Dr. Daniel Xing
Email: X.xing3@liverpool.ac.uk
Operations Modelling and Simulation
Lecture 2
EBUS-504
Operations Modelling and Simulation
Lab1
University of Liverpool
Management School, UK
TA: Mr. Lais Wehbi
Email: L.wehbi@liverpool.ac.uk
Continue your project development
Now, Company ABC puts all the three side panels (I-type, II-type, III-type) under
production. Each panel is firstly heated with combining different raw materials with a
mould in an oven and then after all the panels are cooled down and split, the mould will
be returned for cleaning and the panels need to go through different further production
steps with respect to their types. The production details for each panel are as follows:
Type I-type II-type III-type
Raw materials P1-P3-P2 P2-P3-P2 P1-P4
Oven 3 mins setup + 15 mins production 5 mins setup
+ 20 mins production
3 mins setup + 25 mins production
Conveyor needed? No Yes (Oven to Cooling) Yes (Oven to Cooling)
Cooling 20 mins 30 mins 30 mins
Split (1 mins setup after 10
operations)
2 mins (auto) 2 mins (auto) 2 mins (auto)
Mould cleaning 5 mins (auto) 7 mins (auto) 6 mins (auto)
After split Trim (10 mins manual) – Paint (15
mins manual) – Package (3 mins auto
and batch size is 3-5. Can be packed
with II-type)
Trim (10 mins manual) – Polish (5 mins
auto) – Paint (10 mins manual) –
Package (3 mins auto and batch size is
3-5. Can be packed with I-type)
Trim (15 mins manual) –Paint (8 mins
manual) – Polish (3 mins auto) – Wax
(2 mins auto) – Package (1 mins auto
and lot size is 2. Cannot be packed
with other types)
Continue your project development
The shopfloor currently has 3 ovens, 5 employees, 10 moulds, 2 conveyor (20 part
length and it takes 4 mins to move a panel from one side to another), 3 split stations, 2
mould cleaning stations, 2 trim stations, 1 paint station, 1 polish, 1 wax and 2 package
stations.
Procurement details for raw materials are:
P1: first arrival is 0, inter arrival is 20 mins, lot size is 2
P2: first arrival is 0, inter arrival is 15 mins, lot size is 4
P3: first arrival is 0, inter arrival is 15 mins, lot size is 2
P4: first arrival is 5, inter arrival is 25 mins, lot size is 5
Dr. Daniel Xing
Email: X.xing3@liverpool.ac.uk
Operations Modelling and Simulation
Lecture 2
EBUS-504
Operations Modelling and Simulation
Lab2
University of Liverpool
Management School, UK
TA: Mr. Lais Wehbi
Email: L.wehbi@liverpool.ac.uk
Continue your project development
1. Identify the warm-up period based on the current setting.
2. Now since a disruption occurred in ABC’s upstream suppliers, the arrival of P1 and
P3 are not as reliable as before and their inter-arrival times are following, N~(24,4)
and N~(18,3), two normal distributions, respectively. Please choose the proper time
window and use Welch’s moving average method to determine the new warm-up
period. Also, if the use of oven costs us £10 per minute, then how much is the total
cost after 1000 minutes?
Dr. Daniel Xing (x.xing3@liverpool.ac.uk)
EBUS-504
Operations Modelling and Simulation
Build your first SD model
University of Liverpool
Management School,
UK
mailto:c.iris@liverpool.ac.uk
Agenda
Model description (Vensim ®)
•Causal Loop Diagram
•First model – Getting involved with Vensim
•Model formulations
•
Results
analysis / Graphs
•Causal loop diagram-based Model improvements
•Building up the new model
•Results and analysis, comparing previous results
•Customise graphs
•Generate equation information from the Vensim model
Description of system
The company produce and sales prefabricated windows frames. In general,
the main behaviors that describes are the followings
•The production level is characterised by a RAMP function
•Company realized that sales, production, workforce and inventory are relevant.
The dynamics of the system can be defined by the following characteristics
•Items produced go into inventory (Without production, inventory will never go up. )
•Items are sold from the inventory (Without any inventory, there is no possible sales)
•Without any workforce, there is no production.
•If sales goes up the company tries to expand production (Sales impact target
production)
•Target production impacts target workforce level.
• Productivity impacts production and target workforce level.
• Considering target workforce level and work level, company can decide net hire
rate.
• There is a time to adjust workforce. You cannot get new workforce immediately.
Causal loop diagram
From the system description, the preliminary causal loop diagram can be
drawn as follows
Vensim model of the system
Tips for building up the Vensim Model ;
•When production occurs, goods are not immediately sold.
•They are stored in an Inventory until a sale occurs.
•Higher sales will result in higher production through other
variables
INVENTORY: It is a Level (Stock) variable: Flow In and Flow Out
WORKFORCE: It is a Level (Stock) variable. More people make more products
PRODUCTION, SALES, NET HIRE RATE: They are all rate variables as they flow
in or out of Stock variables
TARGET PRODUCTION, TARGET WORKFORCE, PRODUCTIVITY: Ordinary
variables
BEHAVIOURAL RELATIONSHIPS
•Production is proportional to workforce
•Net hire rate depends on the workforce value
•Production is to be affected by a productivity rate
First model – Initial Vensim model
POPULATION BEHAVIOUR
First model – Initial Vensim model
POPULATION BEHAVIOUR
First model – Initial Vensim model
POPULATION BEHAVIOUR
Parameters of the system;
• Initial value of inventory : 300 units
• Sales : The sales amount is 100 units for 20 months. After 20 months, it
is 150 units
• Productivity is 1
• Time to adjust workforce level is: 10 months
• Initial workforce level: 100 workers
Equations;
• Inventory = Production – Sales
• Target Production = Sales
• Target Workforce = Target Production / Productivity
• Net hire rate = (Target Workforce – Workforce)/Time to adjust workforce
• Production = Workforce * Productivity
First model – Initial Vensim model
POPULATION BEHAVIOUR
Results
Quiz 5: Vensim modeling for production
management
Question 1: Produce same model in Vensim and test
the same model for an initial of 30 workers. How
does production, workforce and inventory profile look
like?
Question 2: Carefully analyse the results from the
model. Check production, workforce and inventory
graphs. Are results correct? Is there any fundemental
error in the model? If so, what is it?
Dr. Daniel Xing (x.xing3@liverpool.ac.uk)
EBUS-504
Operations Modelling and Simulation
Build your first SD model
University of Liverpool
Management School,
UK
mailto:c.iris@liverpool.ac.uk
1
Module Specification
EBUS504 – OPERATIONS MODELLING AND SIMULATION
Contents
1. Module Details …………………………………………………………………………………………………………………………………………………………………………………………………………………. 1
2. Aims and Content ………………………………………………………………………………………………………………………………………………………………………………………………………………
3
3. Learning and Teaching Methods ………………………………………………………………………………………………………………………………………………………………………………………….
5
4. Assessments …………………………………………………………………………………………………………………………………………………………………………………………………………………….. 5
5. Module Outcomes (learning outcomes, skills and other attributes) …………………………………………………………………………………………………………………………………………
6
6. Supplementary Information………………………………………………………………………………………………………………………………………………………………………………………………..
7
1. Module Details
Module Title: OPERATIONS MODELLING AND SIMULATION
Short Title: OPS MODELLING AND SIMULATION
Module Code: EBUS50
4
Marketing Module Synopsis: This module will give students an understanding of the role of modelling and simulation in the development and improvement of
business processes in a commercial environment. Important elements include analytical techniques of systems, statistical aspects of
modelling and system dynamics. Extensive use will be made of a variety of commercially available modelling and simulation tools
such as Witness.
Credits: 15
Level: Level 7
Delivery Location(s) Liverpool Campus
2
Semester: First Semester
Academic Year: 2022-23
Faculty: Faculty of Humanities and Social Sciences
School/Institute (Level 2): Management School
Curriculum Board (level 1): ULMS PG
Module Coordinator: Xinjie (Daniel) Xin
g
Other staff: David Horne, Julie Reddy, Luc Bostock, Laura Brough, Leon Bedeau, Luke Dowdall, Michael McDonough, Mary Jlassi, Thomas Lloyd,
Nicola Wood,, Tolga Bektas
External Examiner(s):
Pre-requisites: N/A
Co-requisites: N/A
Barred Combinations: N/A
CE/CPD Provision: No
Maximum Places: N/A
Subject: 100079: Business Studies 100%
HESA Cost Centre(s): Business & management studies
3
Notes:
Status: Modification
The table below is automatically completed from programme data held in Curriculum Manager; during 2019/20 it is likely to have no data or incomplete data until all
programme records are in Curriculum Manager.
In Programmes: Programme Validation
Status
Module Status: Programme Stage / Group /
Sub-group
Operations and Supply Chain Management Master of Science (MSc) 2022-23 Validated Optional Semester 1
Business Analytics and Big Data Master of Science (MSc) 2022-23 Validated Optional Semester 1
Project Management (MSc) 2022-23 Validated Optional Semester 1
The table below must be completed for module approval, including confirmation that there are zero costs to the student.
Student Cost(s
)
Costs range:
Cost Type: Description: Value type (exact, approximate or max/min
range):
Cost (exact or approximate): Minimum Cost: Maximum Cost:
Student Cost There are no studen
t
costs associated with
this module.
Exact 0.00
2. Aims and Content
Educational Aims:
To understand a range of modelling analytical methods and their appropriate applications;
To understand the dynamic nature of systems and their behavioural characteristics;
4
To understand how real system modules are developed, tested and validated;
To develop confidence in the use of commercially available simulation tools such as Excel, Witness, Matlab and Vensim.
Overview:
This module will give students an understanding of the role of modelling and simulation in the development and improvement of business processes in a commercial
environment. Important elements include analytical techniques of systems, statistical aspects of modelling and system dynamics. Extensive use will be made of a variety
of commercially available modelling and simulation tools such as Matlab and Witness.
Outline Syllabus:
Introduction to modelling theory.
The use of modelling to support Inventory management, the witness interface for process simulation.
The use of Discrete event simulation, industry examples.
Flow diagram approaches and the application in case studies from industry.
Data analytics tools to support data processing, modelling and simulations, data analysis techniques.
The use of System dynamic Modelling.
Demonstrating the practical aspects of developing simulation models with a review of the benefits and problems encountered.
Assignment Exercises.
Reading lists and resources:
Type Category Title Description
General Resource Link to Reading Lists Reading lists are maintained at readinglists.liverpool.ac.uk
5
3. Learning and Teaching Methods
Summary of Learning and Teaching Methods:
On campus delivery with social distancing.
2 hour face-to-face synchronous lecture per week x 12 weeks
1 hour face-to-face seminar every other week x 6 weeks
1 hour face-to-face peer-to-peer learning every other week (unscheduled) x 6 weeks
Self-directed learning x 114 hours
The following table must be completed for module approval, accounting for all hours associated with the credit value of the module, e.g. for 15 credits there should b
e
150 hours of learning and teaching activity, including independent learning.
Learning and Teaching Method: Length (Minutes): Times per Week
(if
applicable):
Number of Weeks (if
applicable):
Calculated Hours (if
applicable):
Hours:
Self-Directed Learning N/A N/A N/A N/A 114
E-lecture 60 1 12 12 12
Seminar 60 1 6 6 6
E-lecture (Unscheduled) 60 1 12 12 12
Peer Learning (Unscheduled) 60 1 6 6 6
4. Assessments
Assessment Strategy:
Modelling and simulation assignment, 5 weeks x 2 hours each, 100%
All fields in the table below must be completed for module approval.
6
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Coursework Simulation
There is a resit opportunity.
Standard UoL penalty applies for late
submission.
This is an anonymous assessment.
Summative Other N/A N/A N/A 5 weeks x
2 hours
each
100 % Sem 1 No Yes
Please see Appendix 1 for details of the outcomes tested by the above assessments.
5. Module Outcomes (learning outcomes, skills and other attributes)
Ref No. Learning Outcome / Skill: Category:
LO1 Be able to design models for business process reengineering; Learning Outcomes
LO2 Be able to specify, and justify a computer simulation for business process modelling; Learning Outcomes
LO3 Be able to apply statistical and analytical techniques for business optimisation and evaluation; Learning Outcomes
S1 Adaptability. Students will develop adaptability by engaging with case studies from their lab sessions in order to understand
modelling and simulation processes and the features of different modelling tools.
Skills
S2 Problem solving skills. Students will develop problem solving skills through lab sessions and case studies as part of their assignment. Skills
S3 Commercial awareness. Students will develop knowledge of commercial contexts of technology applications. Skills
S4 Teamwork. Students will be expected to work together in groups for some lab sessions. Skills
S5 Organisational skills. Students will be expected to work together to solve some hands-on case studies jointly. Skills
S6 Communication skills. Students will develop communication skills by engaging with case studies, report writing and working in groups. Skills
S7 IT skills. IT skills will be developed during practical lab sessions. Skills
7
Ref No. Learning Outcome / Skill: Category:
S8 International awareness. Students will develop international awareness through case studies of business and technologies in an
international context.
Skills
S9 Lifelong learning skills. Students will develop skills of lifelong learning through preparation for their assessments and self-directed
study of cases in preparation for class discussions.
Skills
S10 Ethical awareness. Students will develop their awareness of ethical issues through research and preparation for assessment. Skills
S11 Leadership. Leadership skills will be developed during in-lecture discussions and lab session practices. Skills
6. Supplementary Information
If a risk assessment is required for this module for students under 18, please record a summary of the risks: N/A
Module Specification Appendix 1: Assessments and the Outcomes Tested
Module Title OPERATIONS MODELLING AND SIMULATION
Module Code EBUS504
In the table below, all fields should be completed for approval, except for the Weighting field for a Formative Type assessment method.
Assessment Method Type Weighting Marked out of Pass Mark Learning Outcomes / Skills Tested
Coursework Summative
100 % 100 50 LO1, LO2, LO3, S1, S11, S2, S3, S4, S5, S6,
S7, S8, S9
ASSIGNMENT
The University of Liverpool Management School
2022 – 2023
EBUS504 Operations Modelling and Simulation
DEADLINE: January 13th, 2023 before 12 noon
Lateness Penalty: Five percentage points shall be deducted from the assessment mark for
each working day after the due date up to a maximum of five working days; however, the
mark will not be reduced below the pass mark for the assessment (50%). Work assessed at
below 50% will not be penalised for late submission of up to five working days. Work received
more than five working days after the submission deadline will receive a mark of zero.
Cheating: This is an individual assignment. You can discuss your general understanding of the
exercise with colleagues of other groups, but you must write up your unique project report
yourself. Standard UoL code applies. University regulations about cheating – especially
COLLUSION and PLAGIARISM (copy from sources without acknowledgement or other student
reports) – apply.
Hand-in procedure: Hand your work electronically by submitting a copy through the Turnitin
link on CANVAS. If your work is late for medical or other good cause, attach a copy of your
certificate and/or explanation.
Notes:
You must submit:
● One electronic copy (doc, docx or PDF) through CANVAS
(EBUS504_SMITH_20091234 )
● An electronic copy of the Witness, Vensim and Excel files developed through on
CANVAS (all in one zip or rar file with your name and ID as filename e.g.
EBUS504_SMITH_20091234.zip)
1. Practical questions: System Dynamics (40 Marks)
The COVID-19 pandemic has a massive negative impact on human wellbeing and the global economy
since its outbreak at the end of 2019. Early studies have shown that using Personal Protective
Equipment (PPE) helps for protection against the spread of the disease. Therefore, retailers have put
an enormous effort on the stable, reliable, and rapid management of PPE supply chain. During the
pandemic, the procurement and inventory management for PPE has gained immense attention.
Retailers believe that system dynamics might help them plan procurement, inventory and sales
planning for PPE. It is very well known that if there is no PPE inventory, there can be no sales. In other
words, PPEs are sold from inventory. It is also known that if there is no PPE procurement, there is no
PPE inventory. Each PPE item first goes into inventory once they arrive. If the PPE sales increase,
retailers purchase more PPE.
To be on the relatively safe side, retailers have a target inventory which is equal to coverage level (c
months) times PPE sales (i.e. target inventory is c months of sales). There is a time to replenish PPE
inventory and it is called lead time.
a) Draw the Causal-loop diagram, put the sign (positive or negative) for the whole model and write
equations for variables. (10 Marks).
b) A retailer has a coverage level of 4 months and the lead time of PPE is 1.5 months. Assume that the
retailer has an initial inventory level of 120000 PPE and the demand of PPE has a step-wise function.
Demand is 18000 units between 0-19 months, demand is 45000 between 25-65 months, and finally
demand is 66000 units between 75-100 months. (20 Marks).
– Establish complete model on Vensim and report model as screenshot in the report. Run this model
on Vensim for 120 months with time step of 0.35.
– Discuss results for inventory level, procurement level and show graphs of results.
– Make recommendations to the retailer.
c) Apart from retailers, governments also have a similar problem of PPE procurement and inventory
management as their frontline workers need PPE for free of charge. If you are asked to solve this
problem for a government organisation, what would change in your model and in your parameters?
Critically discuss this new setting. (10 Marks).
2. Practical questions: operations modelling (60 Marks)
a) Based on the specification of your project in Lab 1, please propose a solution in Witness to
simplify your shopfloor set-up (i.e. remove unnecessary entities) and smooth your post-split
production process (i.e. less blockage) but not to compromise your current productivity. Draw a
cross-functional flowchart to demonstrate the new production design. Upload this new model in
your ZIP file and name it as MOD1 (10 Marks).
b) Based on MOD1, if the cycle times of your oven are uniform (15,19) for I-type, normal (20, 3) for
II-type and uniform (20, 27) for III-type. Please use appropriate method to identify when your system
will reach a steady-state. Detailed analysis is expected to support your argument (10 Marks).
c) Based on MOD1, use appropriate analytical method(s) to identify the bottleneck of your model
and give detailed analysis (10 Marks).
d) Based on MOD1, assuming one of your three ovens is broken down, please propose a backup plan
(based on your current resource) to continue your production and try to make the corresponding
disruption as little as possible. Detailed analysis is expected to support your plan and your new
model should be named as MOD2 in your ZIP file (10 Marks).
e) Based on MOD2, all the paint stations are now becoming manual machines and you are given
10000 pcs P1, 10000 pcs P2, 10000 pcs P3, and 10000 pcs P4 to be planned. The initial labour source
costs you £3000/person. Assuming each labour has 100% energy at the start of your simulation and
every 480 minutes, all labours’ energy level will be reset back to 100%. It consumes 2% energy
/working minute for each labour and every one minute idle time can help a labour restore 0.5%
energy. If any job will run out of a labour’s 100% energy, he/she will refuse to carry out any further
work until it is reset to 100% and one major unsatisfaction will be marked. When any labour has
accumulated 3 major satisfactions, he or she will resign from your company and it will cost you
£5000 to recruit a replacement. If I-type product can be sold for £800/pc, II-type product can be sold
for £950/pc and III-type can be sold for £1200/pc, please advise the optimal labour size and optimal
number of I-type, II-type and III-type products to be produced based on your given inventory (i.e.
10000 pcs P1, 10000 pcs P2, 10000 pcs P3, and 10000 pcs P4). You should save your optimised
model as MOD3 in your ZIP file. Detailed analysis is required and please critically reflect the
implications of your solution with respect to real-life operations (20 Marks). Hint: 1) ISTATE(element
name) function can return you the state of a specific element when this function is called. 2) Use IF
action together with AND can verify multiple conditions at the same time. For example:
IF (A>=5) AND (B>=4)
C=C+1
ENDIF
1
Module Specification
EBUS504 – OPERATIONS MODELLING AND SIMULATION
Contents
1. Module Details …………………………………………………………………………………………………………………………………………………………………………………………………………………. 1
2. Aims and Content ………………………………………………………………………………………………………………………………………………………………………………………………………………
3
3. Learning and Teaching Methods ………………………………………………………………………………………………………………………………………………………………………………………….
5
4. Assessments …………………………………………………………………………………………………………………………………………………………………………………………………………………….. 5
5. Module Outcomes (learning outcomes, skills and other attributes) …………………………………………………………………………………………………………………………………………
6
6. Supplementary Information………………………………………………………………………………………………………………………………………………………………………………………………..
7
1. Module Details
Module Title: OPERATIONS MODELLING AND SIMULATION
Short Title: OPS MODELLING AND SIMULATION
Module Code: EBUS50
4
Marketing Module Synopsis: This module will give students an understanding of the role of modelling and simulation in the development and improvement of
business processes in a commercial environment. Important elements include analytical techniques of systems, statistical aspects of
modelling and system dynamics. Extensive use will be made of a variety of commercially available modelling and simulation tools
such as Witness.
Credits: 15
Level: Level 7
Delivery Location(s) Liverpool Campus
2
Semester: First Semester
Academic Year: 2022-23
Faculty: Faculty of Humanities and Social Sciences
School/Institute (Level 2): Management School
Curriculum Board (level 1): ULMS PG
Module Coordinator: Xinjie (Daniel) Xin
g
Other staff: David Horne, Julie Reddy, Luc Bostock, Laura Brough, Leon Bedeau, Luke Dowdall, Michael McDonough, Mary Jlassi, Thomas Lloyd,
Nicola Wood,, Tolga Bektas
External Examiner(s):
Pre-requisites: N/A
Co-requisites: N/A
Barred Combinations: N/A
CE/CPD Provision: No
Maximum Places: N/A
Subject: 100079: Business Studies 100%
HESA Cost Centre(s): Business & management studies
3
Notes:
Status: Modification
The table below is automatically completed from programme data held in Curriculum Manager; during 2019/20 it is likely to have no data or incomplete data until all
programme records are in Curriculum Manager.
In Programmes: Programme Validation
Status
Module Status: Programme Stage / Group /
Sub-group
Operations and Supply Chain Management Master of Science (MSc) 2022-23 Validated Optional Semester 1
Business Analytics and Big Data Master of Science (MSc) 2022-23 Validated Optional Semester 1
Project Management (MSc) 2022-23 Validated Optional Semester 1
The table below must be completed for module approval, including confirmation that there are zero costs to the student.
Student Cost(s
)
Costs range:
Cost Type: Description: Value type (exact, approximate or max/min
range):
Cost (exact or approximate): Minimum Cost: Maximum Cost:
Student Cost There are no studen
t
costs associated with
this module.
Exact 0.00
2. Aims and Content
Educational Aims:
To understand a range of modelling analytical methods and their appropriate applications;
To understand the dynamic nature of systems and their behavioural characteristics;
4
To understand how real system modules are developed, tested and validated;
To develop confidence in the use of commercially available simulation tools such as Excel, Witness, Matlab and Vensim.
Overview:
This module will give students an understanding of the role of modelling and simulation in the development and improvement of business processes in a commercial
environment. Important elements include analytical techniques of systems, statistical aspects of modelling and system dynamics. Extensive use will be made of a variety
of commercially available modelling and simulation tools such as Matlab and Witness.
Outline Syllabus:
Introduction to modelling theory.
The use of modelling to support Inventory management, the witness interface for process simulation.
The use of Discrete event simulation, industry examples.
Flow diagram approaches and the application in case studies from industry.
Data analytics tools to support data processing, modelling and simulations, data analysis techniques.
The use of System dynamic Modelling.
Demonstrating the practical aspects of developing simulation models with a review of the benefits and problems encountered.
Assignment Exercises.
Reading lists and resources:
Type Category Title Description
General Resource Link to Reading Lists Reading lists are maintained at readinglists.liverpool.ac.uk
5
3. Learning and Teaching Methods
Summary of Learning and Teaching Methods:
On campus delivery with social distancing.
2 hour face-to-face synchronous lecture per week x 12 weeks
1 hour face-to-face seminar every other week x 6 weeks
1 hour face-to-face peer-to-peer learning every other week (unscheduled) x 6 weeks
Self-directed learning x 114 hours
The following table must be completed for module approval, accounting for all hours associated with the credit value of the module, e.g. for 15 credits there should b
e
150 hours of learning and teaching activity, including independent learning.
Learning and Teaching Method: Length (Minutes): Times per Week
(if
applicable):
Number of Weeks (if
applicable):
Calculated Hours (if
applicable):
Hours:
Self-Directed Learning N/A N/A N/A N/A 114
E-lecture 60 1 12 12 12
Seminar 60 1 6 6 6
E-lecture (Unscheduled) 60 1 12 12 12
Peer Learning (Unscheduled) 60 1 6 6 6
4. Assessments
Assessment Strategy:
Modelling and simulation assignment, 5 weeks x 2 hours each, 100%
All fields in the table below must be completed for module approval.
6
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Coursework Simulation
There is a resit opportunity.
Standard UoL penalty applies for late
submission.
This is an anonymous assessment.
Summative Other N/A N/A N/A 5 weeks x
2 hours
each
100 % Sem 1 No Yes
Please see Appendix 1 for details of the outcomes tested by the above assessments.
5. Module Outcomes (learning outcomes, skills and other attributes)
Ref No. Learning Outcome / Skill: Category:
LO1 Be able to design models for business process reengineering; Learning Outcomes
LO2 Be able to specify, and justify a computer simulation for business process modelling; Learning Outcomes
LO3 Be able to apply statistical and analytical techniques for business optimisation and evaluation; Learning Outcomes
S1 Adaptability. Students will develop adaptability by engaging with case studies from their lab sessions in order to understand
modelling and simulation processes and the features of different modelling tools.
Skills
S2 Problem solving skills. Students will develop problem solving skills through lab sessions and case studies as part of their assignment. Skills
S3 Commercial awareness. Students will develop knowledge of commercial contexts of technology applications. Skills
S4 Teamwork. Students will be expected to work together in groups for some lab sessions. Skills
S5 Organisational skills. Students will be expected to work together to solve some hands-on case studies jointly. Skills
S6 Communication skills. Students will develop communication skills by engaging with case studies, report writing and working in groups. Skills
S7 IT skills. IT skills will be developed during practical lab sessions. Skills
7
Ref No. Learning Outcome / Skill: Category:
S8 International awareness. Students will develop international awareness through case studies of business and technologies in an
international context.
Skills
S9 Lifelong learning skills. Students will develop skills of lifelong learning through preparation for their assessments and self-directed
study of cases in preparation for class discussions.
Skills
S10 Ethical awareness. Students will develop their awareness of ethical issues through research and preparation for assessment. Skills
S11 Leadership. Leadership skills will be developed during in-lecture discussions and lab session practices. Skills
6. Supplementary Information
If a risk assessment is required for this module for students under 18, please record a summary of the risks: N/A
Module Specification Appendix 1: Assessments and the Outcomes Tested
Module Title OPERATIONS MODELLING AND SIMULATION
Module Code EBUS504
In the table below, all fields should be completed for approval, except for the Weighting field for a Formative Type assessment method.
Assessment Method Type Weighting Marked out of Pass Mark Learning Outcomes / Skills Tested
Coursework Summative
100 % 100 50 LO1, LO2, LO3, S1, S11, S2, S3, S4, S5, S6,
S7, S8, S9
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Lecture 3
Bottleneck analysis
University of Liverpool
Management School,
UK
Key learning outcomes
1. Understand what is a “bottleneck” to a simulation;
2. Use of bottleneck for different analysis;
Building a Simulation Model
3. STRUCTURED
WALK-THROUGH
2. DATA AND
MODEL DEFINITION
1. PROBLEM
FORMULATION
6. VALIDATE
MODEL
5. PERFORM
PILOT
RUNS
4. BUILD MODEL
AND VERIFY
10. DOCUMENT AND
IMPLEMENT RESULTS
9. ANALYSE OUTPUT
DATA
8. MAKE PRODUCTION
RUNS
7. DESIGN
EXPERIMENTS
Bottleneck
The term Bottleneck is used to describe “a point of congestion in any
system from computer networks to a factory assembly line. In such a
system, there is always some process, task, machine, etc. that is the
limiting factor preventing a greater throughput and thus determines the
capacity of the entire system.” (Goldratt and Cox, 1984)
Bottleneck is critical
1. It determines the throughput of the entire system, i.e. the production
pace;
2. Most effective way to improve the entire system;
3. It constrains the utilisation and performance of other resources.
2
mins
1min
8mins 4mins
Finding bottleneck is not always straightforward
Examples:
1. The production of product A requires a sequential processes and their
operation time is 3mins, 5mins and 7mins respectively;
2. Product A is assembled by 4 components (2Bs, 1C and 1D) with
2mins.
Each type of component requires a pre-processing operation with
machine time 3mins, 5mins, and 4mins respectively.
3. A supermarket has three tills to serve its customers. Each till needs
2mins on average to finish the service and customers arrive the store
every 1min.
4. A line production is comprised by 3 machines with operation time
6mins, 8mins and 4mins respectively. Every machine needs a 2mins
setup by L1 (there is only one labour available) and part arrives
every
2mins.
Analytical-based methods
Input rate vs.
output rate
Bottleneck of your system is always identified when input rate is faster than
output rate
The busiest resource (capacity analysis)
Filter out the entity in the system which takes the longest time to complete a job
The most congested place (throughput analysis)
The place where a part takes the longest time to enter and leave it.
Product production lifecycle analysis
From raw material(s) until the completion of an end-product, analysing how
much time in percentage that each component needs to be operated with.
How do we find the bottleneck?
How can we use the aforementioned techniques to locate your bottleneck?
Use Gantt chart for a solution!!
2min 1mins 8mins 4mins
P1
arrives
every 2
mins
Why bottleneck is so important?
1. It defines the maximal throughput rate of your system.
2. It helps modellers quickly locate queues
3. It helps you identify the total outputs at a certain point. (How do you
calculate it?)
4. It defines the maximal utilisation rate for each entity of your system.
(How do you calculate it?)
5. Most importantly, it provides further improvement directions. (Why and
how will you anticipate your improvement?)
Bottleneck and simple queues
1. Where will you build up queues?
2. How do we interpret different queues?
1min 2mins 8mins 4mins
P1
arrives
every
1min
Bottleneck and simple queues
1. Where will you build up queues?
2. How do we know the waiting time for the 10th part? 50th part? Or the nth
part?
3. How do we know the queue size at minute 50? Or minute 100? Or the
nth minute?
2mins 1min 8mins 4mins
Intro for next week – steady state analysis
Recall the example and think the following questions:
1. What is the difference between the first output and any future outputs?
2. Why do we need to exclude warm-up period?
3. What if some rates are uncertain?
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Lecture 2
Bottleneck analysis
University of Liverpool
Management School,
UK
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Witness Intro
Build your first model in Witness
University of Liverpool
Management School,
UK
Objective of this session
• Understand Witness modelling and simulation foundations;
• Learn the basic Witness functions and elements;
• Build your first Witness model and walk around
Witness
Statistics
;
• Understand different input rules;
First look of Witness GUI
Standard
toolbar
Menu
Witness
toolbar
Simulation space
List of
simulation
elements
Interactive
window
Designer elements for
quick built-upSimulation toolbar
Basic elements
✓ Part- representing
materials and products;
✓ Buffers- representing
storage, warehouse, and
queues etc.;
✓ Machine- representing
the machinery resource
which can be used for
processing materials or
serving customers;
✓ Labour- representing
manpower for different
operational purposes.
Element types
• Part types
➢ Active – output from external world, details of its output need to be specified.
➢ Passive – produced internally, no output details is needed.
• Machine types
➢ Single: One in one out;
➢ Batch: X in one out but inputs are not transformed;
➢ Assembly: X in one out and outputs are assembled from the input parts;
➢ Production: One in X out and the output types can be defined.
Elements of a sample model
• Model description
A1
B1
M1
L1
A1
o Arrives every 3 minutes
o First arrival at 2 minutes
o Lot size: 4
o Output: Push to B1
M1
o Input: pull from B1
o Cycle time: 5 minutes
o Setup: L1 spends 2 minutes for
every operation and start from
the first operation
o Output: Push to ship
Elements interactive play
• Input and output rules
❑ Part:
✓ Only active parts has output rules
❑ Machine:
✓ Input rule: wait (passive input rule) or different proactive input rules
✓ Output rule: wait (passive onput rule) or different proactive onput rules
❑ Buffer
✓ No input nor output rule
❑ Conveyor
✓ Same as machine
Define input and output rules
• Method 1 – write your syntax in element detail dialog box
Define input and output rules
• Method 2 – Visual input & output rule
Labour rules
• In setups
Labour rules
• For manual machines
Basic modelling steps
• Step 1: Define Witness elements (use designer elements for
build-up);
• Step 2: Change element graphics if necessary
• Step 3: Detail your elements;
• Step 4: Define your input and output rules;
• Step 5: Simulate, verification and analysis.
Simulate your model
Reset your
simulation
Pause your
simulation
Step run your
simulation
Run your
simulation
Fast forward your simulation
to the defined
end time
Current time of your
simulation
Warmup period
Pre-defined simulation
end time
Animated simulation
active/de-active and
speed
Motion speed of your
animation
Statistics
Statistics
Statistics
Statistics
Dr. XINJIE XING
EBUS
–
504
Operations Modelling and Simulation
Introduction to
System Dynamics
University of Liverpool
Management School,
UK
Learning outcomes
• Understand and realise what a system is.
• Visualise the System Dynamic perspective for
any process.
• Apply causal loops diagram to represent the
System Dynamic approach.
• Use the tool VENSIM to model and simulate
manufacturing and supply chain processes.
Recommended reading material
• Chapter 4 of Kramer, N.J.T.A. and de Smit,J., “Systems thinking”, Martinus
Nijhoff Social Science Division, 1977, ISBN 90 207 0587 3, The Netherlands.
• Campuzano, F. and Mula, J. (2011). Supply Chain Simulation. A System
Dynamics Approach for Improving Performance. Springer, 1st Edition. ISBN
978-0-85729-718-1
• Ford, A. (2009). Modeling the environment , 2nd Edition.
• Hernández, J.E., Zarate, P., Dargam, F., Delibašić, B., Liu, S. and Ribeiro, R.
(2012). Decision Support Systems – Collaborative Models and Approaches in
Real Environments. Lecture Notes in Business Information Processing,
Springer, Volume 121. DOI: 10.1007/978-3-642-32191-7
• Towill, D.R., “System dynamics, background, methodology and applications”,
IEE Computing and Control Engineering Journal, October 1993, pp201-208 and
pp261-268.
What a System is?
• A system can be broadly defined as an integrated set of
elements that accomplish a defined objective.
• People from different engineering disciplines have
different perspectives of what a “system” is.
For example:
• Software engineers often refer to an integrated set of computer programs as a
“system.”
• Electrical engineers might refer to complex integrated circuits or an integrated
set of electrical units as a “system.”
• As can be seen, “system” depends on one’s perspective, and the “integrated
set of elements that accomplish a defined objective” is an appropriate
definition.
System perspective – relationships
Aggregated
view
System perspective – relationships
Containing
system
Intra
connection
System of
interest
Sub-system
System perspective – relationships
Containing
system
System A System B
System C System D
System E
E = f ( A , B , C , D )
Generally math operators
such as:
+
, -, /, x
Behaviours
Behaviours
Behaviours Behaviours
Behaviours
Dynamic approach of systems
• Changing over
time
• Tightly coupled
• Governed by feedback
• Nonlinear: changing dominant structure
• Adaptive
• Counterintuitive
• Characterised by tradeoffs
• History-dependent
• Policy resistant
System are complex, and they can help us to understand, explain,
anticipate, and make decisions considering an inexact
Representation of the reality.
System Dynamics
System Dynamics
We can make adjustments to the structure which are
consistent with the behaviour we would like to produce.
Behaviour
System Structure
Events
System Dynamics
• Can be seen as the application of control systems
principles to problems associated with;
• Manufacturing management
• Supply Chain
• Logistics
• Forecasting
• Organisations
• Socioeconomics
• Human behaviours
http://www.control-systems-principles.co.uk/
Additional information about control systems
System dynamics for traffic management
System dynamics for population planning
Relationship between states is paramount in system dynamics
System Dynamics – Electric Power Industry
Andrew Forda, System Dynamics and the Electric Power Industry, System Dynamics Review Vol. 13, No. 1, (Spring 1997):
57–85
System Dynamics – Inventory Management
Listl A. Notzon I. 2000 An operational application of system dynamics in the automotive industry: inventory
management at BMW Proceedings of the 18th International Conference of the Systems Dynamic Society Bergen 129 138
System Dynamics – Market model
Weil H. 2007. Application of system dynamics to corporate strategy: the evolution of issues and frameworks. In 50th
Anniversary System Dynamics Conference, Boston, MA.
System Dynamics – Healthcare systems
David Lane, Camilla Monefeldt and Jonathan Rosenhead. Emergency – but no Accident
– a system dynamics study of an accident and emergency department. Operational research society.
System Dynamics – Causal Loop diagrams
▪ Represent the feedback structure of systems
▪ Capture
o The hypotheses about the causes of dynamics
o The important feedbacks
System Dynamics – Causal Loop diagrams
• Bank Balance VS Earned
interest
▪ Bank Balance → Earned interest
▪ Earned interest → Bank Balance
• Study effort VS
Grade
▪ Study effort → Grade
▪ Grade → Study effort
Bank Balance Earned interest
Study effort Grade
Some relationships examples
Causal Loop diagrams – Polarity I
• The polarity information is used to address the positive ‘+’ or
negative ‘–’ relationship between variables. This can provide a
preliminary view and understanding about how the system will
behave.
• Positive relationship/feedback loop: Is represented by the symbol
‘+’ and means that increments in the first variable will generate
increments in the second variable, whether decrements in the first will
generate decrements in the second.
• Negative relationship/feedback loop: Is represented by the symbol
‘–’ and means that increments in the first variable will generate
decrements in the second variable, whether decrements in the first will
generate increments in the second.
Signing Arcs
+
+
+
–
Bank Balance Earned interest Study effort Grade
….FOR INSTANCE ….
Causal Loop diagrams – Polarity II
• Positive feedback loops
• Are represented by the symbol which is located in the centre of
the loop.
• This type of loop tends to generate the well-known “snowball”.
effect in where variable values continues to increase or decrease.
• Generate behaviors of growth, amplify, deviation, and reinforce.
• Negative feedback loops
• Are represented by the symbol which is located in the centre of
the loop.
• Tend to produce “stable”, “balance”, “equilibrium” and “goal-
seeking” behavior over
time
+
–
Bank Balance → Earned interest, Earned interest → Bank Balance
The better my Bank Balance is
The more Interest I earn
The more Interest I earn
The better my Bank Balance is
Causal Loop diagrams – Positive Feedback Loop
+
+
Bank Balance Earned interest+
The more Interest I earn
The better my Bank Balance is
The more grade I get
The more grade I get
The more study effort I made
The more I sleep The less tired I am
–
Causal Loop diagrams – Negative Feedback Loop
Study effort Grade
+
–
Study effort → Grade, Grade→ Study effort
The less study effort I made
The less grade I get
The less grade I get The more study effort I made
Causal Loop diagrams – Loop Dominance
• There are systems which have more than one
feedback loop within them.
• A particular loop in a system of more than one loop
is most responsible for the overall behavior of that
system.
• The dominating loop might shift over time.
• When a feedback loop is within another, one loop
must dominate.
• Stable conditions will exist when negative loops
dominate positive loops.
Causal Loop diagrams – Nested Feedback Loop
Tim Haslett, Charles Osborne, (2000) “Local rules: their application in a system”, International Journal of Operations & Production
Management, Vol. 20 Iss: 9, pp.1078 – 1092
Use of managers
local rates
Delay for
other parts
Speed of return
to stock out bins
Stock outs
Usage rates
Part in bins Posting of kanbans
Manufacturing of parts
Queue length
Delays
+ –
–
–
+
+
+ +
+
+
+
+
–
–
– -+
• Items that affect other items in the system but are
not themselves affected by anything in the system.
• Arrows are drawn from these items but there are no
arrows drawn to these items.
Causal Loop diagrams – exogenous items
-Study effort Grade
+
–
Tougher
environmental
conditions
–
• Items that affect other items in the system but are
not themselves affected by anything in the system.
• Arrows are drawn from these items but there are no
arrows drawn to these items.
Causal Loop diagrams – 2nd example exogenous
+Births Population
+
+
Birth rate
+
Systems often respond sluggishly
Causal Loop diagrams –
delay
s
-Birth School
attendance
+
– Foreign
students
+
Delay
Delay
Birth rate
+
Causal loop diagram – Industry example
• A formal modelling approach based on systems thinking
• It is used for complex problems where system variables change over time
• It specifically applies to problems where feedback plays a significant role
• Example: Sales staff motivation scheme in a niche market
o Sales staff get paid more for more
sales
o Staff are motivated to sell more if they are paid more
o The market has a limited capacity for the product
Motivation
Sales
Income
Productivity
increases
increases
increases
increases
SALES
STAFF
Available
Sales
Decreases
After a
delay
decreases
Market
size
constraint
decreases
MARKET
Cumulative
sales
time
Causal loop diagram – In general
Variable A
Variable B
( + )
Variable A Variable B
( – )
Positive Link:
An increase in A will result in an Increase in B
Negative Link:
An increase in A will result in an decrease in B
Positive Link with time delay:
An increase in A will result in an Increase in B
after a time delay (dt)Variable A Variable B
( + )
| |
Variable A Variable B
( – )
| |
Negative Link with a time delay:
An increase in A will result in an decrease in B
after a time delay (dt)
delay
delay
Causal loop diagram – In general
Variable A
Variable B
Variable C
Variable E
Variable D
( – )
( + )
( + )
( + )
( – )
Positive Loop
(even number of –ve links)
Negative Loop
(odd number of –ve links)
Variable A
Variable B
Variable C
Variable E
Variable D
( – )
( + )
( + )
( – )
( – )
( – )( + )
Basic Behaviour Patterns
time
S-Shape
time time
time
Exponential Goal seeking
Oscillating
Quiz 1
POPULATION BEHAVIOUR
From one study about the population behaviour in one particular area, it has
been found that a relationship between births and deaths exist in order to realise
the current population. The study stands for the fact that birds add to the size of
the population, in where a larger population will tend to have more births in the
future. On the other hand, deaths will reduce the number of population, then a
larger population will tend to have greater number of deaths. In both cases, the
rates of birth and death are an exogenous variable.
• Identify the main elements that define this model and their relationships.
• Build up the causal loop diagram.
• Identify the positive and negative feedback loops linked to this study.
Source: Ford, A. (2009). Modeling the environment , 2nd Edition.
Quiz 2
AUTOMOTIVE MARKET
In this example, the automotive market is defined in a way that the car
production builds the inventory of cars at the dealer. For this, it has been found
that a higher inventory leads to a lower market price, and lower market prices
cause less car production in the future. In terms of the economics of the
environment, if the price of cars were to increase, the retail sale of cars would
tend to fall and, retail sales drain the inventory of cars held in stock at the
dealership. This means that a decline in the inventory will cause the dealers to
raise their prices in the future.
• Identify the main elements that define this model and their relationships.
• Build up the causal loop diagram.
• Identify the positive and negative feedback loops linked to this study.
Source: Ford, A. (2009). Modeling the environment , 2nd Edition.
Quiz 3
POKET MONEY
This quiz is about to model the process when a child receive pocket money from
its parents. On one hand, the more money the parents earn the more money they
are likely to give to their child. On the other hand, the behaviour of the child can
be defined by two feedback loops. The first is oriented to describe the highly
probable fact that spending of the child increases with the available amount of
pocket money, and spending decreases this amount. The other feedback loop
describes the observation that the aunt hands over money to the child whenever it
comes to visit. Nevertheless, the child does not like its aunt too much, so with
increasing budget it is less inclined to see her.
• Identify the main elements that define this model and their relationships.
• Build up the causal loop diagram.
• Identify the positive and negative feedback loops linked to this study.
Source: Binder, T., Vox, A., Belyazid, S., Haraldsson, H. and Svensson, M. (2004)
Developing system dynamics models from causal loop diagrams, presented at the 22nd International
Conference of the System Dynamics. Society, Oxford, UK.
Dr. XINJIE XING
EBUS-504
Operations Modelling and Simulation
Introduction to System Dynamics
University of Liverpool
Management School,
UK
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Lecture 7
Introduction to
Linear Programming
University of Liverpool
Management School,
UK
Linear Programming
▪ Linear programming is used to solve optimization problems where all
the constraints, as well as the objective function, are linear equalities or
inequalities.
▪ Linearity is the property of a mathematical relationship (function) that
can be graphically represented as a straight line.
▪ E.g. mass and weight. W=mg
▪ Newton’s second law. F=ma
Key elements of LP
Linear programming is the method of considering different inequalities
relevant to a situation and calculating the best value that is required to be
obtained in those conditions. Some of the assumptions taken while working
with linear programming:
• The number of constraints should be expressed in the quantitative terms
• The relationship between the constraints and the objective function should be linear
• The objective function can be optimised
Components of LP:
▪ Decision variables
▪ Constraints
▪ Data
▪ Objective functions
Key characteristics
Constraints – The limitations should be expressed in the mathematical form, regarding
the resource.
Objective Function – In a problem, the objective function should be specified in a
quantitative way.
Linearity – The relationship between two or more variables in the function must be linear.
It means that the degree of the variable is one.
Finiteness – There should be finite and infinite input and output numbers. In case, if the
function has infinite factors, the optimal solution is not feasible.
Non-negativity – The variable value should be positive or zero. It should not be a negative
value.
Decision Variables – The decision variable will decide the output. It gives the ultimate
solution of the problem. For any problem, the first step is to identify the decision
variables.
Recall our previous example
Your company is selling A and B two types of carpets. Machine 1, 2, 3 are
used for production. Particularly, production of per square meter A needs
M1 for 1 hour and M2 for 2 hours and production of per square meter B
needs M1 for 1 hour, M2 for 1 hour and M3 for 1 hour. M1 cannot be used
over 300 hours per period, M2 cannot be used over 400 hours per period
and M3 cannot be used over 250 hours per period. The market price for A
is £50/m2 and for B is £100/m2. How many A and B do you plan to
produce per period to get the best revenue?
Mathematical formulation
𝑥1: square meters of A
𝑥2: square meters of B
Objective:
max
𝑥1
𝑥2
50𝑥1 + 100𝑥2
s.t.
𝑥1 + 𝑥2 ≤
300
2𝑥1 + 𝑥2 ≤
400
𝑥2 ≤ 250
𝑥1, 𝑥2 ∈ 𝑅+
Mathematical formulation
max
𝑥1𝑥2
50𝑥1 + 100𝑥2
s.t.
𝑥1 + 𝑥2 ≤ 300
2𝑥1 + 𝑥2 ≤ 400
𝑥2 ≤ 250
𝑥1, 𝑥2 ∈ 𝑅+
1 1
2
0
1
1
𝑥1
𝑥2
≤
300
400
250
50 100
𝑥1
𝑥2
Co-efficient
matrix
Variable
vector
Column
vector
𝑥1 𝑥2
Vectors and matrix
All constraints define the search space of our system. Particularly,
Coefficient matrix: a matrix consisting of the coefficients of the variables in
a set of linear equations. The matrix is used in solving systems of linear
equations.
➢ Its dimension is always 𝑚 ∗ 𝑛.
➢ 𝑚 rows indicate 𝑚 number of constraints.
➢ 𝑛 columns indicate 𝑛 number of variables will be considered.
Decision vectors: a vector space defined by decision variables.
➢ Its dimension is always 𝑛 ∗ 1
Multiplication between matrix and vector
Matrix-vector product
A general form for LP
max 𝑧 = 𝑐𝑇𝑥
s.t. 𝐴𝑥 = 𝑏
𝑥 ≥ 0
Where
𝐴 is the coefficient matrix
𝑐 =
𝑐1
.
.
.
𝑐𝑛
, 𝑏 =
𝑏1
.
.
.
𝑏𝑛
, 𝑥 =
𝑥1
.
.
.
𝑥𝑛
Solve LP graphically
𝑥1 + 𝑥2 ≤ 300
𝑥1
𝑥2
300
300
2𝑥1 + 𝑥2 ≤ 400
400
200
𝑥2 ≤ 250
50𝑥1 + 100𝑥2 = 0
Corner point
Solve LP
What if your LP problem has more than 3 variables?
Use Excel to solve a LP problem
Use Solver function to solve a LP
Build your cells for obj coefficients, coefficient matrix,
column vectors and decision vectors
Use Excel to solve a LP problem
Use Solver function to solve a LP
➢ Define your objective function and constraints
Build your objective function
Build your constraint function
Use Excel to solve a LP problem
Use Solver function to solve a LP
➢ Call solver to solve the problem
The cell for your obj function
The cells for your constraint functions
The cells for your column vector
Proposed exercise
1. A store wants to liquidate 200 of its shirts and 100 pairs of pants from last season. They have
decided to put together two offers, A and B. Offer A is a package of one shirt and a pair of pants
which will sell for 30. Offer B is a package of three shirts and a pair of pants, which will sell for50.
The store does not want to sell less than 20 packages of Offer A and less than 10 of Offer B.
How many packages of each do they have to sell to maximize the money generated from the
promotion?
Formulate your problem accordingly. Use both graphic and Excel solver to find the optimal
solution.
Proposed exercise
1. A factory uses a raw material whose price and availability vary seasonally. The price, availability
and factory requirement for each quarter of the next year are given in the following table.
The cost per ton of storing the material from one quarter to the next is £4 + 10% of the purchase
price. The material may also be stored for two quarters at double the above cost per ton, but will not
keep for longer than two quarters. No stock is held initially and none is required at the end. Find the
pattern of buying and storing that minimises the total cost. State any assumptions that you make.
Formulate your problem accordingly. Use Excel solver to find the optimal solution.
Quarter 1 2 3 4
Price /ton 110 100 120 130
Availability
(tons)
1000 1700 800 400
Requirement
(tons)
750 900 1000 850
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Lecture 7
Introduction to Linear Programming
University of Liverpool
Management School,
UK
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Lecture 4
Bottleneck analysis-2
University of Liverpool
Management School,
UK
Key learning outcomes
1. Bottleneck analysis recap;
2. Understand steady-state;
3. Analysis under uncertainty;
4. Setup uncertain parameters in Witness
5. Use variables and extract data for analysis
Why bottleneck is so important?
1. It defines the maximal throughput rate of your system.
2. It helps modellers quickly locate queues
3. It helps you identify the total outputs at a certain point.
4. It defines the maximal utilisation rate for each entity of your system.
5. Most importantly, it provides further improvement directions.
Any more?
Let’s do with some exercise
1. The production of product A requires a sequential processes and their
operation time is 3mins, 5mins and 7mins respectively;
2. Product A is assembled by 4 components (2Bs, 1C and 1D) with
2mins.
Each type of component requires a pre-processing operation with
machine time 3mins, 5mins, and 4mins respectively.
3. A supermarket has three tills to serve its customers. Each till needs
2mins on average to finish the service and customers arrive the store
every 1min.
4. A line production is comprised by 3 machines with operation time
6mins, 8mins and 4mins respectively. Every machine needs a 2mins
setup by L1 (there is only one labour available) and part arrives every
2mins.
Analytical-based methods
Input rate vs.
output rate
Bottleneck of your system is always identified when input rate is faster than
output rate
The busiest resource (capacity analysis)
Filter out the entity in the system which takes the longest time to complete a job
The most congested place (throughput analysis)
The place where a part takes the longest time to enter and leave it.
Product production lifecycle analysis
From raw material(s) until the completion of an end-product, analysing how
much time in percentage that each component needs to be operated with.
Analytical-based methods
The ultimate rule to determine a bottleneck under a deterministic setting:
“It is the only resource which makes all other resource waiting”:
✓ Any reduction in its utilisation can reduce the overall throughput
✓ Double its capacity can double the utilisation of any other resources if their
current utilisations are below 50%.
Analytical-based methods
Pros:
✓ Easy to build an overall understanding of your system;
✓ Helpful for model validation purposes;
✓ Light up the initial system improvement plans;
✓ Very effective for deterministic models;
Cons:
❖ Hard to identify the bottleneck when system structure is complex;
❖ Ineffective for stochastic models;
❖ Hard to capture all model details (good for long-term planning but not
short-term)
❖ Can be time consuming and potential human errors
Simulation-based methods
a) Methods based on machine utilisations
Simulating your model and determine the bottleneck based on the largest
average machine cycle time or the largest machine utilisation.
b) Methods based on waiting times or queue lengths
Simulating your model and the bottleneck should be at the process with the
largest DROP in waiting time or LONGEST queue length.
Simulation-based methods
c) The Arrow Method Based on Starving and Blocking
If the frequency of manufacturing blockage of machine m_i is larger than the
frequency of manufacturing starvation of machine m_i+1, the bottleneck is
downstream of machine of machine m_i. If the frequency of the manufacturing
starvation of machine m_i is larger than the frequency of manufacturing
blockage of m_i-1, the bottleneck is upstream of machine m_i.
Simulation-based methods
d) The “turning point” method
Key concepts:
1. a bottleneck machine will often make the upstream machines blocked and
downstream machines starved.
2. a bottleneck machine will also have a lower overall sum of blockage and
starvation time.
Simulation-based methods
d) The “turning point” method
Simulation-based methods
e) machine production rate sensitivity analysis
the most critical bottleneck machine has the highest sensitivity value of the
system production rate to a machine’s production rate.
i.e.
system system
i j
PR PR
j i
PR PR
Increase the
production rate of
the potential
bottleneck with the
same percentage
Compare the
increase of system
production rate
from each round
Determine the
bottleneck which
leads the highest
system production
rate increase
Simulation-based methods
e) machine production rate sensitivity analysis
the most critical bottleneck machine has the highest sensitivity value of the
system production rate to a machine’s production rate.
Simulation-based methods
Pros:
✓ Easy to detect the bottleneck;
✓ Effective for large scale problems;
✓ It can handle stochastic systems;
Cons:
❖ Hard to see the rationale behind the results, it tells you “where” and
“what” but not “why”;
❖ Errors of simulation model can lead to wrong detection;
❖ It requires analytical support to draw the final conclusion in some
cases.
Resume our discussion about queues
1. How do we know the waiting time for the 10th part? 50th part? Or the nth
part?
2. How do we know the queue size at minute 50? Or minute 100? Or the
nth minute?
2mins 1min 8mins 4mins
Resume our discussion about queues
1. Mathematical induction
➢ The 2nd part: 6 mins
➢ The 3rd part: 3mins + 8mins
➢ The 4th part: 8mins + 8mins
➢ The 5th part: 5mins + 8mins + 8mins
➢ The 6th part: 2mins + 8mins + 8mins + 8mins
➢ The 7th part: 7mins + 8mins + 8mins + 8mins
➢ The 8th part: 4mins + 8mins + 8mins + 8mins + 8mins
What do you see from above? Can you conclude a generic formulation using
nth part, bottleneck cycle time T_b and part inter-arrival time T_a?
Resume our discussion about queues
When n=1
W_n=0;
When n>=2
W_n = W_(n-1) – T_a + T_b
Why?
Resume our discussion about queues
When n=1
W_n=0;
When n>=2
W_n = W_(n-1) – T_a + T_b
Why?
Resume our discussion about queues
Let’s change our angle
The nth part
Arriving at what
time makes it no
waiting?
What is the actual
arriving time?
Why the first one is different? – steady state analysis
Steady state:
In systems theory, a system or a process is in a steady state if the
variables which define the behaviour of the system or the process are
unchanging in time
1. Why do we need to exclude warm-up period?
2. How do we determine warm-up period?
Steady-state analysis
1. In a deterministic setting:
The system is deemed to show a repetitive pattern as long as the
simulation run is long enough.
2. In a stochastic setting:
The stochastic processes associated with the output variables of interest
become stationary.
o For example, if the inter arrival time of a part is following a Poisson
distribution or a normal distribution.
Steady-state analysis
Source from: Birta and Arbez (2013)
Steady-state analysis
✓ Selecting the size of the time cells (e.g. Every 5 minutes)
✓ Determine the total number of time cells
✓ Determine the number of replications
✓ Obtain the value as the average over the n replications of the i th cell
averages ( i.e. assuming i is the index for the i th cell and j is the index
for the j replication), then we have:
ia
,i jy
Steady-state analysis
Welch’s moving average method:
If plotted against index i, the resulting graph is ‘choppy’ and difficult to interpret
We introduce a smoothing operation to smooth out the rapid variations to
obtain a smoother curve that captures the long-run trend.
is a moving average value and parameter w represents a window
size that controls the smoothing operation.
( )ia w
Steady-state analysis
When i <= w, there
are not enough
values preceding
time cell I to fill the
window so we use (i-
1) replace w.
Steady-state analysis
ia (3)ia
(5)ia
The larger the window size, the smooth
plot you’ll get, but less details can be
captured.
Use Witness to help statistics
✓ Define random parameters
o E.g. Normal distribution syntax: normal(mean, SD, random stream);
Use Witness to help statistics
✓ Create and use variables
Use Witness to help statistics
✓ Create and use variables
Use Witness to help statistics
How do we define a time cell and continuously extract data to
Excel worksheet?
Use Witness to help statistics
✓ Use dummy parts and counter variable
Use Witness to help statistics
✓ Use dummy parts and counter variable
Use Witness to help statistics
✓ Corrected solution
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Lecture 4
Bottleneck analysis-4
University of Liverpool
Management School,
UK
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Lecture 6
Introduction to optimization
University of Liverpool
Management School,
UK
Key learning outcomes
1. Concept of optimisation
2. Use charts in Witness
3. Use advanced experimenter for obtaining optimal solutions
Improve bottleneck
Run the sample model from Week 5 to 1000 minutes
Where is bottleneck?
Improve bottleneck
Use pie chart to help find bottleneck
Go to Element States tab
Find your
target
element
Improve bottleneck
Create pie charts for all machines and run the model again
How do we interpret this result?
Improve bottleneck
See the demo on Witness for bottleneck analysis
Question:
Where is the end of our improvements?
How do we make such decisions in real world?
Optimisation
The field of “optimization” is concerned with how this process
can be quantitatively modelled, and, within the bounds of these
quantitative models, how the best decisions can be made.
▪ At the centre of every policy or planning decision are choices intended
to achieve one or more outcomes
▪ It is “the science of better.” This field is often known as operations
research, and has close ties with industrial or systems engineering.
Optimisation
What is an optimisation problem comprised of?
▪ An
objective function
: a single quantity to be either maximised or
minimised. E.g. the minimised costs, maximised safety etc.
▪ Decision variables: aspects of the problem that decision makers have
control over. E.g. number of machines, procurement frequencies etc.
▪ Constraints: Any kind of limitation on the values that the decision
variables they take. E.g. limited resources such as total amount of
budget, certain standards such as maintenance times, or some trivial
ones such as outputs can’t be negative.
A few examples
Example 1 – You have 60 feet of fence available, and wish to
enclose the largest rectangular area possible. What dimensions
should you choose for the fenced-off area?
Solution: The objective is clear from the problem statement: you wish to maximize the
area enclosed by the fence. The decision variables are not directly given in the problem.
Rather, you are told that you must enclose a rectangular area. To determine a rectangle,
you need to make two decisions: its length and its width. These are both decision
variables you can control directly, and there are no indirect decision variables because the
length and width directly determine its area. There is one obvious constraint — the
perimeter of the fence cannot exceed 60 feet — and two less obvious ones: the length and
width must be nonnegative. Since the length and width are independent of each other (the
perimetric constraint notwithstanding), there is no need to add a “consistency constraint”
linking them
A few examples
Simple mathematical formulation
L represents length
W represents width
Objective: max
𝐿,𝑊
𝐿𝑊
s.t. (subject to)
2𝐿
+
2𝑊 ≤ 60
𝐿,𝑊 ∈ 𝑅+
A few examples
Example 2 – Your company is selling A and B two products. Machine 1,
2, 3 are needed for processing them. Particularly, one final product A
needs M1 for 1 hour and M2 for 2 hours and one final product B needs M1
for 1 hour, M2 for 1 hour and M3 for 1 hour. M1 cannot be used over 300
hours per period, M2 cannot be used over 400 hours per period and M3
cannot be used over 250 hours per period. The market price for A is £50
and for B is £100. How do you plan your production per period to get the
best revenue?
Can you write the mathematical formulation?
A few examples
Answer:
𝑥1: number of A
𝑥2: number of B
Objective: max
𝑥1𝑥2
50𝑥1 + 100𝑥2
s.t.
𝑥1 + 𝑥2 ≤ 300
2𝑥1 + 𝑥2 ≤ 400
𝑥2 ≤ 250
𝑥1, 𝑥2 ∈ 𝑍
+
Optimisation
The next question is: how do we solve those problems?
Use experimenter in Witness to solve problem
Each A5 can be sold for £2000. A new M1-4 costs you £13000. Increasing
every 25% efficiency for M1-4 costs you £3800 and increasing the
efficiency for C1-C3 costs you £4000 per 10%. If you are given £30000 to
spend, how will you make your investment decisions?
Experimenter function
Investment decision on
machine efficiency
Investment decision on
conveyor efficiency
Effects of decision variables
Experimenter function
Auxiliary variables
used for
objective function and
constraints
Additional auxiliary variables
used for constraints
Experimenter function
Use function element to define
objective function
Experimenter function
Use advanced experiment mode
to find the optimal solution
Experimenter function
Add new parameters
Parameters: all associated decision variables + some
auxiliary variables
Constraints: conditions that limits your optimisation
Responses: your objective function
Minimum & Maximum: The range for your
decision variable
Step size: How do you change the value
when search for optimal in each scenario
Suggested: Initial search value for your
decision variable
Experimenter function
The full variable list
New machine decisions
Conveyor efficiency decisions
Machine efficiency decisions
Auxiliary variables
Experimenter function
Constraint: all spendings are no more than £30000
Coefficient for each variable
Constraint condition
Click “Add” after the below
information is populated
Experimenter function
Response: Function001
Since Function 001 is already
defined, so we just need to select it
as our objective function
You can also manually write your function in this box as well
Experimenter function
Run your solver
Make sure your objective function is
selected here
Click it to run
Experimenter function
Retrieve your solution
Red line shows the best optimal value and blue line shows
the actual objective value in each scenario
Click here for results
Solution set for each scenario
Final
Can you find the optimal solution for our Example 2
(Page 12) with Witness experimenter function?
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Lecture 6
Introduction to optimization
University of Liverpool
Management School,
UK
Dr. XINJIE XING
EBUS-5
0
4
Operations Modelling and Simulation
Vensim modelling and analysis
University of Liverpool
Management S
c
hool,
UK
Key Benefits of the ST/
SD
• A deeper level of learning
• Far better than a mere verbal description
• A clear structural representation of the
problem or process
• A way to e
x
tract the behavioral implications
from the structure and dat
a
• A “hands on” tool on which to conduct WHAT
IF
Stock and Flow Notation–Quantities
• STOCK
• RATE
•
Auxiliary
Stock
Rate
i
1
i
2
i
3
Auxiliary
o1
o2
o3
•
Input/Parameter/Lookup
• Have no edges directed toward them
• Output
• Have no edges directed away from them
i1
i2
i3
Auxiliary
o1
o2
o3
Stock and Flow Notation–Quantities
Inputs and Outputs
• Inputs
• Parameters
• Lookups
• Outputs
Input/Parameter/Lookup
a
b
c
Stock and Flow Notation–edges
• Information
• Flow
a b
x
Some rules
• There are two types of causal links in causal models
• Information
• Flow
• Information proceeds from stocks and
parameters/inputs toward rates where it is used to
control flows
• Flow edges proceed from rates to states (stocks) in
the causal diagram always
q1
q2
q3
q4
q
5
q
6
q
7
q
8
Causal loop example
q3
q6
q2
q7
q1
q4
q5 q8
System dynamic model equivalent –
EXAMPLE
Manual Simulation example
INVENTORY MANAGEMENT
Manual Simulation example
INVENTORY MANAGEMENT
Lets do the Maths!!
SCARED???
Manual Simulation example
INVENTORY MANAGEMENT
Lets do the Maths!!
SD to the rescue!!
SD
Manual Simulation example – Lets do the
Maths
INVENTORY MANAGEMENT
The SD Model
Manual Simulation example – Lets do the
Maths
INVENTORY MANAGEMENT
Information’s Patterns
Production
11
1 1
Manual Simulation example – Lets do the
Maths
INVENTORY MANAGEMENT
Information’s Patterns
Sales
5
3
13
2
0
Manual Simulation example – Lets do the
Maths
INVENTORY MANAGEMENT
The Maths
Inventory behaviour
Production-sales
=
30
(initial value)
Manual Simulation example – Lets do the
Maths
INVENTORY MANAGEMENT
The Maths
Period Production Inventory Sales
1
2
3
4
5
6
7
8
9
10
i = Period i
Inventory[i]
=
Inventory[i-1]+(Production[i-1]-Sales[i-1])
Inventory[1]
=
Inventory[0]+(Production[0]-Sales[0])
Inventory[1]
=
30+(0-0)
30
Manual Simulation example – Lets do the
Maths
INVENTORY MANAGEMENT
The Maths
Period Production Inventory Sales
0
1
2
3
4
5
6
7
8
9
10
i = Period i
Inventory[i]
=
Inventory[i-1]+(Production[i-1]-Sales[i-1])
1
1
1
11
11
11
1
1
1
1
30
31
32
24
32
40
28
48
36
34
0
0
5
3
3
3
5
13
2
2
Inventory[1]
=
Inventory[0]+(Production[0]-Sales[0])
Inventory[1]
=
30+(0-0)
30
1 233
Manual Simulation example – Lets do the
Maths
INVENTORY MANAGEMENT
Information’s Patterns
Inventory
30
31 32
24
32
40
28
48
36
34
Recall the after-class model from Lab 5
From the system description, the preliminary causal loop diagram can be
drawn as follows
Recall the after-class model from Lab 5
Question 2: Carefully analyse the results from the model. Check
production, workforce and inventory graphs. Are results correct? Is
there any fundemental error in the model? If so, what is it?
Vensim modeling for production management
without stockout
Question 2: Carefully analyse the results from the original model. Check
production, workforce and inventory graphs. Are results correct? Is
there any fundemental error in the model? If so, what is it?
– At some point during the horizon, inventory goes into negative
– However, this is not allowed according to the description
– Why inventory goes below zero?
Vensim modeling for production management
without stockout
Question 2: Carefully analyse the results from the model. Check
production, workforce and inventory graphs. Are results correct? Is
there any fundemental error in the model? If so, what is it?
– Why inventory goes below zero?
– Production cannot ramp up swiftly to match the sales increase
– You can observe sales graph increases stepwise, while
production graph increases gradually
– This is due to the fact that you need to hire new workers to
produce items and it takes 10 months to adjust workforce
How to prevent inventory to go below zero?
– Target production can be set to a value higher than sales
– Inventory coverage period can be imposed
– You may want to cover 3 months of inventory in your target production.
– Therefore;
– Target Inventory = Inventory coverage(3)* Sales
– Then you should obtain a set of new inventory amount which is
– (Target Inventory – Inventory)
– Asssume that you want inventory to be corrected in 2 months (Time to adjust
inventory)
– Therefore;
– Inventory correction = (Target Inventory – Inventory)/Time to adjust
invetory
– SO TARGET PRODUCTION SHOULD ACTUALLY BE:
– Target Production = Sales + Inventory correction
How to prevent inventory to go below zero?
Results for updated system dynamics model
Some typical examples – A Linear Graph
Source: Adapted from Maryland Virtual High School
A Linear Model
Problem Change in Y
Y
1 acceleration speed
2 weekly allowance savings
3 faucet output in gal/min volume of water in
bathtub in gal
Source: Adapted from Maryland Virtual High School
4. Graph the amount of radioactive material as it decays over time.
5. Graph the amount of money left in my son’s savings from his summer
job if his weekly spending is a fixed percentage of the money still in
his savings.
6. Graph the temperature of a cup of coffee as it cools to room
temperature.
How are these problems similar?
Source: Adapted from Maryland Virtual High School
Exponential Decay
Source: Adapted from Maryland Virtual High School
A Decay Model
Problem Change in Y Y
4 A fraction of the isotope radioactive isotope
5 A fraction of savings savings
6 A fraction of the
difference between
coffee and room
temperatures
coffee temperature
Source: Adapted from Maryland Virtual High School
7. Graph the number of burnt trees in a forest fire as trees are
transformed from living to burning to burnt.
8. Graph the number of immune people as people progress from being
healthy to being sick to recovering to become immune to the
disease.
How are these problems similar?
Source: Adapted from Maryland Virtual High School
Bounded Growth
Source: Adapted from Maryland Virtual High School
Transformation to Bounded Growth
Problem X Change in X Y Change in
Y
Z
7 Green
trees
Catch fire
rate
Burning
trees
Burnt out
rate
Burnt trees
8 Healthy
people
Get sick rate Sick
people
Recovery
rate
Immune
people
Source: Adapted from Maryland Virtual High School
9. Graph two populations, the predator and its prey, for a period of many
years.
10. Graph glucose and insulin levels during a day in which three meals are
eaten at regular intervals.
11. Graph the motion of a frictionless vertical spring.
How are these problems similar?
Source: Adapted from Maryland Virtual High School
Periodic Behavior
Source: Adapted from Maryland Virtual High School
Interdependence
Source: Adapted from Maryland Virtual High School
Interdependent stocks
• We can understand the industrial
environment as a set of stocks and
activities linked by flow of information
and flow of material, submitted to time
delays.
• For example, we can represent a
company as a set of aggregates
stocks.
Exercise
Consider a store where people enter, receive
some service, then move to the cash register
and have to wait in a checkout line before
they can pay
and leave.
Only one person can
be served at a time, and initially one person is
already at the service center being served. It
takes 5 minutes to be served and 1 minute to
get from the service center to the checkout
line. There are already 8 people waiting in the
checkout that last 2 minutes, and one person
is currently being served. One customer
arrives every 4 minutes and the first customer
arrives in the third minute after we began the
analysis
Identified beviours
• people enter,
• receive some service, then
• move to the cash register and
• have to wait in a checkout line before they can pay
and leave.
• Problems from different disciplines can be
represented by similar model structures.
(Goal 1)
• Graphing the expected output for a model can show
the expected model structure, including the variables
and the rates of change between variables.
(Goal 2)
• Each model structure has particular mathematical
relationships between its variables and their rates of
change.
(Goal 3)
What have we learned?
Dr. XINJIE XING
EBUS-504
Operations Modelling and Simulation
Vensim modelling and analysis
University of Liverpool
Management School,
UK
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Lecture 5
Use of variables and attributes
University of Liverpool
Management School,
UK
Key learning outcomes
1. What are variables and attributes?
2. Use variables and attributes under different scenarios
3. Use variables and attributes in Witness to improve your
model
Recall the definitions
Variables
Variables provide an abstraction for features of the model whose values typically change as the
model evolves over the course of the observation interval
Attributes
• Characteristic of all entities: describe, differentiate
• All entities have same attribute “slots” but different values for different entities, for example:
• Time of arrival
• Due date
• Priority
• Color
• Attribute value tied to a specific entity
• Like “local” (to entities) variables
• Some automatic in Arena, some you define
Recall the definitions
Variables Attributes
Independent Attached to one group of entities
Their values change as model evolves Each entity can have a collection of attributes
Information under one attribute remain unchanged
e.g. e.g.
Number of outputs the colour of your parts
Time to despatch a delivery the number of components for an assembly
Number of serviced customers/day the age of someone in 2020
A simple scenario
A simple scenario
, B3, B4
, B2, B4
, B2, B4
A simple scenario
A simple scenario
M1 Logic
A simple scenario
M2,3,4 Logic
A simple scenario
A simple scenario
Free set of questions
• Q1: How many parts have arrived from each kind?
• Q2: For how long they are in the
system?
• Q3: Which buffer holds the most of the parts?
• Q4: How long does each part wait in every buffer or conveyor?
• Q5: In average, how long does it take to generate one A5?
A simple scenario
A simple scenario
In the following example, an attribute will be created in order to
capture the arrival time from Part A2, A3, A4 to B2, B3 and B4.
Therefore, we will calculate how long a part a A2, A3, and A4 stay at
each buffer.
In order to calculate this time, three variables are going to be
created, which will capture this time.
In Witness, we use the internal variable TIME to know the exact time
of the simulation.
A simple scenario
Attr_A2_Time_in: attribute that captures the arrival time for A2 to
B2. In this case, at B2 Actions on input the following expression is
considered: Attr_A2_Time_in = Time
Remark: it will be the same for A3 and A4.
A simple scenario
A2_waiting, A3_waiting and A4_waiting are variables
representing the total waiting time for the most recent outputted A2,
A3, and A4 in their corresponding buffers.
At Actions on output in each buffer, we have:
A2_waiting = TIME – Attr_A2_Time_in
A3_waiting = TIME – Attr_A3_Time_in
A4_waiting = TIME – Attr_A4_Time_in
Why not attributes here?
A simple scenario
Run simulation to 1000 minutes
Proposed Exercise
1. Numbers of parts A1, A2, A3, A4, and A5 generated;
2. Time it takes to generate a part A5
3. How long does it take for the 100th A5 to be produced?
New scenarios
Company ABC purchases a group of white balls to produce different
final products. The purchasing will be done every 10 minute with
batch size 5 and there is 2 balls in initial stock. M1 can paint all the
white balls (one at a time and it costs 3 minutes) into three different
colours (blue, red and green). Then based on the colour of a ball, a
blue ball will be further processed by M2-M3 and red ball will be
further processed by M3-M4 and a green ball will be further
processed by M2-M4. All M2, M3, M4 are single machines with cycle
time 5 minutes.
How can we use variables and attributes to better simulate above
system?
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Lecture 5
Use of variables and attributes
University of Liverpool
Management School,
UK
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Lecture 1
Principles of
Simulation and modelling
University of Liverpool
Management School,
UK
Background of your lecturer
Dr. Xinjie (Daniel) Xing. Module leader – x.xing3@liverpool.ac.uk
o Senior lecturer in operations management (deputy director for BABD programme)
o PhD in operations research in maritime logistics
o Research interests lie in transport & logistics, sustainable supply chain, and
blockchain applications.
o Publications available at world leading journals such EJOR, TRE, IJOPM, ANOR etc.
o Leading a few (both internal and external) research projects in logistics and
blockchain fields.
Office hours: appointment by emails (email manners!!)
Email turnaround time: Three working days (i.e. exclude weekends and national holidays).
mailto:x.xing3@liverpool.ac.uk
Objective
Learning objective from this module
• Understand the dynamic nature of systems and their behavioural characteristics
• Understand a range of modelling analytical methods and their appropriate applications
• Understand how models are developed, tested and validated from real system
• Understand basic concepts of optimisation
• Be confident in use of commercially available tools (Witness, Vensim and Matlab)
Curriculum overview
• 1. Introduction to modelling and simulation and first look of Witness(wk1)
• 2. Process mapping techniques + Witness functions and advance rules (wk2)
• 3. Model state analysis + Bottleneck analysis (wk3)
• 4. Bottleneck analysis 2 and queues (wk4)
• 5. Use of variables and attributes (wk5)
• 6. Optimisation in Witness (wk6)
• 7. Introduction to linear programming and integer programming (wk7&8) (Matlab
application)
• 8.
System
dynamics (wk9-11) （Vensim application）
• 9. Revision week (wk12)
System
System
System
System
A collection of interacting entities that produces some form of
behaviour that can be observed over an interval of time (Birta
and
Arbez, 2013
).
It is inherently complex with high level of granularity.
Example of systems:
Tangible:
1. Transportation system
2. Power-generating system
3. Warehouse system
Intangible:
1. Health care system
2. Social systems
3. Economic systems
Modelling and simulation
Models and real world systems
Types of systems
A discrete system is one in which the state variables change
only at discrete or countable points in time.
✓ Customers arrives at different time points
✓ Car production scheduling
A continuous system is one in which the state variables change
continuously over time.
✓ The amount of water flow over a dam
✓ Vibration of materials
✓ Evaluation of radioactive decay
From system to modelling and simulation
1. Cost effective approach for analysis
It is always resource consuming to run the actual system for analysis purposes.
2. Simplification
A real system contains many branches and noises which cause difficulties for
understanding its key behaviours and logic.
3. Repetition
For various reasons, the run of a system cannot be slowed down or rewinded.
4. Hazards
Some systems are highly uncertain and hazards involved, which may not easy to be
observed or analysed directly.
Simulation and modelling
Simulation and modelling refer to a type of tools which helps to
gain insight into features of systems’ behaviours.
✓ A model is a representation or abstraction of the system under
investigation (the SUI)
✓ Normally computer-based but not always (manual simulation will be
discussed in later slides)
Role of modelling and simulation:
1. Comparison of control policy options;
2. Education and training;
3. Engineering design;
4. Evaluation of decision or action
alternatives;
5. Evaluation of strategies for
transformation or change;
6. Forecasting;
7. Prototyping and concept evaluation;
8. Risk/safety assessment;
9. Uncertainty reduction in decision
making;
Pros and Cons of simulation modelling
Advantages:
1. Cheaper to execute;
2. Alternative strategies for
dangerous scenarios;
3. Saves time;
4. Get away with anything morally or
ethically unacceptable (e.g.
assessing radiation dispersion);
5. Effective tool for something
irreversible (e.g. change of country
policy)
Disadvantages:
1. Inappropriate statement of goals
(project management);
2. Inappropriate granularity of the
model;
3. Ignoring unexpected behaviour;
4. Inappropriate mix of essential
skills;
5. Inadequate flow of information to
the client (big data management);
Building a Simulation Model
3. STRUCTURED
WALK-THROUGH
2. PROBLEM
FORMULATION
1. DATA AND
MODEL DEFINITION
6. VALIDATE
MODEL
5. PERFORM
PILOT
RUNS
4. BUILD MODEL
AND VERIFY
10. DOCUMENT AND
IMPLEMENT RESULTS
9. ANALYSE OUTPUT
DATA
8. MAKE PRODUCTION
RUNS
7. DESIGN
EXPERIMENTS
•Define goals, boundaries, and assumptions;
• Define concepts (entities, attributes, event list, etc…)
• Define interactions and relationships;
• Define data
Define your model
– Goals
What is the ultimate purpose of the SUI?
What are the key indicators of the SUI?
– Boundaries
The context of the model (geographical boundaries, physical
boundaries, timeframes etc.)?
What terminates the
model?
– Assumptions
Level of granularity
Effective simplification to achieve the goal
Goals, boundaries, and assumptions
System goals
• Objectives must be clear and specific and agreed upon.
• Some Examples of Objectives
o Identify the best design to meet output targets
o Identify the optimum number of operators/machines/vehicles etc. to use
o Maximise the utilisation of resources
o Identify the maximum output you can produce from a system
o Identify the main bottleneck resources
o How to improve performance of —–?
o What is the impact of changing ——-?
o Where is the waste in the system?
o Which of these scenarios do I adopt?
System Boundary
• Academic Institution
✓ Academic Department
✓ Academic Programme
✓ Computer Services Department
▪ Manufacturing Company
✓ Subsidiary
✓ Accounts Department
✓ Manufacturing System
✓ Materials Management
• Retail Sector
✓ One Shop
✓ Computer System
✓ Logistics
System
System
System
A group of
interrelated elements
operating to achieve
a goal.
Quick questions
• Why clear definitions of model goals are critical to modelling
projects?
• How does a model goal affect the future project
implementation?
• How does a model goal affect the boundary definition of a
model?
Pieces of a Simulation Model
• Entities
• “Players” that move around, change status, affect and are affected by other
entities
• Dynamic objects — get created, move around, leave (maybe)
• Usually represent “real” things
• Our model: entities are the parts
• Can have “fake” entities for modeling “tricks”
• Breakdown demon, break angel
Though Arena has built-in ways to model these examples directly
• Usually have multiple realizations floating around
• Can have different types of entities concurrently
• Usually, identifying the types of entities is the first thing to do in building a
model
Examples of entities
Birta and
Arbez, 2013
Data Collection
• Internal Documents
• Observations (Work Study)
• Survey data
o Internal: company specific
o External: Industry/Sector standards, Benchmarking
• Own Knowledge
• Interviews with experts
o Fact finding
o Problem identification
o Solution Review
Define your data
• Constant and parameters – serve simply as names for the values of features
or properties within a model which remain invariant over the course of any
particular experiment with the model
• Time and other variables – Variables provide an abstraction for features of
the model whose values typically change as the model evolves over the course of
the observation interval. Time is a special variable: (1) never depend upon any
other variables; (2) most other variables are dependent on time
• Input, state and output variables – Variables for defining the specifications
of the inputs, and outputs of the SUI and dynamic behaviors of different entities
within the SUI
Pieces of a Simulation Model
• Attributes
• Characteristic of all entities: describe, differentiate
• All entities have same attribute “slots” but different values for different
entities, for example:
• Time of arrival
• Due date
• Priority
• Color
• Attribute value tied to a specific entity
• Like “local” (to entities) variables
• Some automatic in Arena, some you define
Pieces of a Simulation Model
• Event
An instantaneous occurrence that changes the state of a system (such
as the completion of a service, or the arrival of an entity).
• Event notice
A record of an event to occur at the current or some future time, along
with any associated data necessary to execute the event; at a minimum
the record includes the event type and the event time.
• Event list
A list of event notices for future events, ordered by time of occurrence;
also known as the Future Events List.
Pieces of a Simulation Model
• Activity
A duration of time of specified length (e.g. a service time or inter-arrival
time), which is known when it begins (although it may be defined in
terms of a statistical distribution).
• Delay
A duration of time of unspecified indefinite length, which is not known
until it ends (e.g. a customer’s delay in a last-in-first-out waiting line
which, when it begins, depends on future arrivals).
• Simulation Clock
A variable representing simulated time.
Simulator Elements
Exercise
• Company ABC is a car parts supplier focusing on side panels and car floors. They
currently have 5 moulds and two ovens used for making panels. 3 different side panels
are being produced and each of them require different raw materials and production
processes. Both ovens are automatic and are associated with the same unit production
costs and unit carbon emission rate. All the panels need to be fully cooled down in a
cooling pool before they are split from moulds. Also, floor mats are being produced in
parrel by a different machine, but they share the same painting station with panels.
Some labours are required to do painting and setup oven. Each panel has its own
market price and they can also be bundled (and with floors) for different bundle prices
as well.
(a) Develop a list of possible goals for this model?
(b) Define the different data to be used by this model. (e.g. entities? Parameters?
Variables? Attributes? Events? Etc.)
Building a Simulation Model
3. STRUCTURED
WALK-THROUGH
2. PROBLEM
FORMULATION
1. DATA AND
MODEL DEFINITION
6. VALIDATE
MODEL
5. PERFORM
PILOT RUNS
4. BUILD MODEL
AND VERIFY
10. DOCUMENT AND
IMPLEMENT RESULTS
9. ANALYSE OUTPUT
DATA
8. MAKE PRODUCTION
RUNS
7. DESIGN
EXPERIMENTS
Model formulation and conceptual model
“Model formulation is the step where our knowledge of a natural system is
translated in mathematical form.” (Soetaert and Herman, 2009)
❖ It is primarily quantitative but can be supported with qualitative
descriptions;
❖ It is the first key document of modelling and simulation;
❖ Normally supported with charts and graphs;
❖ It helps to build the conceptual model
Conceptual Model is a refinement process that consolidates all relevant
structural and behavioural features of a SUI in a concise and precise
manner.
Examples of conceptual model and the corresponding
model formulation
Xing et al. (2022)
Example of conceptual model
Project-based learning process
Company ABC uses 5 moulds to produce side panels for its car manufacturer.
There are currently 2 automatic ovens are being used and side panel A, B, & C
need to be produced. Each side panel requires the use of different raw materials,
different heating time in ovens and each material has different procurement
settings. There are currently 3 labours working in the shopfloor to set up ovens
and split panels from moulds. All moulds need to be fully cooled down in cooling
before they are split and returned back to use. Side panels can be despatched
for sales after split process.
➢ Freely select your group members and your team can work on
this project together throughout the whole semester.
➢ New challenges will be added continuously.
➢ Part of the project results will be used for your final assessment.
✓ Beginning of your project
First look of Witness and build the first model for your
project
Please see separate slides for the intro of Witness.
✓ Build your first sample model
Panel type: A
Required materials: P1- coming every 4 mins with lot size 1 (and
one mould: no need at this moment!!)
Machines: Oven (configuration 3 mins, process time 5 mins), Split
(2 mins)
Buffers: Cooling and storages.
Labour: L1
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Lecture 1
Principles of Simulation and modelling
University of Liverpool
Management School,
UK
Dr. Daniel Xing(x.xing3@liverpool.ac.uk)
EBUS-504
Operations Modelling and Simulation
System Dynamic software: Vensim
University of Liverpool
Management School,
UK
mailto:x.xing3@liverpool.ac.uk
Menu and Tool Bar
Source: ®VENSIM 2012
Layout
Source: ®VENSIM 2012
MENU
• File : Open Model, Save, Print, dll.
• Edit : copy and paste, search, dll
• View : manipulating the sketch of the model and for viewing a model
• Layout : manipulate the position and size of elements in the sketch.
• Model : Simulation Control and the Time Bounds dialogs, the model
checking features, and importing and exporting datasets.
• Tools : sets Vensim’s global options and allows you to manipulate Analysis
tools
• Windows : to switch among different open windows.
• Help : provides access to the on-line help system.
Source: ®VENSIM 2012
Toolbar
Source: ®VENSIM 2012
Sketch
Tools
Lock — sketch is locked.
Move/Size — move, sizes and selects sketch objects: variables, arrows, etc.
Variable — creates variables ( Constants , Auxiliaries and Data).
Box Variable — create variables with a box shape (used for Levels or Stocks).
Arrow — creates straight or curved arrows.
Rate — creates Rate (or flow) construct
Model Variable — adds an existing model variable
Shadow Variable — adds as a shadow variable
Merge — merges two variables into a single variable, etc
Input Output Object — adds input Sliders and output graphs and tables to the sketch.
Sketch Comment — adds comments and pictures to the sketch.
Unhide Wand — unhides (makes visible) variables in a sketch view.
Hide Wand — hides variables in a sketch view.
Delete — deletes structure, variables in the model, and comments in a sketch.
Equations — creates and edits model equations using the Equation Editor.
Reference Modes — use to draw and edit reference models.
Source: ®VENSIM 2012
Tools
Source: ®VENSIM 2012
Tools
Source: ®VENSIM 2012
Tools
Source: ®VENSIM 2012
Analysis Tool Output
Source: ®VENSIM 2012
• Variable allows you to choose a variable in your model and select it as the
Workbench Variable.
• Time Axis allows you to change or focus the period of time over which
Analysis tools operate.
• Scaling enables you to change the scales of output graphs.
• Datasets allows you to manipulate the stored datasets (runs).
• Graphs brings up the Custom Graph Control.
• Placeholders is a control that sets Placeholder Values
Control Panel
Source: ®VENSIM 2012
Source: ®VENSIM 2012
Code behind the model
Source: ®VENSIM 2012
Operators
Source: ®VENSIM 2012
Example notation
Source: ®VENSIM 2012
Settings
Source: ®VENSIM 2012
Settings – iInfo/Psswd
Source: ®VENSIM 2012
Settings – Sketch
Source: ®VENSIM 2012
Settings – units
Source: ®VENSIM 2012
Dr. Daniel Xing(x.xing3@liverpool.ac.uk)
EBUS-504
Operations Modelling and Simulation
System Dynamic software: Vensim
University of Liverpool
Management School,
UK
mailto:x.xing3@liverpool.ac.uk
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-50
4
Operations Modelling and Simulation
Lecture
2
Process mapping techniques + Witness functions
University of Liverpool
Management School,
UK
Objective
Learning objective from today
• Understand different types of process mapping tools
• Witness:
✓ Displays and element details
✓ Buffers, machines, parts and conveyors
✓ Input and output rules
✓ Labours and configuration for setup
✓ Route function
Building a Simulation Model
3. STRUCTURED
WALK-THROUGH
2. DATA A
N
D
MODEL DEFINITION
1. PROBLEM
FORMULATION
6. VALIDATE
MODEL
5. PERFORM
PILOT
RUNS
4. BUILD MODEL
AND VERIF
Y
10. DOCUMENT AND
IMPLEMENT RESULTS
9. ANALYSE OUTPUT
DATA
8. MAKE PRODUCTION
RUNS
7. DESIGN
EXPERIMENTS
Process Mapping Techniques
• Graphical representation of how system components interact
• Describes the flow of information/material/jobs/documents etc.
• Tools for mapping
o Flowcharts
o Cross Functional Maps
o Gantt Charts
Process Mapping
ID Task Name Start End Duration
Oct 14 2001 Oct 21 200
1
14 15 16 17 18 19 20 21 22 23 24 25 26 2
7
1 4d 4h19/10/200115/10/2001Task 1
2 1d22/10/200119/10/2001Task 2
3 2d 4h17/10/200115/10/2001Task
3
4 1d 4h22/10/200119/10/2001Task 4
5 3d 4h26/10/200123/10/2001Task
5
STAR
T
Log Order
Receipt
Electronic
Record
Add to
queue
Select Next
in
Queue
Enough
F
T
Assemble
Order New
Stock
Log Order
Completed
Dispatch
END
Check
Stock
Proc. 1
Process name
D
e
p
.
B
D
e
p
C
D
e
p
.
D
D
e
p
.
A
Proc. 2 Check
Proc 4
Proc 5
Proc 7
Proc
6
(a)
(b)
Proc. 3
(shared)
(e)
(d)
(g)
(f)
(k)
(c)
(h)
(i)
(j)
Functional-based process
A1
A2
A3
B1
B2
B3 B4
C1
C2
C3
functional
Mixed Products
High utilisation of resources
Increased specialisation
Cross Functional Process Maps
Cross-functional charts are graphical maps that show how work is carried out in
an organisation. They show
Input/Output
Sequence
People, function or roles that perform each step
Process
input output
Decision
input
Option 1
Option 2
Cross Functional Process Maps
Proc. 1
Process name
D
e
p
.
B
D
e
p
C
D
e
p
.
D
D
e
p
.
A
Proc. 2 Check
Proc 4
Proc 5
Proc 7
Proc 6
(a)
(b)
Proc. 3
(shared)
(e)
(d)
(g)
(f)
(k)
(c)
(h)
(i)
(j)
Exercise
Applying to study at UoL
A student needs firstly to fill an application post with support documents. The filled
information will be passed to the admission office for automating a temporary student
ID. Once the ID is created, the applicant will be notified immediately and profile of this
ID will be sent to the associated course director for an application assessment. If the
course director rejects this student, a rejection letter will be created and it will also be
sent to the faculty office to update computer record. If this student is accepted, a copy
application will be generated for further consideration if all academic conditions are
met. If so, the course director will suggest an unconditional offer to the faculty office to
update the computer record. If not, the course director needs to specify what
conditions are further needed and this will also result in an update of computer
record
in the faculty office. Based on the computer record, the faculty office will decide
whether a conditional offer is needed for the applicant. If so, a conditional offer is
generated and it will also be replied to the student for further instruction. If not, an
unconditional offer is written and the applicant will be instructed to prepare for
enrolment.
Example: Applying To Study at Liverpool University
Applying To study at Liverpool University
U
A
O
C
o
u
rs
e
D
ir
F
a
c
u
lt
y
S
tu
d
e
n
t Fill
Application
Post with
support
Documents
enter
information in
computer
& generate ID
Write back to
student with ID
Assess
Appication
Accept
Write Rejection
letter
Copy
Application
Specify
Conditions
Satisfy
Cond.
Recommend
Un
conditional
offer
Write
Unconditional
Offer Letter
Update
Computer
record
Update
Computer
record
Inform
Faculty office
Prepare to
enroll
Conditional
Write
conditional
Offer Letter
Meet
Conditions
Y
N
N
Y
Y
N
Product-oriented Processes
product oriented
A1 B3 C2
A1 B4 C3
Product A
Product B
Reduction in
•Processing times (dedicated processes)
•Changeover
•WIP
•Transportation
GANTT Chart: Product-Based
Flow of parts in a cell or department with
duration of each activity
Example
Assume Parts A and B arrive to a cell with
a number of process M1,M2,
M3
Each part has the following routes
B 1 B A
M 1 A B A
B 2 B
M 2 A B A
B 3 B
M 3 A B
Bout A B
Time
0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
2
1
2
2
2
3
2
4
2
5
2
6
2
7
2
8
M1
M2
M3B3
B2
B1
GANTT Chart: Product-Based
A M1 M2 B3 M3 M1 M2
B B1 M1 M2 B1 M1
C M2 M3 M2 M3
Time 0
1
0
2
0
3
0
4
0
5
0
6
0
7
0
8
0
9
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
1
8
1
9
2
0
2
1
2
2
2
3
2
4
2
5
2
6
2
7
2
8
• Variation on GANTT charts using Product as the
base line
• Example (Manufacturing Cell):
• A visits M1,M2,M3
• B visits M1,M2
• C visits M2,M3
• M1 and M2 processing time (5)
• M3 processing time (8)
M1
M2
M3B3
B2
B1
Example and exercise
M1
3mins
M2
5mins
Pa every
6mins
M1
3mins
M2
5mins
Pa every
6mins
Pb every
4mins
B1
M3
3mins
B2
M4
6mins
B3
Witness introduction part 2
1: Style
Graphic representation for any entities in Witness that is supposed to have an
animation movement (e.g. parts, labours). It can be description only or an Icon.
2: Icon (Monochrome)
Graphic representation for any entities in Witness in statically. It can be
customised with Editor function and a monochrome image can represent entity
states (use keys to see the meaning of different colours) later.
3: Part queues and labour queues
Presenting the location of your expected queues, built-up direction,
count and queue animation.
✓ Display types – displays can be created as many as you like for
one entity
Witness introduction part 2
✓ Based on the example from Witness Intro-1, create a state light
and a counter for your buffer
Witness introduction part 2
✓ Based on the example from Witness Intro-1, create a state light
and a counter for your buffer
You can
change the
font of your
counter
display here
Witness introduction part 2
✓ Based on the example from Witness Intro-1, create a state light
and a counter for your buffer
Why do we
have two part
queues?
Witness introduction part 2
1: A conveyor has length, movement time and capacity
▪ Length can be measured by part dimention.
▪ Indexed time: it specifies the amount of time it takes a part to move
through one part length of the conveyor.
2. Input and output rules (with position)
3. Use Shift and Control key to break a conveyor and bend a
conveyor.
✓ Conveyors
Witness introduction part 2
1:Pull from multiple places (pull from {position 1}, {position 2}, …)
• Flexible inputs
• Cannot define sequence
• Pull from next position if the former position is empty.
2. Sequence rule (sequence /failure_option location1, {location2}
{location3…}).
▪ Both flexible and strict sequence
▪ Quantity for each pull can be specified.
✓ Input from / output to multiple places
Witness introduction part 2
1:Push to multiple places (push to {position 1}, {position 2}, …)
• Easy manage but not good for overall utilisation
performance.
• Differentiate queues
2. Least/most parts (least/most parts|free location1 {, location2 …})
▪ Balanced queue
▪ Not consider different queue capacities
✓ Input from / output to multiple places
Witness introduction part 2
✓ Route function
Witness introduction part 2
✓ Route function
Witness introduction part 2
✓ Route function
Witness introduction part 2
✓ Route function
Witness introduction part 2
✓ Route function
Witness introduction part 2
✓ Route function
Witness introduction part 2
✓ Route function
Use Route tab to add stages
Define the details for each stage
Witness introduction part 2
✓ Route function
Dr. Daniel Xing
Email: x.xing3@liverpool.ac.uk
EBUS-504
Operations Modelling and Simulation
Lecture 2
Process mapping techniques + Witness functions
University of Liverpool
Management School,
UK
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