讲解 ETF5650: Business Optimisation Skills Assignment 2, 2024讲解 Python编程

ETF5650: Business Optimisation Skills

Assignment 2, 2024

(Queuing theory, business process modelling and simulation)

Instructions

· This is an individual assignment

· Answer all THREE questions and show all workings

· Submit answers to questions 1 and 2 in a docx file and the answer to question 3 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, 14 May 2024. 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.

· VERY IMPORTANT: You must not use generative artificial intelligence (AI) to generate any materials or content in relation to this assessment task.

Format of the file for submission in Moodle:

Your surname_initials_(ID number).xlsx

E.g. Tan_A_(12345678).xlsx

Upload your .docx file and .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

QUESTION 1 [2+2+2+6+2+(2+2+2)+2 = 22 Marks]

The Colombo Community Hospital's Board of Management is seeking to formulate a comprehensive strategy for a significant expansion of the emergency treatment section. The Board has enlisted the assistance of students enrolled in ETF5650 to analyse historical trends in emergency admission rates and formulate guidelines to determine the optimal number of beds and staffing requirements.

The Chief Hospital Administrator, emphasized the importance of the emergency department to the students of ETF5650 with the following statement:

The responsibility for this assignment was assumed by ETF5650 students, who began examining the patterns of emergency admissions. Their analysis unveiled fluctuations based on the hour of the day and the day of the week, with the highest peak observed between 6 pm and 8 pm on Saturdays. Consequently, the ETF5650 students decided to concentrate on this particular time period.

1.1 Do you concur with this decision? Provide reasoning for your agreement or disagreement.

1.2 The ETF5650 students collected data on emergency admissions that occurred between 6 pm and 7 pm and between 7 pm and 8 pm for all Saturdays over the past 12 months. This allowed them to gather a sample of 104 observations of hourly admission rates during the peak activity period.

The sample data is given in Table 1.

Hourly admission ()	Observed frequency ()	Hourly admission ()	Observed frequency ()
0	0	8	14
1	0	9	13
2	1	10	11
3	4	11	8
4	6	12	5
5	10	13	3
6	13	14	2
7	14

Table 1

Show that the over-all average number of admissions during the peak period on Saturday is 7.8654 per hour. HINT: Suppose number of admissions in an hour is with frequency . Then the mean of the frequency distribution is computed as

1.3 Draw a plot of the frequency distribution given in Table 1.

1.4 Does the sample data resemble a Poisson distribution?

HINT: First, plot the observed frequency distribution (data given in Table 1) and overlay it with the theoretically obtained expected frequency distribution. Then, see if the two plots are similar or not. If they are similar, then the fit is good.

NOTE: How to obtain expected frequency?

Let = number of arrivals within one hour. In this context, probability distribution of is Poisson.

Poisson probability distribution of is given by where is the mean of the Poisson distribution which is assumed 7.8654 (average number of admissions per hour and is given in part 1.2).

Then the expected frequency of is computed as . This gives how many of 104 observations we may expect to have hourly admission at .

1.5 At Colombo Community Hospital, having more than one receiving doctor is not feasible. The standard protocol dictates that upon admission, each patient undergoes examination by the receiving doctor, who then assigns the patient to the suitable facility within the emergency treatment section.

ETF5650 students want to analyse this situation as a single-server queuing process (M/M/1/ ). They know that a service rate is required. Hence, they recorded actual service times on four consecutive Saturdays between 6pm and 8pm. A total of 71 observations was included in the sample.

Assit, a member of the ETF5650 group tasked with analysing the operation at Colombo Community Hospital, raised the question:

"We observed 71 service completions over 8 hours. So, shall we use these 71 service times and compute the service rate as 71/8 = 8.8750 per hour?"

However, the other students in the group did not support this approach. What are your thoughts on this?

1.6 The ETF5650 group calculated the average service time as 4.7578 minutes. They plotted a histogram of the observed service times and noticed that the pattern satisfies the condition required for application of the M/M/1/ queuing system.

(a) What conclusions can be drawn from traffic intensity or server utilisation factor of this queuing system?

(b) What is the expected number of patients in the system?

1.7 Do you agree with ETF5650 students that the given situation may be assumed as an M/M/1/ queuing system?

QUESTION 2 [3+(2+6+2) = 13 marks]

Consider the business process chart shown in Figure 2. The parenthesis gives, for each activity, the expected waiting time and the expected processing time in minutes in that order. Assume that the loop may be repeated only once if needed.

(a) Calculate the average cycle time of this business process.

(b) There are 10 units of resource R1, 12 units of resource R2 and 12 units of resource R3. Table 2 shows the type of resource that each activity requires.