Delicious Sandwich is expecting that the demand per hour will be around 190 customers. In response to
Question:
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 |
Management Accounting Information for Decision-Making and Strategy Execution
ISBN: 978-0137024971
6th Edition
Authors: Anthony A. Atkinson, Robert S. Kaplan, Ella Mae Matsumura, S. Mark Young