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ETF5650: Business Optimisation Skills
创建日期：2024-08-17 17:14:44
标签： ETF5650
Business Optimisation Skills

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ETF5650: Business Optimisation Skills

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?

(c) What is the expected time a patient spends waiting for the service? 

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.

Activity

Resource

A

R1

B

R2

C

R1

D

R2

E

R3

F

R1

G

R1

H

R3

I

R3

J

R3

K

R1

Table 2

(i) If 100 jobs go through the process, what is the average time they spend at the work station where activity B is carried out?

(ii)  What is the bottleneck of this business process?

(iii) If you are asked serve in one of the three resource groups, which one would you choose? Give reasons for your choice.

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MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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