Vensim software work required for 3 students 3 copies

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Dr. XINJIE XING

EBUS-504

Operations Modelling and Simulation

Vensim modelling and analysis

University of Liverpool

Management School,

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

Auxiliary

• Input/Parameter/Lookup

• Have no edges directed toward them

• Output • Have no edges directed away from them

Auxiliary

Stock and Flow Notation--Quantities

Inputs and Outputs

• Inputs

• Parameters

• Lookups

• Outputs

Input/Parameter/Lookup

Stock and Flow Notation--edges

• Information

• Flow

a b

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

q3 q4

Causal loop example

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!!

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

1 1

Manual Simulation example – Lets do the

Maths

INVENTORY MANAGEMENT

Information's Patterns

Sales

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

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)

Manual Simulation example – Lets do the

Maths

INVENTORY MANAGEMENT

The Maths

Period Production Inventory Sales

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)

1 233

Manual Simulation example – Lets do the

Maths

INVENTORY MANAGEMENT

Information's Patterns

Inventory

31 32

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

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,