OPR371S/001/0/2021
Tutorial Letter 001/0/2021
Operational Research III
OPR371S
Year module
Department of Mechanical and Industrial
Engineering
This tutorial letter contains important information
about your module.
BARCODE
CONTENTS
Page
1
INTRODUCTION .......................................................................................................................... 3
2
PURPOSE AND OUTCOMES ...................................................................................................... 4
2.1
Purpose ........................................................................................................................................ 4
2.2
Outcomes ..................................................................................................................................... 4
3
LECTURER(S) AND CONTACT DETAILS................................................................................... 4
3.1
Lecturer(s) .................................................................................................................................... 4
3.2
Department ................................................................................................................................... 5
3.3
University ...................................................................................................................................... 5
4
RESOURCES ............................................................................................................................... 6
4.1
Prescribed book(s) ........................................................................................................................ 6
4.2
Recommended book(s) ................................................................................................................. 6
4.3
Electronic reserves (e-reserves) ................................................................................................... 6
4.4
Library services and resources ..................................................................................................... 6
5
STUDENT SUPPORT SERVICES ................................................................................................ 7
6
STUDY PLAN ............................................................................................................................... 8
7
PRACTICAL WORK ..................................................................................................................... 9
8
ASSESSMENT ............................................................................................................................. 9
8.1
Assessment criteria....................................................................................................................... 9
8.2
Assessment plan .......................................................................................................................... 9
8.3
Assignment numbers .................................................................................................................. 10
8.3.1
General assignment numbers ..................................................................................................... 10
8.3.2
Unique assignment numbers ...................................................................................................... 10
8.4
Assignment due dates ................................................................................................................ 10
8.5
Submission of assignments ........................................................................................................ 10
8.6
The assignments ........................................................................................................................ 12
8.7
Other assessment methods ........................................................................................................ 12
8.8
The examination ......................................................................................................................... 12
9
FREQUENTLY ASKED QUESTIONS ........................................................................................ 12
10
SOURCES CONSULTED ........................................................................................................... 12
11
IN CLOSING ............................................................................................................................... 12
12
ADDENDUM ............................................................................................................................... 13
2
OPR371S/101/0/2021
Dear Student
As part of this tutorial letter, we wish to inform you that Unisa has implemented a transformation
charter based on five pillars and eight dimensions. In response to this charter, we have also
placed curriculum transformation high on the agenda. For your information, curriculum
transformation includes the following pillars: student-centred scholarship, the pedagogical
renewal of teaching and assessment practices, the scholarship of teaching and learning, and
the infusion of African epistemologies and philosophies. These pillars and their principles will be
integrated at both the programme and module levels, as a phased-in approach. You will notice
the implementation thereof in your modules, and we encourage you to fully embrace these
changes during your studies at Unisa.
1
INTRODUCTION
I am pleased to welcome you to this module (OPR371S – Operational Research III) and hope
that you will find it both interesting and rewarding. You will be well on your way to success if you
start studying early in the semester/ year and resolve to attempt both the tutorial questions as
well as assignment(s) properly. The assignment(s) will be graded and will constitute a certain
percentage towards to the final module grade.
You will receive several tutorial letters during the year. A tutorial letter is our way of
communicating with you about teaching, learning and assessment.
Tutorial Letter 001 contains important information about the scheme of work, resources and
assignments for this module. We urge you to read it carefully and to keep it at hand when
working through the study material, preparing the assignment(s), and addressing questions to
your lecturers.
Tutorial Letter 001 as it gives you an idea of generally important information when studying at a
distance and within a College.
In Tutorial Letter 001, you will find the tutorial questions, assignments, and assessment criteria
as well as instructions on the preparation and submission of the assignments. Please note the
following important information: The assessment of this module has changed from a
venue-based examination to continuous assessment. That mean you will not write a sitdown examination at the end of the academic year. You will find the assignments to be
submitted at the end of the document. You must submit each of the assignments
because they are all contributing to your mark to determine whether you will pass the
module. It is also important to note that if you fail the module because you did not submit
all the assignments, you will have to repeat the module as there are no longer a
supplementary examination available.
It will also provide all the information you need about the prescribed study material and other
resources and how to obtain it. Please study this information carefully and make sure that you
obtain the prescribed material as soon as possible.
3
General and administrative information about this module are available in this tutorial letter.
Please study this section of the tutorial letter carefully.
I would like to point out that you must read all the tutorial letters you receive during the semester
immediately and carefully, as they always contain important and, sometimes, urgent
information.
Some of this tutorial matter may not be available when you register. Tutorial matter that is not
available when you register will be posted to you as soon as possible but is also available on
MyUnisa.
I hope that you will enjoy this module and wish you all the best!
2
PURPOSE AND OUTCOMES
2.1
Purpose
Operational Research III is an essential part of industrial engineering and is essential for you,
who will be pursuing a career in engineering after graduation.
2.2
Outcomes
OPR371S seeks to achieve the following purpose and outcomes:
1. The skills to apply the techniques of quantitative analysis in many types of organizational
decision-making situations.
2. Apply workplace improvement techniques and methods to a work situation.
3.
To apply mathematical models to solve complex problems
3
LECTURER(S) AND CONTACT DETAILS
3.1
Lecturer
Your lecturer is
Prof. D.J. Kruger
Tel number:
011 471 2174
Fax number:
011 471 2142
e-mail:
dkruger@unisa.ac.za
Mondays to Fridays from 08h00 to 15h00. Any emails received after this time will be attended
at the next working day. Please adhere to these hours.
Role of the Lecturer:
•
•
•
•
•
4
Provide technical expertise
Teaching and learning
Set assignments.
Set examination papers.
Mark examination papers
OPR371S/101/0/2021
Under no circumstances should the lecturer be contacted about examination dates,
results or receipt of assignment or assignment marks or any other general administrative
matters.
3.2
Department
You may contact the Department of Mechanical and Industrial Engineering by post, e-mail,
telephone, or online through MyUnisa.
Please refer to the booklet: my Studies @ Unisa that you received with your study material.
Departmental Address:
Department of Mechanical and Industrial Engineering
Unisa (Florida Campus)
Private Bag X6
Florida
1710
Phone: 011 471 2963
Use the general E-mail address: dmie@unisa.ac.za
Find our department on the Internet at the online address: http://www.unisa.ac.za
Always state your STUDENT NUMBER and your Module Code OPR371S in all correspondence
and enquiries to ensure prompt and efficient response from us.
Whenever you contact the Department of Mechanical and Industrial Engineering, ensure that
the first thing you mention after greeting is your subject code!
3.3
University
You may contact your lecturers by post, email, telephone or on MyUnisa
Physical address: University of South Africa
C/O Christiaan de Wet and Pioneer Avenues
Florida
Roodepoort
City of Johannesburg
Postal Address:
University of South Africa
Private Bag X6
Florida
5
1710
Fax Number:
012 429 4150 / +27 12 429 4150
Email:
study-info@unisa.ac.za
Online address:
http://my.unisa.ac.za
Always use your student number when you contact the university
4
RESOURCES
4.1
Prescribed book(s)
Title:
Quantitative Analysis for Management
Author:
Render, B, Stair, R.M., Hanna, M.E., and Hale T.S.
Edition:
13th (Global Edition) or latest edition
Publisher:
ISBN:
4.2
Pearson
978-1-292-21765-9
Recommended book(s)
All other Quantitative Analysis Textbooks and articles. Recommended books can be requested
online, via the Library catalogue.
4.3
Electronic reserves (e-reserves)
There are no electronic reserves for this module.
E-reserves can be downloaded from the Library catalogue. More information is available at:
http://libguides.unisa.ac.za/request/request
4.4
Library services and resources
The Unisa Library offers a range of information services and resources:
•
•
•
For detailed Library information, go to https://unisa.ac.za/library
For research support and services (eg personal librarians and literature search services),
go to https://www.unisa.ac.za/sites/corporate/default/Library/Library-services/Researchsupport
The Library has created numerous Library guides: https://libguides.unisa.ac.za
Recommended guides:
•
•
•
•
6
Request and download recommended material:
https://libguides.unisa.ac.za/request
Postgraduate information services:
https://libguides.unisa.ac.za/request/postgrad
Finding and using Library resources and tools:
https://libguides.unisa.ac.za/research-support
Frequently asked questions about the Library:
OPR371S/101/0/2021
•
•
https://libguides.unisa.ac.za/ask
Services to students living with disabilities:
https://libguides.unisa.ac.za/disability
Assistance with technical problems accessing the Unisa Library or resources:
https://libguides.unisa.ac.za/techsupport
You may also send an e-mail to Lib-help@unisa.ac.za (please add your student number in the
subject line).
5
STUDENT SUPPORT SERVICES
The Study @ Unisa brochure is available on MyUnisa: www.unisa.ac.za/brochures/studies
This brochure has all the tips and information you need to succeed at distance learning and,
specifically, at Unisa.
Contact with fellow students
Study Groups
It is advisable to have contact with fellow students. One way to do this is to form study groups.
The addresses of students in your area may be obtained from the following department:
Directorate: Student Administration and Registration
PO Box 392
UNISA
0003
MyUnisa
The MyUnisa platform forms the backbone of communication to you regarding this module. If
you have access to a computer that is linked to the internet, you can quickly access resources
and information at the University. The MyUnisa learning management system is Unisa's online
campus that will help you to communicate with your lecturers, with other students and with the
administrative departments of Unisa – all through the computer and the internet.
To go to the MyUnisa website, start at the main Unisa website, http://www.unisa.ac.za, and then
click on the “Login to MyUnisa” link on the right-hand side of the screen. This should take you to
the MyUnisa website. You can also go there directly by typing in http://my.unisa.ac.za.
Please consult the publication my Studies @ Unisa, which you received with your study material
for more information on MyUnisa.
In line with Open Distance Learning (ODL) principles, Unisa has established relations
with Multipurpose Community Centres across the country in areas identified as remote.
Registered Unisa students across South Africa’s rural areas and townships can access
free internet for academic purpose (Access to MyUnisa, E-mails, Digital Library, Internet
Research and other Computer Based Training modules) courtesy of Unisa. A list of these
Multipurpose Community Centres can be found at the end of this document (the list is
accurate at the time of production of this document) or at the following web address:
7
http://www.unisa.ac.za/contents/facilities/docs/TELECENTRES-WEB%20(3).pdf
Please make full use of these centres.
Discussion Classes
There will be no discussion classes scheduled for this subject. Please contact your lecturer with
problems you may experience with the study material. If the need arises, you can make an
appointment with the lecturer for a personal visit to discuss the problems being experienced.
Tutorials
There will not be prescribed tutorials but the assignment questions as well as problems in the
prescribed textbook and recommended reading can be used as tutorials.
Videoconferencing
Videoconferencing available on request from students, or at the discretion of the lecturer. If you
wish to have, videoconference sessions please propose to the lecturer and readily available
tools from the internet will be used for these.
Important information appears in My Studies @ Unisa brochure
6
STUDY PLAN
The module can largely be broken up into a few subsections and a modular approach is utilised
studying the module. The following lists the subsections:
1.
Introduction to Quantitative Analysis
2.
Probability concepts and Analysis
3.
Fundamentals of Decision Theory
4.
Decision Trees and Utility Theory
5.
Forecasting
6.
Inventory Control Models
7.
Linear Programming Models
8.
Transportation and Assignment Models
9.
Network Models
10.
Project Management
11.
Waiting Lines and Queuing Theory
12.
Simulation Models
13.
Markov Analysis
14.
Statistical Quality Control
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OPR371S/101/0/2021
Consistent work is important to the successful study of this module (and all other modules at
UNISA). Queries from earlier chapters must be clarified as soon as possible instead of “leaving
it to the end”. As concepts often cut across subsections, these queries can accumulate into a
large problem if unattended to.
In addition to the prescribed and recommended textbooks, you should look for additional
textbooks. However, as some textbooks may contain outdated information or concepts, it’s
better to search for one in which the latest edition was published not more than 10 years ago.
Use My Studies @ Unisa brochure for general time management and planning skills.
7
PRACTICAL WORK
There is no practical work for this module.
8
ASSESSMENT
8.1
Assessment criteria
There are several assessment criteria that will be utilised in this module. First, you must
complete two formative assessments represented by the assignments that you must submit
throughout the academic year. The dates of submission and unique numbers are furnished
elsewhere in this document. The purpose of the formative assessment is to modify and improve
your attainment of the relevant outcomes discussed elsewhere in the document. It is important
that you submit both the formative assessments for assessment.
8.2
Assessment plan
The overall assessment consists of three parts, assignments, practical and examination.
The mark for OPERATIONS RESEARCH III (OPR371S) is calculated as follows:
•
The year mark contributes 100% of the final mark
The final mark is based on all the assignment marks obtained and their contribution towards the
final mark is as shown in the table below:
ASSIGMENT NUMBER
CONTRIBUTION TOWARDS FINAL MODULE
MARK
1
10%
2
20%
3
20%
4
25%
5
25%
Total
100%
9
8.3
Assignment numbers
8.3.1 General assignment numbers
Assignments are numbered consecutively per module, starting from 01
8.3.2 Unique assignment numbers
UNIQUE ASSIGNMENT NUMBERS
8.4
Assignment 1
729857
Assignment 2
837749
Assignment 3
868172
Assignment 4
819105
Assignment 5
854086
Assignment due dates
The due dates for the submission of the assignments are:
THE FINAL SUBMISSION DATES FOR ASSIGNMENTS ARE:
Assignment 1
14 May 2021
Assignment 2
11 June 2021
Assignment 3
16 July 2021
Assignment 4
20 August 2021
Assignment 5
1 October 2021
Note: The cut-off dates given here are the official, last dates on which a given
assignment may be submitted. Students must adhere to these dates only. All
other dates referring to cut-off submission dates for assignments, as may be
posted on MyUnisa or elsewhere, refers to administrative dates as managed
by the Assignment Department and does NOT influence or change the above
dates.
8.5
Submission of assignments
Assignments are part of the learning material for this module. As you do the assignments, study
the reading texts, consult other resources, discuss the work with fellow students or tutors or do
research, you are actively engaged in learning. Looking at the assessment criteria given for
each assignment will help you to understand what is required of you more clearly.
In some cases, additional assessment might be available on the MyUnisa site for your module.
For students attending tutorial sessions, tutors may also set additional tasks and give feedback
in class.
Failure to submit all the assignments on time may cause you to fail the module.
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OPR371S/101/0/2021
PLEASE NOTE: Enquiries about assignments, (e.g., whether the University has received
your assignment or the date on which an assignment was returned to you). You might
also find information on MyUnisa. To go to the MyUnisa website, start at the main Unisa
website, http://www.unisa.ac.za, and then click on the ‘login to MyUnisa’ link under the
MyUnisa heading on the screen. . This should take you to the MyUnisa website. You can
also go there directly by typing in http://my.unisa.ac.za.
Please note: Although students may work together when preparing assignments, each
student must write and submit his or her own individual assignment. In other words, you
must submit your own ideas in your own words, sometimes interspersing relevant short
quotations that are properly referenced. It is unacceptable for students to submit
identical assignments on the basis that they worked together. That is copying (a form of
plagiarism) and none of these assignments will be marked. Furthermore, you may be
penalised or subjected to disciplinary proceedings by the University.
You will find your assignments for this subject under the heading Addendum (Point no 12) at
the back of this tutorial letter. The assignments are compulsory. Please submit the
assignment, duly completed, to UNISA before the closing dates stated in this section.
Assignments should be addressed to:
The Registrar
PO Box 392
UNISA
0003
You may submit written assignments and assignments done on mark-reading sheets either by
post or electronically via MyUnisa. Assignments may not be submitted by fax or e-mail unless in
special circumstances and this must be discussed with the lecturer prior to the submission. For
detailed information and requirements as far as assignments are concerned, see the brochure
my Studies @ Unisa that you received with your study material.
To submit an assignment via MyUnisa:
•
Go to MyUnisa.
•
Log in with your student number and password.
•
Select the module.
•
Click on assignments in the left-hand menu.
•
Click on the assignment number you want to submit.
Follow the instructions on the screen.
You will receive the correct answers automatically for multiple-choice questions. For written
assignments, markers will comment constructively on your work. However, comprehensive
memorandums on compulsory assignments will be sent to all students registered for this
module in MyUnisa.
As soon as you have received the memorandums, please check your answers. The
assignments and the memorandums on these assignments constitute an important part of your
11
learning and should help you to be better prepared for the next assignment and the
examination.
VERY IMPORTANT POINTS TO CONSIDER:
•
IT IS COMPULSORY TO SUBMIT ALL THE ASSIGNMENTS
•
NO LATE ASSIGNMENT SUBMISSIONS WILL BE ACCEPTED
•
KEEP A CLEAR COPY OF ALL THE ASSIGNMENTS FOR YOUR OWN
REFERENCE. THIS IS IMPORTANT, AS ASSIGNMENTS DO GET LOST SOMETIMES
•
SUBMISSIONS OF ALL ASSIGNMENTS MUST BE IN ACCORDANCE WITH
THE BOOKLET:
MyStudies@Unisa. The booklet: my Studies @ Unisa explains how you may submit
assignments electronically. Note: if you choose to submit your assignments electronically,
make sure that you have fixed your Excel or Word files in such a way that it will print on
one page wide and not spill over on to a second page. The assignment section just
prints the file, they do not check to see whether parts of a page are cut off
8.6
The assignments
Find the assignments under Addendum (point 12) at the end of the Tutorial Letter.
8.7
Other assessment methods
No other assessment methods are utilised in assessing your progress in this module.
8.8
The examination
Take note: This module is now a continuous assessment module and there is not an
examination at the end of the year. The assignments you have submitted will determine whether
you pass the module
9
FREQUENTLY ASKED QUESTIONS
ARE THERE ANY ADDITIONAL SELF-ASSESSMENTS I SHOULD CONSIDER OTHER
THAN THE ASSIGNMENTS?
A set of Practice Questions will be posted on MyUnisa as additional information. They are not to
be submitted and no memos will be provided. However, I will be available to discuss any
difficulties you may have with these problems. You can also look for plenty of practice questions
in the prescribed textbook.
My Studies @ Unisa brochure contains an A-Z guide of the most relevant study information.
10
SOURCES CONSULTED
You should consult wider than only the prescribed textbook when preparing your assignment for
submission and for the examination. Possible source to consult is other text covering
Operational Research topics which include textbooks and journal articles. Doing so would
prepare you to enhance your understanding of the application of the theory better.
11
IN CLOSING
In closing, I would like to implore you to prepare yourself well for the submission of the
assignment questions at the respective due dates. It is an important part of preparing for the
year end examination.
Problems that you have experienced during your assignment
12
OPR371S/101/0/2021
preparation will persist if you do not address it to the lecturer. Please remember that there is no
such thing as a stupid question.
12
ADDENDUMS
Complete and submit the assignment below on or before the due dates. Please note that
these assignment questions are for self-evaluation process and can be used as an indication of
the difficulty of the exam. However, it DOES NOT indicate the scope of the exam i.e. questions
that do not appear in these assignments may appear in the exam. The prescribed text and is
the only indication of the scope of the exam. PLEASE REMEMBER THE UNIQUE NUMBER.
ASSIGNMENT 1
DUE DATE: 14 May 2021
UNIQUE ASSIGNMENT NUMBER: 729857
Question 1
A friend of yours is selling handcrafted objects at craft markets in your hometown.
He requested your assistance in determining whether it will be possible to have a
more profitable business. You undertook an investigation and found his variable
cost to be R20 each. The selling price of the objects are R50. The cost of renting a
booth at the craft market is R150. He further informed you that he is attempting to
identify a new supplier that will reduce his variable cost of production to R15 per
unit. Assisting him you are required to:
a. Calculate the break-even point for the existing position
(7)
b. If the negotiations for a new supplier is successful, calculate the new breakeven point
(7)
[14]
Question 2
You are an avid fan of one of the large Gauteng soccer clubs. As part of their youth
development entrepreneurship program, they invited tenders from youth to
produce and sell programmes at their home matches. You saw it as an opportunity
to earn an income while studying. You were successful in your submission to the
club. Upon further investigation, you found there is a fixed cost of R400 for the
printing of programs. You will incur a variable cost of R3 per program. Furthermore,
you will incur a fee of R1 000 payable to the club to sell the programs at the home
games. You envisage selling the programs for R5. This is scenario 1 in your
planning process. After careful consideration, you have become concerned that
sales may fall. The reason is the team is experiencing a terrible losing streak and
match attendance has fallen off. From your investigation you are of the opinion you
will only sell 500 programs at the next home match. You plan to increase the price
and still attempt to sell 500 programs. This is scenario 2 in your planning process.
13
To make an informed decision regarding the viability of the endeavour you are
required to:
a. Calculate the number of programs you will have to sell under scenario 1 to
break even
(8)
b. Calculate the price you will have to charge to break even at 500 as envisaged
in scenario 2
(6)
[14]
Question 3
Currently you are enrolled for the module Operational Research III in your studies
towards the National Diploma in Industrial Engineering. The lecturer awards a mark
from an A to F. Thus, you can obtain a mark expressed as A, B, C, D or F. The
distribution of marks awarded for the past 2 years is represented in the table
below:
Marks awarded
A
B
C
D
F
Total
Number of students
80
75
90
30
25
300
If this past distribution is a good indicator of future marks, you are required to
compute the probability of you receiving a C grade in the module.
[9]
Question 4
You have recently qualified as an Industrial Engineer and found employment at an
organisation manufacturing nails. The company manufacture quality nails in lengths
of 1 inch, 2-inch, 3-inch, 4-inch and 5-inche for various uses. Management
requested you to investigate quality issues. During your investigation you have
found an overrun occurs where nails are slightly defective. The defective nails are
placed in a common bin and is sold to the public. In yesterday’s production run,
651 of the 1-inch nails, 243 of the 2-inch nails, 41 of the 3-inch nails 451 of the 4inch nails and 333 of the 5-inch nails was placed in the bin. To advance tour
investigation, you would like to determine the probability of finding a certain length
of nail if you reach into the bin. Compute the probability that:
a. Reaching into the bin you will find a 4-inch nail.
(8)
b. Reaching into the bin you will find a 5-inch nail.
(2)
14
OPR371S/101/0/2021
c. If a certain application requires a nail that is 3 inches or shorter, that you will
be able to satisfy the requirement of the application. What is the conclusion
that can be drawn from the information?
(5)
[15]
[52]
ASSIGNMENT 2
DUE DATE: 11 June 2021
UNIQUE ASSIGNMENT NUMBER: 837749
Question 1
A trade magazine is published for the manufacturing industry. Most of the large,
medium and micro concerns subscribe to the magazine. The company where you
are employed as an Industrial Engineer is no exception. In the last issue, the
magazine produced an article where a prediction was made that the demand for
motor vehicles would be high. Apparently, the South African consumer will continue
buying vehicles even if car prices increases and the economy is not performing well.
The magazine predicted a favourable market for motor vehicles at 70%. In their
opinion, the probability of an unfavourable market is 30%. Senior management at
your place of employment also read this article and were very sceptical of the
predictions. The following table depicts the alternative and their payoffs:
Model
A
B
C
Favourable market
R300 000
R250 000
R75 000
Unfavourable market
-R200 000
-R100 000
-R18 000
Consequently, every model A would contribute R300 000 to profit if the market is
favourable and would incur a loss of R200 000 if the market is unfavourable. The
profit contribution and loss for each model is given in the table above.
They requested you to prepare a report on the matter and present it at the next
EXCO meeting. You are required to:
a. Determine which decision model should be used.
(2)
b. Compute the optimal decision.
(10)
c. You are of the opinion that the R3000 000 for model A with a favourable
market is too high. How much lower would this figure need to be for you to
change your decision made in part b above?
(8)
[20]
15
Question 2
You have won money playing the lottery. You decided to invest the money to pay
for your future studies. The payoff table below depicts the profits that would be
realised during the next year of three investment alternatives you are considering:
Alternative
Probability
Stock market
Bonds
CDs
State of Nature
Good economy
Poor economy
0,50
0,50
80 000
-20 000
30 000
20 000
23 000
23 000
You are required to:
a. Determine which decision would maximise expected profits.
(10)
b. Compute the maximum amount that should be paid for a perfect forecast of
the economy.
(5)
c. Develop an opportunity loss table for your investment.
(3)
d. Compute the minimum EOL and indicate which decision would minimise EOL.
(9)
[27]
Question 3
Your father is a specialist physician. He and a group of friends, all of them specialist
physicians, are contemplating the construction of a private clinic where patients
with specific diseases relevant to their specialities will be treated. As a result,
patients with diseases other than their specialities will not be admitted. In the
group discussion taking place amongst the prospective partners, they agreed that if
medical demand is high (a positive market exist), they estimated a net profit of
R100 000 can be realised. If the market is not favourable, they could incur a loss of
R40 000. Another option for the group is not to proceed with the envisaged
construction of the clinic (do nothing). The group have no data to base their
decision on and as a result, they estimate that there is a 50/50 chance that the
clinic will be successful. A market research company that offers to perform a study
to determine the feasibility of the clinic has approached the group. The cost of the
study is R5 000. The market research company claim they can predict an outcome
reasonably accurate utilising Bayes’ theorem and predict the following probabilities
for the clinic:
Probability of a favourable market given a favourable study = 0, 82
The probability of an unfavourable market given a favourable study = 0, 18
Probability of a favourable market given an unfavourable study = 0, 11
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OPR371S/101/0/2021
Probability of an unfavourable market given an unfavourable study = 0, 89
Probability of a favourable research study = 0, 55
Probability of an unfavourable research study = 0, 45
The group is uncertain of their next step and your farther approached you for
assistance. You are required to:
a. Construct a decision tree reflecting the options available to the group
(19)
b. Compute the EMV to recommend a suitable strategy
(17)
c. Compute the expected value of sample information and make a
recommendation regarding the market study
(5)
[41]
[88]
ASSIGNMENT 3
DUE DATE: 16 July 2021
UNIQUE ASSIGNMENT NUMBER: 868172
Question 1
You are employed as an Industrial Engineer at a reputable company selling a wide
range of well-known products. Management is concerned with the performance of
the company. They presented you with the following data:
Year
2012
2013
2014
2015
2016
2017
2018
Time period
1
2
3
4
5
6
7
Sales (units)
100
110
122
130
139
152
164
They have requested you to investigate the figures and predict the sales for 2019.
You are required to:
a. Find the least squares trend line.
(33)
b. Predict the sales for 2021.
(6)
[39]
17
Question 2
You are employed as an Industrial Engineer at a chemical plant manufacturing
fertiliser. The plant manufactures a 50-kilogram bag of fertiliser for a specific chain
of hardware stores which have a large gardening section. Management is concerned
about the viability of this order. You are requested to investigate and report your
findings to management. Your investigation of the demand for the past 11 years
produces the following data:
Year
1
2
3
4
5
6
7
8
9
10
11
Demand (thousands)
4
6
4
5
10
8
7
9
12
14
15
In preparing your report to management you are required to:
a. Develop a 3-year moving average of demand.
(17)
b. Utilising MAD determine the accuracy of the forecasts.
(3)
[20]
Question 3
It is a requirement that you complete the module Industrial Engineering Practice I
and II before you can graduate. Your brother owns a hardware store, and on the
occasions, you have worked in the store you have notice his business experience
problems with inventory holding. You offered your assistance in solving some of the
inventory problems. During your observations you determine the annual demand
for number six screws is 100 000. For the purpose of the Work Integrated Learning
exercise, your brother made you responsible for all purchases. After studying
previous records, you estimate the ordering cost to be R10 every time the business
places an order for the screws. Furthermore, you estimate that the cost of carrying
one screw in inventory for a year is one-half of one cent. Observing the process
over time, you determine it takes approximately 8 working days for an order of
number six screw to arrive once you place an order. The demand for number six
screws is constant, and on average, you observe the store sells 500 of these screws
each day. You are of the opinion stocks outs can be eliminated if the screws are
ordered at the correct time. Your brother is unhappy with the number of orders you
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place for the screws. He is of the opinion orders should be placed twice a year. You
are required to:
a. Through the application of the correct equation, compute the number of
screws to be ordered at a time if you wish to minimise total inventory cost.
(5)
b. Through the application of the correct equation, compute the number of
orders to be placed annually as well as the annual ordering cost.
(4)
c. Through the application of the correct equation, compute the average
inventory as well as the annual holding cost.
(5)
d. Through the application of the correct equation, compute the reorder point
(ROP).
(2)
e. If you adhere to the policy prescribed by you brother, how much how much
more would this cost every year over the policy you developed? If only two
orders were placed each year, what effect would this have on the ROP?
(9)
[25]
[84]
ASSIGNMENT 4
DUE DATE: 20 August 2021
UNIQUE ASSIGNMENT NUMBER: 819105
Question 1
You are an avid fan of one of the large Gauteng soccer clubs. As part of their youth
development entrepreneurship program, they invited tenders from youth to
produce and sell programmes at their home matches. You saw it as an opportunity
to earn an income while studying. You were successful in your submission to the
club. Upon further investigation, you found there is a fixed cost of R400 for the
printing of programs. You will incur a variable cost of R3 per program. Furthermore,
you will incur a fee of R1 000 payable to the club to sell the programs at the home
games. You envisage selling the programs for R5. This is scenario 1 in your
planning process. After careful consideration, you have become concerned that
sales may fall. The reason is the team is experiencing a terrible losing streak and
match attendance has fallen off. From your investigation you are of the opinion you
will only sell 500 programs at the next home match. You plan to increase the price
and still attempt to sell 500 programs. This is scenario 2 in your planning process.
To make an informed decision regarding the viability of the endeavour you are
required to:
19
c. Calculate the number of programs you will have to sell under scenario 1 to
break even
(8)
d. Calculate the price you will have to charge to break even at 500 as envisaged
in scenario 2
(6)
[14]
Question 2
Your father is a specialist physician. He and a group of friends, all of them specialist
physicians, are contemplating the construction of a private clinic where patients
with specific diseases relevant to their specialities will be treated. As a result,
patients with diseases other than their specialities will not be admitted. In the
group discussion taking place amongst the prospective partners, they agreed that if
medical demand is high (a positive market exist), they estimated a net profit of
R100 000 can be realised. If the market is not favourable, they could incur a loss of
R40 000. Another option for the group is not to proceed with the envisaged
construction of the clinic (do nothing). The group have no data to base their
decision on and as a result, they estimate that there is a 50/50 chance that the
clinic will be successful. A market research company that offers to perform a study
to determine the feasibility of the clinic has approached the group. The cost of the
study is R5 000. The market research company claim they can predict an outcome
reasonably accurate utilising Bayes’ theorem and predict the following probabilities
for the clinic:
Probability of a favourable market given a favourable study = 0, 82
The probability of an unfavourable market given a favourable study = 0, 18
Probability of a favourable market given an unfavourable study = 0, 11
Probability of an unfavourable market given an unfavourable study = 0, 89
Probability of a favourable research study = 0, 55
Probability of an unfavourable research study = 0, 45
The group is uncertain of their next step and your farther approached you for
assistance. Yu are required to:
You are required to construct a decision tree reflecting the options available to the
group of specialist physicians.
[19]
Question 3
You are employed as an Industrial Engineer at a chemical plant manufacturing
fertiliser. The plant produces a 50-kilogram bag of fertiliser for a specific chain of
hardware stores which have a large gardening section. Management is concerned
about the viability of this order. You are requested to investigate and report your
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OPR371S/101/0/2021
findings to management. Your investigation of the demand for the past 11 years
produces the following data:
Year
1
2
3
4
5
6
7
8
9
10
11
Demand (thousands)
4
6
4
5
10
8
7
9
12
14
15
In preparing your report to management you are required to:
a. Develop a weighted 3-year moving average in which the sales in the most
recent year are given a weight of 2 and sales in the other 2 years are each
given a weight of 1.
(17)
b. Utilising MAD determine the accuracy of the forecasts.
(3)
[20]
Question 4
You are employed as an Industrial Engineer at a valve manufacturer. The company
provide valves and fluid control devices to the mining industry and many
municipalities. Recently, stock outs occurred which led to customer complaints and
cancelling of orders. The cancellation of order, if it continues, can negatively impact
the profitability of the organisation. Senior management requested you to
investigate and prepare a plan to exclude stock outs. Your investigation produced
the following information: One of the most popular valves, the Western, has an
annual demand of 4 000 units. The cost of each vale is R90. Inventory carrying cost
is estimated to be 10% of the cost of each valve. Your investigation further showed
that the average ordering cost is R25 per week. Furthermore, the lead time for the
valve is two weeks and the demand during this period is approximately 80. You
have decided to implement inventory control and you are required to:
a. Compute the Economic Order Quantity (EOQ).
(8)
b. Compute the Reorder Point (ROP).
(3)
c. Compute the average inventory as well as the annual holding cost.
21
(6)
d. Compute the number of orders to be placed annually to prevent stock outs
and compute the annual ordering cost.
(9)
[26]
Question 5
During an upcoming municipal election, your friend decided to stand as an
independent candidate. He is financing his own campaign and on has R40 000
available for advertising. He can utilise two types of advertising Community radio
and television, to reach the maximum number of voters. Each radio advertisement
cost R200 and reaches an estimated 3 000 people. Each television advertisement
costs R500 and reaches an estimated 7 000 people. In planning his campaign your
friend would like to reach as many people as possible. He had some specific
requirements namely that at least 10 advertisements of each type must be used.
Furthermore, the number of radio advertisements must be at least as great as the
number of television advertisements. He requested you to find the optimal mix
where his money will be well spent. You are required to solve the problem utilising
the graphical and the iso profit line method to find the optimal solution.
[20]
[100]
THE FOLLOWING QUESTION MUST BE ANSWERED TOO. IT WILL PROVIDE EVEIDENCE OF
YOUR UNDERSTANDING AND KNOWLEDGE IN UTILISING THE COMPUTER SOFTWARE ExcelQM. THE SOFTWARE IS AVAILABLE ON THE COMPANION WEBSITE OF THE PRESCRIBED
TEXTBOOK. PLEASE UTILISE THE INSTRUCTIONS IN THE TEXTBOOK TO ACCESS THE
SOFTWARE.
Question 6
You have found employment as an Industrial Engineer in a financial service
company. It is one of the largest long-term insurance companies in South Africa.
The organisation sells a fixed term life insurance policy. The provision in the policy
stipulates if the policy holder dies during the term of the policy, the organisation
the beneficiary of the policy R100 000. If the policy holder does not die, the
organisation pays out nothing and there is no further value to the policy. The
organisation uses actuarial tables to determine the probability that a person with
certain characteristics will die during the coming year. For a individual, it is
determined that there is a 0,001 chance that the person will die in the next year
and a 0,999 chance that the person will live, and the organisation will pay out
nothing. The cost of the policy is R200 per year. Based on the on the EMV
criterion, should the individual buy this insurance policy? How would utility theory
assist in explaining why a person would buy this insurance policy?
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OPR371S/101/0/2021
ASSIGNMENT 5
DUE DATE: 1 October 2021
UNIQUE ASSIGNMENT NUMBER: 854086
Question 1
You are employed as an Industrial Engineer at a company that manufacture
breakfast cereal. Each box of cereal is labelled “net weight 10 ounces”. Each hour,
random samples of size n = 4 boxes are weighed to check process control. Five (5)
hours of observations yielded the following information:
Time
9h00
10h00
11h00
12h00
13h00
Box 1
9,8
10,1
9,9
9,7
9,7
Weight
Box 2
10,4
10,2
10,5
9,8
10,1
Box 3
9,9
9,9
10,3
10,3
9,9
Box 4
10,3
9,8
10,1
10,2
9,9
Management has expressed their doubt about the integrity of the process and
requested you to investigate whether the readings is within the acceptable limits.
You are required to:
a. Construct the limits for
and R – charts.
(16)
b. Determine if the process is in control.
(7)
c. Inform the quality department what other steps they should follow at this
point.
(2)
[25]
Question 2
Your father is the proud owner of a 1955 sports car. On any given day, he never
knows whether the car would start. Ninety percent of the time it would start if it
started the previous morning. Conversely, 705 of the time it will not start if did not
start the previous morning. Your fathers friend makes fun of this situation and he
bets your farther R5 that the car would not start 5 day from now. Your father asked
your advice and you are required to:
a. Construct the matrix of transition probabilities.
(4)
b. Compute the probability that the car would start tomorrow if it started today.
(3)
23
c. Compute the probability that the car will start tomorrow if it did not start
today.
(3)
d. Compute the probability that the car will not start 5 days from now if it did
not start today.
(5)
e. Compute the probability that the car will not start 5 days from now if it did
not start today.
(5)
f. Compute the probability that the car will start in the long run if the matrix of
transition probabilities does not change.
(5)
[25]
Question 3
You are employed at the Durban container harbour as an Industrial Engineer. Over
the preceding 5 years the volume of containers shipped to the port has steadily
increased. Fully loaded container ships arrive at night in the port. The number of
ships docking on any given night ranges from 0 to 5. The probability of 0, 1, 2, 3,
4, or 5 arrivals is depicted in the following table:
Nightly unloading rate
0
1
2
3
4
5
Probability
0,03
0,12
0,40
0,28
0,12
0,05
You undertook a study revealing that due to the size of the ships and the nature of
the cargo, the number of ships unloaded each night also tend to vary. From the
study you compiled the unloading rate:
Unloading rate
1
2
3
4
5
6
Probability
0,03
0,12
0,40
0,28
0,12
0,05
Due to the schedules of the ships, the off-loading of containers must take place
within the schedule of each ship. Due to the increase in ships arriving at the port,
management is concerned that delays would occur, and the port authority will have
to pay the shipping lines compensation if the ship is not unloaded in time. To
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OPR371S/101/0/2021
achieve this objective, you are required to compile a simulation for 15 days which
would depict the number of nightly arrivals, total to be unloaded, number unloaded.
Furthermore, compute the average number delayed, the average number of
arrivals and the average number unloaded.
Utilise the following random numbers when simulating:
For the arrivals:
37, 77, 13, 10, 02, 18, 31, 19, 32, 85, 31, 94, 81, 43 and 31
For the number to be unloaded:
69, 84, 12, 94, 51, 36, 17, 02, 15, 29, 16, 52, 56, 43, and 26
[25]
Question 4
You are employed by an organisation that manufacture electronic components. The
equipment utilised in the manufacturing process is highly sophisticated. As a result,
the equipment breaks down frequently. The organisation retains a service crew to
repair machine breakdowns that occur on an average of ʎ = 3 per day
(approximately Poisson in nature). The crew can service an average of µ = 8
machines per day (distribution resembles the exponential distribution. Any
downtime of a machine impacts the profit margins of the organisation negatively.
Management requested you to investigate and report your findings. To do so, you
are required to:
a. Compute the utilisation rate of this service system.
(4)
b. Compute the average downtime for a machine that is broken
(6)
c. Compute the number of machines that are waiting to be serviced at any given
time.
(3)
d. Compute the probability that more than one machine is in the system.
Compute the probability that more than two are broken and waiting to be
repaired and compute the probability that more than three is broken down
and repaired. Compute the probability that more than four is broken down
and repaired.
(12)
[25]
[100]
UNISA
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