Dr. Daniel Xing

Email: [email protected]

Operations Modelling and Simulation

Lecture 2

EBUS-504

Operations Modelling and Simulation

Lab1

University of Liverpool

Management School, UK

TA: Mr. Lais Wehbi

Email: [email protected]

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 5Dr. Daniel Xing

Email: [email protected]

Operations Modelling and Simulation

Lecture 2

EBUS-504

Operations Modelling and Simulation

Lab2

University of Liverpool

Management School, UK

TA: Mr. Lais Wehbi

Email: [email protected]

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 ([email protected])

EBUS-504

Operations Modelling and Simulation

Build your first SD model

University of Liverpool

Management School,

UK

mailto:[email protected]

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 = (Ta1

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: EBUS504

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) Xing

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: ModificatiASSIGNMENT

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.doc)

● 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 of1

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: EBUS504

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) Xing

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: ModificatiDr. Daniel Xing

Email: [email protected]

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.

2mins 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?)

Dr. Daniel Xing

Email: [email protected]

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

StatisticsDr. 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 systemDr. Daniel Xing

Email: [email protected]

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

1: square meters of A

2: square meters of B

Objective: max

1 2

50 1 + 100 2

s.t.

1 + 2 ≤ 300

2 1 + 2 ≤ 400

2 ≤ 250

1, 2 ∈ +

Mathematical formulation

max

1 2

50 1 + 100 2

s.t.

1 + 2 ≤ 300

2 1 + 2 ≤ 400

2 ≤ 250

1, 2 ∈ +

1 1

2

0

1

1

1

2

≤

300

400

250

50 100

1

2

Co-efficient

matrix

Variable

vector

Column

vector

1 2

Vectors and matrix

All constraints define the search spDr. Daniel Xing

Email: [email protected]

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 deteDr. Daniel Xing

Email: [email protected]

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

,Dr. XINJIE XING

EBUS-504

Operations Modelling and Simulation

Vensim modelling and analysis

University of Liverpool

Management School,

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 extract the behavioral implications

from the structure and data

• A “hands on” tool on which to conduct WHAT

IF

Stock and Flow Notation–Quantities

• STOCK

• RATE

• Auxiliary

Stock

Rate

i1

i2

i3

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

q5

q6

q7

q8

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 descriptiDr. Daniel Xing

Email: [email protected]

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_waitiDr. Daniel Xing

Email: [email protected]

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 – [email protected]

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:[email protected]

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 foDr. Daniel Xing([email protected])

EBUS-504

Operations Modelling and Simulation

System Dynamic software: Vensim

University of Liverpool

Management School,

UK

mailto:[email protected]

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([email protected])

EBUS-504

Operations Modelling and Simulation

System Dynamic software: Vensim

University of Liverpool

Management School,

UK

mailto:[email protected]Dr. Daniel Xing

Email: [email protected]

EBUS-504

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 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

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 2001

14 15 16 17 18 19 20 21 22 23 24 25 26 27

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

START

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.

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