quantitative bus week 6

Case Analysis #3

1. Eugene is a business analyst at Burger King. He was assigned a task where he needs to

analyze data on consumer arrivals and concluded that the arrival rate is 15 customers per hour.

He also found out that the cashier can process an average of 18 customer orders per hour.

a. Calculate 𝜆 and 𝜇 per 10 minutes period.

b. Plug the value of 𝜆 and 𝜇 into the arrival rate and service rate cell of Case_Data.xlsm file,

and calculate the value of 𝑃0, 𝐿𝑞 , 𝐿, 𝑊𝑞 , 𝑊, 𝑃𝑤 . And create a column (name it ‘Baseline’) in a

new tab (name it ‘scenario’), showing the value of 𝑃0, 𝐿𝑞 , 𝐿, 𝑊𝑞 , 𝑊, 𝑃𝑤. Interpret each value

using at least 20 words.

c. Suppose the service rate increases from its original value (value of 𝜇 in part A) to 𝜇=4, but the

arrival rate stays the same as in part a. Calculate the value of 𝑃0, 𝐿𝑞 , 𝐿, 𝑊𝑞 , 𝑊, 𝑃𝑤 based on the

original value of 𝜆 and the updated values of 𝜇. Create a column (name it ‘Scenario 1’) in a

scenario tab, showing the updated value of 𝑃0, 𝐿𝑞 , 𝐿, 𝑊𝑞 , 𝑊, 𝑃𝑤 .

d. Suppose the arrival rate increases from its original value (value of 𝜆 in part A) to 𝜆 =2.8, but

the service rate stays the same as in part a. Calculate the value of 𝑃0, 𝐿𝑞 , 𝐿, 𝑊𝑞 , 𝑊, 𝑃𝑤 based on

the updated values of 𝜆 and the original value of 𝜇. Create a column (name it ‘Scenario 2’) in a

scenario tab, showing the updated value of 𝑃0, 𝐿𝑞 , 𝐿, 𝑊𝑞 , 𝑊, 𝑃𝑤 .

e. Now you have three columns in the scenario tab. Compare the values of 𝑃0, 𝐿𝑞 , 𝐿, 𝑊𝑞 , 𝑊, 𝑃𝑤

across Baseline, Scenario 1(‘Service rate increase’ option), and Scenario 2(‘Arrival Rate increase’

option), and discuss how the change in service rate or arrival rate would affect the following

based on the results from part b-d using at least 200 words (This is an essay question, but the

answer must be based on the results to receive full credits):

 Probability that no customers are in the system, P0

 Average number of customers waiting in line, Lq

 Average number of customers in the system, L

 Average time a customer spends waiting in line, Wq

 Average time a customer spends in the system, W

 Probability an arriving customer has to wait, Pw

f. This is an open-ended question, and there is no definite answer. “Waiting” is a core concept of

the “queueing model”. What is your biblical perspectives on this core concept? Explain this by

quoting at least three bible verses. (Minimum words requirement: 100 words)