ETF5650: Business Optimisation Skills
Assignment 2, 2022
(Queuing theory, business process modelling and simulation)
Instructions
• This is an individual assignment
• Answer all questions and show all workings
• Submit answers to questions 1 and 3 in a docx file and the answer to question 2 in an EXCEL file.
• Submit the .docx file and .xlsx file via “Assignment 2 submission” link in the Moodle site. Submission is not allowed until one week before the deadline.
• Submit both files before 11.55pm, 23 May 2022. Late submission incurs penalties.
• VERY IMPORTANT: Copy and paste the declaration given in page 2 in a text box on a separate sheet in the .xlsx file and sign or print your name with date.
Format of the file for submission in Moodle:
Your surname_initials_(Teaching Associate’s first name).xlsx
E.g. Tan_A_(Heidi).xlsx OR Tan_A_(Chin).xlsx
Upload your .xlsx file to Moodle as follows;
Click on the “Assignment 2 Submission” link and upload your file.
You have to accept the Submission Statement before clicking the Submit button. Once you upload the file, the following message will appear “File uploaded successfully.” To confirm that your upload was successful, click on the “Assignment Submission” uploading link. You can then see the uploaded file name.
The aim of this assignment is to give you more insights on some analytical concepts and for you to get hands on experience in the application of the techniques that fall within the areas examined.
NOTE: You are allowed to submit only once. So, submit only the final version.
Total mark is 50
Signature: Date:
QUESTION 1 [2+2+2+1+3+2+2 = 14 Marks]
Figure 1: Fast shop market operation
(c) How long is a customer at fast shop market expected to wait in the queue before reaching the server?
(d) Determine the probability that the server is idle.
(e) Suppose fast shop market management do not want average number of customers waiting in the queue to be more than 0.5. If the service rate cannot be changed, what is the maximum arrival rate that satisfies this condition?
(e) When answering parts (c)-(e), what assumptions do you make about customer behaviour. Discuss.
(g) Suppose customers arrive now at the rate you determined in part (e). Under these conditions (service rate will be the same as before), how much more time will the server be free over a an 8-hour shift compared to the free time under the current state of operational conditions?
QUESTION 2 [8+2+4+2 = 16 marks]
Inter-arrival time of items for processing by two workers are negative exponentially distributed with mean 6.8 minutes. These items are served by two workers Jenny and Tommy in that order. They perform operations on these items in series as shown in Figure 2.
Figure 2
Jenny services the items according to a normal density function with mean service time 6.2 minutes and standard deviation 1 minute and Tommy services the items according to a normal density function with mean service 5.5 minutes and standard deviation 1 minute.
Set up a spreadsheet model to simulate the above business operation and answer the following.
(a) Simulate 300 arrivals (300 items are placed randomly on the conveyor-belt) assuming start time is zero.
(b) Hence, determine the average time spent in the system.
(c) What percentage of arriving units, on average, have to wait before obtaining service from Tommy?
(d) What percentage of system time will an arriving unit have to wait on average?
NOTE: All answers should change when F9 is pressed. Marks are awarded based on how you model the business operation and do the computations in the EXCEL spreadsheet.
QUESTION 3 [6+(4+10) = 20 marks]
(a) Set up a flow chart for the following fragment of a business process for assessing loan applications.
All loan applications must pass two checks: (i) loan risk assessment check (a financial officer does this) and (ii) property appraisal (a property valuer appraises the property). Loan risk assessment requires a credit history check on the applicant. Once both the loan risk assessment and the property appraisal are completed, a loan officer assess the applicant’s eligibility. If the applicant is eligible for a loan, an acceptance pack is prepared and sent to the applicant. If the applicant is not eligible for a loan, the loan provider informs the applicant in writing. The acceptance pack includes a repayment schedule, which the customer needs to agree upon by sending the signed documents back to the loan provider. The latter then verifies the repayment agreement: if the applicant disagrees with the repayment schedule, the loan provider cancels the application; if the applicant agrees, the loan provider approves the application. In either case, the process completes with the loan provider notifying the applicant of the application status.
(b)
Consider the business process chart shown in Figure 3. The parenthesis gives, for each activity, the expected waiting time and the expected processing time in minutes. Assume that the loop is executed only once (re-work is done only once).
(i) Calculate the average processing time of this business process.
(ii) There are 10 units of resource R1, 1 unit of resource R2 and 10 units of resource R3. Table shows the type of resource that each activity requires.
Activity
Resource
A
R1
B
R2
C
R1
D
R2
E
R3
F
R1
G
R1
H
R3
I
R3
J
R3
K
R1
L
R3
Table 3
If the actual throughput is 6 jobs per hour, what is the business process capacity utilisation?
10%
H (8,7) I (5,20)
J (5,20
B (15,18) D (12,17)
16% K (5,10)
A (20,12) E (5,10) G (5,25)
32%
C (5,30) F (3,12) L (4,10)
Figure 3