15
0.025352
0.517313
0.481687
16
0.024084
0.542397
0.457603
17
0.02288
0.565277
0.434723
18
0.021736
0.587013
0.412987
19
0.020649
0.607663
0.392337
20
0.019617
0.62728
0.37272
21
0.018636
0.645916
0.354084
22
0.017704
0.66362
0.33638
23
0.016819
0.680439
0.319561
24
0.015978
0.696417
0.303583
25
0.015179
0.711596
0.288404
26
0.01442
0.726016
0.273984
27
0.013699
0.739716
0.260285
28
0.013014
0.75273
0.24727
29
0.012364
0.765093
0.234907
30
0.011745
0.776839
0.223162
(6) Delicious Sandwich is expecting that the demand per hour will be around 190 customers. In response to this, they have decided to run 4 cashiers to take and complete orders. Each cashier can handle about 50 customers an hour (yes…they are efficient cashiers!). Based on the analysis given below, what would you recommend for the manager of Delicious Sandwich? Your response will be graded on thoroughness.
Parameter
Value
Parameter
Value
Minutes
Seconds
M/M/s
Arrival rate (lambda)
190
Average server utilization
0.95
Service rate (mu)
50
Average number in the queue (Lq)
16.93695
Number of servers
4
Average number in the system (Ls)
20.73695
Service cost $/time
10
Average time in the queue (Wq)
0.089142
5.348512
320.9107
Waiting cost $/time
12
Average time in the system (Ws)
0.109142
7
392.9107
Cost (Labor + # waiting * wait cost)
243.2435
Cost (Labor + # in system * wait cost)
288.8434
Number of servers
Total Cost Based on Waiting
Total Cost Based on System
1 (insufficient capacity)
n.a.
n.a.
2 (insufficient capacity)
n.a.
n.a.
3 (insufficient capacity)
n.a.
n.a.
4
243.2435
288.8434
5
68.22457
113.8246
6
64.93918
110.5392
7
71.55172
117.1517
8
80.49597
126.096
k
Prob (num in sys = k)
Prob (num in sys <=k)
Prob (num in sys >k)
0
0.00513
0.00513
0.99487
1
0.019495
0.024625
0.975375
2
0.03704
0.061664
0.938336
3
0.046917
0.108581
0.891419
4
0.044571
0.153152
0.846848
5
0.042342
0.195494
0.804506
6
0.040225
0.23572
0.76428
7
0.038214
0.273934
0.726066
8
0.036303
0.310237
0.689763
9
0.034488
0.344725
0.655275
10
0.032764
0.377489
0.622511
11
0.031126
0.408614
0.591386
12
0.029569
0.438184
0.561816
13
0.028091
0.466275
0.533726
14
0.026686
0.492961
0.507039
15
0.025352
0.517313
0.481687
16
0.024084
0.542397
0.457603
17
0.02288
0.565277
0.434723
18
0.021736
0.587013
0.412987
19
0.020649
0.607663
0.392337
20
0.019617
0.62728
0.37272
21
0.018636
0.645916
0.354084
22
0.017704
0.66362
0.33638
23
0.016819
0.680439
0.319561
24
0.015978
0.696417
0.303583
25
0.015179
0.711596
0.288404
26
0.01442
0.726016
0.273984
27
0.013699
0.739716
0.260285
28
0.013014
0.75273
0.24727
29
0.012364
0.765093
0.234907
30
0.011745
0.776839
0.223162
Explanation / Answer
Based on the data presented what i forsee and analyze for the manager of Delicious Sandwitch is to use the workforce to the fullest and see that the workforce is used efficiently for fulfilling the customer needs here he has several options where he can allign shift one in the morning shift and one in the evening shift on the weekend he can have the 2 shifts with extended workhours for the second shift as weekend will always have high penetration/walkin of the customers. As the manager he has to organise a meeting with his staff where he will brief the staff about the challenges they are facing in addressing the customer issues. Its also advised for the Managers to see that the staff is not burdened and needs to take care of them as this will surely see that their will be complaints those needs to be addressed maturedly.
Since the demand per hour of the customers is 190 customers. Suppose they work for 9 hrs the walkin of the customers would be 1,710 customers 1710/4 this will 450 Customers per cashier in a day. Assuming 9 hrs shift.
4 Cashiers to take complete orders. Each cashier can handle 50 customers/hour. aprox 450 Customers per cashier.
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