System Dynamics Modeling Tutorial - paginas.fe.up.ptpaginas.fe.up.pt/~ee01260/AnyLogic Models/Bass Diffusion/AnyLogic… · AnyLogic 6 System Dynamics Modeling Tutorial Step 0. Analyzing

System Dynamics Modeling Tutorial

AnyLogic 6 System Dynamics Modeling Tutorial

Copyright © 1992-2007 XJ Technologies. All rights reserved.

XJ Technologies Company Ltd [email protected] http://www.xjtek.com/anylogic

2 © 1992-2007 XJ Technologies http://www.xjtek.com

http://www.xjtek.com/anylogic


Contents CONTENTS............................................................................................................................... 3

BASS DIFFUSION MODEL ...................................................................................................... 4

STEP 0. ANALYZING THE MODEL......................................................................................... 5

STEP 1. CREATING A NEW MODEL ...................................................................................... 6

STEP 2. ADDING STOCKS ...................................................................................................... 8

STEP 3. ADDING ADOPTION FLOW .................................................................................... 10

STEP 4. ADDING CONSTANTS............................................................................................. 12

STEP 5. DEFINING INITIAL VALUES OF STOCKS.............................................................. 14

STEP 6. ADDING AUXILIARIES ............................................................................................ 15

STEP 7. CONFIGURING SIMULATION ................................................................................. 18

STEP 8. RUNNING THE MODEL ........................................................................................... 20

STEP 9. ADDING CHARTS .................................................................................................... 24

© 1992-2007 XJ Technologies http://www.xjtek.com 3


Bass Diffusion Model AnyLogic supports different modeling techniques. This document covers System Dynamics modeling approach. There are many spheres where system dynamics simulation can be successfully applied—the range of SD applications includes business, urban, social, ecological types of systems. AnyLogic allows you to create complex dynamic models using standard SD graphical notation.

This tutorial will briefly take you through the process of constructing a simulation model using AnyLogic. It is intended to introduce you to AnyLogic interface and many of its main features. We will create a simple illustrative example—the product life cycle model, used for forecasting sales of new products.

The first 10 steps will take you through the process of construction of the classic Bass diffusion model. The model describes a product diffusion process. Potential adopters of a product are influenced into buying the product by advertising and by word of mouth from adopters – those who have already purchased the new product. Adoption of a new product driven by word of mouth is likewise an epidemic. Potential adopters come into contact with adopters through social interactions. A fraction of these contacts results in the purchase of the new product. The advertising causes a constant fraction of the potential adopter population to adopt each time period. Then we will expand our model by considering some details and introducing you to some advanced features of AnyLogic useful in creating system dynamics models. The expanded model may help you to better plan the entry strategy, target the right consumer and anticipate demand so as to have an efficient and effective promotion strategy.

Note that there are several reference files available for this model representing the milestones of the editing. You can use reference files if you experience any difficulties creating a model and you would like to compare your model with the reference file. You can use Welcome Page to open those examples. Welcome Page appears automatically when you open AnyLogic. It can be also opened whenever you like from AnyLogic menu: Help|Welcome.



Step 0. Analyzing the Model First of all, we need to analyze the model to decide how it can be described in the system dynamics terms. We should distinguish the key variables of the model and their patterns of influence and then create stock and flow diagram of the model. When constructing stock and flow diagram, we should consider what variables should be modeled with stocks, flows or auxiliaries.

Stocks (also known as levels, accumulations, or state variables) change their value continuously over time. Flows, also known as rates, change the value of stocks. In turn, stocks in a system determine the values of flows. Intermediate concepts are known as auxiliaries and can change instantaneously.

When constructing a stock and flow diagram, consider what variables accumulate over a period of time. In our model, adopter and potential adopter populations are stocks and the adoption rate – a flow.

The system dynamics presentation of the model is shown in the following figure. Stocks are denoted with squares, flow with a valve, and auxiliaries with circles. Arrows denote causal dependencies in the model.



Step 1. Creating a New Model First, we will create a new model.

Create a new model

1. Click the New Model toolbar button. The New Model dialog box is displayed.

2. Specify the name of the model. In the Model Name edit box, type Bass Diffusion.

3. Specify the location where you want to store your model file. Browse for the existing folder using the Browse buton, or type the name of the folder you want to create in the Location edit box.

4. Click Finish.

New model is created. The diagram you see in the center of the workspace is the graphical editor. To the left of the graphical editor you can see the Project view, to the right - the Palette view, and at the bottom - the Properties view.



When working with a project, do not forget to save it by clicking Save .



Step 2. Adding Stocks Now we will add two stocks to model adopter and potential adopter populations.

Add a stock to model potential adopter population

1. Select the Stock element in the Model stencil of the Palette. 2. Click in the graphical editor where you want to place the stock variable. A new

variable appears on the diagram, displayed as a little blue rectangle.

3. Once you have placed the element onto the diagram, it becomes selected and its properties are displayed in the Properties view. You can adjust element properties here as your model requires.

Please note that the Properties view is a context-sensitive view and it displays the properties of the currently selected element of the model. To adjust properties at a later time, first select the element (e.g. by clicking on the element in the graphical editor) and then modify the required properties.

Properties view . At the moment view displays the properties of the currently selected stock variable.

4. Change the name of the stock. On the General page of the Properties view, type PotentialAdopters in the Name edit box.



Add a stock to model adopter population

1. Add another stock in the same way. Place it to the right of the PotentialAdopters stock as shown in the figure below.

2. Name this stock Adopters. 3. Move text labels of the stocks above stocks' icons. Do it in the following way: first

select a variable by clicking on it (if selected, it is drawn in a blue outline and its label is underlined) and then drag the label wherever you like. Place labels as on the figure below:

We need this since otherwise later these labels will be painted over with arrows pointing from one stock to other. At this point, the stocks are not defined properly. We have not defined integral functions and initial values for our stocks yet. But we will create the adoption flow first.



Step 3. Adding Adoption Flow We have successfully created two stocks representing population pools. It is time to create flows of our model now. Our model has just one flow - a flow of adoption, which increases the adopter population, while decreasing the potential adopter population.

Add a flow from PotentialAdopters to Adopters

1. We will add a flow using AnyLogic flow tool. Flow tool creates flow variable and sets up stocks so their values are changed with the specified flow value automatically.

2. To create flow, double-click PotentialAdopters variable and then click Adopters variable.

3. AnyLogic creates new flow variable and makes it an outflow for PotentialAdopters and an inflow for Adopters. Arrows appeared on the stock and flow diagram denote flow influence on population pools.

4. Select the flow in the graphical editor and change its name from default flowAuxVar to AdoptionRate. When finished, please press Ctrl+Enter to rename flow names mentioned in formulas of stocks also.

4. You can have a look at stock properties now. AnyLogic automatically adjusts

formulas for stocks. The value of inflows i.e. flows that increase stock value, are added and the value of outflows, i.e. flows that decrease stock are subtracted from the current value of the stock. In our case we should have the following formulas defined:



We will define the formula calculating the value of the flow a little bit later.



Step 4. Adding Constants Now we will define constants of our model. In AnyLogic you define a constant by creating a parameter.

Define a constant representing total population

1. Click the Parameter element from the Model page of the Palette view. 2. Click in the graphical editor to place the parameter. 3. On the General page of the Properties view, set up the parameter properties. 4. Change the name of the constant. Type TotalPopulation in the Name edit box. 5. In the Default Value edit box, type 100000. This will be the total population in our

model.

The rate, with which potential adopters come into contact with adopters, is assumed to be constant. So, we will define a constant to represent contact rate.

Define the ContactRate constant

1. Define the constant in the same way. Enter the Name: ContactRate. 2. Assume a contact rate of 100 per person per year. In the Default Value, type 100.

In this model the volume of advertising and the probability that a potential adopter will adopt as the result of exposure to a given amount of advertising are assumed to be constant each period. So, we will add a constant to model the advertising effectiveness—the fractional adoption rate from advertising.



Define a constant representing advertising effectiveness 1. Define a constant in the similar way. Name it AdEffectiveness. 2. Set the value to 0.011.

Define one more constant to specify the adoption fraction—the proportion of contacts that are sufficiently persuasive to induce the potential adopter to purchase the product.

Define the AdoptionFraction constant

1. Name the constant AdoptionFraction. 2. Set the value to 0.015.



Step 5. Defining Initial Values of Stocks Now we are ready to specify the initial values of stocks.

Define the initial number of potential adopters 1. Click the PotentialAdopters variable in the graphical editor. 2. On the General page of the Properties view, type TotalPopulation in the Initial

Value edit box. Use intelli-sense mechanism to avoid typing the whole names of variables and functions. To open the intelli-sense wizard, click at the desired position in the edit box, and then press Ctrl+space.

The wizard listing model variables and functions appears. Scroll to the name you want to add, or type the first letters of the name until it becomes visible in the list. Finally, press Enter to insert the name.

We do not need to set up the initial value for the Adopters stock explicitly since there are no adopters initially and the stock is already initialized with zero by default.



Step 6. Adding Auxiliaries We need to add two auxiliaries representing adoptions resulting from word of mouth and from advertising.

Create the AdoptionFromAd auxiliary

1. Choose the Flow Aux Variable element from the Model page of the Palette view. 2. Click in the graphical editor where you want to place the variable. 3. In the Properties view, change the Name to AdoptionFromAd. 4. Define the formula expression. In the AdoptionFromAd = edit box, type:

AdEffectiveness*PotentialAdopters

Create the AdoptionFromWOM auxiliary 1. Do it in the same way except name the auxiliary AdoptionFromWOM and specify the

following formula: ContactRate*AdoptionFraction*PotentialAdopters*Adopters/TotalPopulation

Now we can formulate the adoption flow using just defined auxiliares. The two sources of adoption are assumed to be independent. Thus, the total adoption rate is the sum of adoptions resulting from word of mouth driven by the population of adopters and adoptions resulting from advertising.

Define the formula for the adoption rate

1. Click the just created flow variable on the diagram.



2. Go to the General page of the Properties view. 3. Change the variable name to AdoptionRate. 4. Specify the formula expression in the AdoptionRate= field:

AdoptionFromAd+AdoptionFromWOM

Now we have completely defined our model. The stock and flow diagram of the model should look like as on the figure below.

You may examine the causal dependencies between stocks, flows and auxiliaries in your model. They are denoted with arrows as in standard SD notation.

• A thick arrow going from flow to stock means that this flow acts as inflow for this stock.

• A thick arrow going from stock to flow means that this flow acts as outflow. • A thin arrow going from A variable to B means that A causes to change B.

You can see that our model has one balancing and one reinforcing feedback loop.



• A balancing feedback loop affects the adoption rate due to advertising. The adoption rate reduces the pool of the potential adopters, which in turn decreases the adoption rate.

• A reinforcing loop affects the adoption rate due to word of mouth. The adoption rate increases the adopter population, resulting in an increase of word of mouth, and thus the increase of the adoption rate.



Step 7. Configuring Simulation Model simulation has a set of specific settings. A group of model settings is called an experiment, and experiments are displayed at the bottom of the model branch in the workspace tree. You can create several experiments for the same model with alternative model settings. One experiment is created by default and named Simulation.

It is a simulation experiment, enabling model simulation with customized parameter values.

There are also other types of experiments (optimization, risk assessment, parameter variations experiment), used when the model parameters play a significant role and you need to analyze how they affect the model behavior, or when you want to find optimal parameters of your model.

If we start the model, it will work 100 time units and then will stop. Since we want to observe only how the model behaves when the adoption process takes place, we need to stop the model when the system comes to equilibrium. The adoption process in this model lasts something over 10 years.

Set the model to stop at time 10

1. In the Project view, click the Simulation:Main experiment item.

2. On the Model Time tab of the Properties window, select the Stop model at specified time check box. In the edit box on the right, type 10. The model will stop after 10 model time units elapse.

Before running the model, we will set the real time mode to control the execution speed and, consequently, animation speed. In real time mode, the model is executed regarding the physical time.

Set the real time execution mode



1. In the Project view, click the Simulation experiment.

2. On the Presentation page of the Properties view, go to the Simulation Speed section and choose the Real time with scale option.

3. Specify the model execution speed, i.e., how many model time units will be executed in one second. In the edit box to the right, type 2.



Step 8. Running the Model Build your project by clicking the Build Model toolbar button. If there are some errors in your model, the building fails and the Problems view appears listing all the errors found in your model. Click All button in the upper right corner of the view to show all errors in the model and then double-click an error in the list to open the location of the error and fix it.

Problems view

After the model is successfully built, you can start it. Running the simulation, you automatically bring the current model up to date.

Start the model

1. Click the Run toolbar button and choose the experiment you want to run from the drop-down list. Your simulation experiment is called Bass Diffusion/Simulation.

In the case this model is the only one opened in the workspace at the moment you will be prompted to run this particular experiment. Later on this button will start the previously run experiment. To run any other experiment, right-click the experiment in the Project view and choose Run from the context menu.

Having started the model, you will see the presentation window. It displays the presentation designed for your simulation experiment. AnyLogic automatically places the show-bench title and the button enabling running your model and switching to the presentation designed for the Main class.



You can see animated stock-and-flow diagram. Elements of the diagram match the system dynamics notation. The actual values of variables are displayed as well.

You can adjust the execution speed to your needs using Slow down and Speed up toolbar buttons.



AnyLogic supports various tools for collecting, displaying, and analyzing data during model execution. The simpliest way to examine current state and history of a parameter or a variable during model simulation is to use inspect window. We want to inspect our variables AdoptionFromAd and AdoptionFromWOM to view the contribution of different adoption sources.

Inspect adoption sources

1. Click the AdoptionFromAd variable in the presentation. The yellow popup box will be shown. If needed, move it by dragging the toolbar of the window and resize it to the desired size by dragging the lower right corner of the window..

2. By default the window is in inspect mode - it displays the current value of the variable. You can switch it to the plot mode by clicking the "rectangle" button in the upper right corner of the window. Now it shows the time plot showing the trend for AdoptionFromAd variable.

3. In the same way, open inspect window for AdoptionFromWOM and switch it to the plot mode.



"Inspect" charts change scales automatically to embrace the plots, displaying the variables changing from the beginning to the end of simulation. We can easily see that when an innovation is introduced and the adopter population is zero, the only source of adoption will be advertising. The advertising effect is largest at the start of the diffusion process and steadily diminishes as the pool of potential adopters is depleted.



Step 9. Adding Charts You can also observe how the values of variables change during the simulation using charts. Namely, we want to examine the adopter and potential adopters populations dynamics. We will also use the same chart to show how the adoption rate changes in our model.

Create a data set for the PotentialAdopters variable

1. In the graphical editor, right-click the PotentialAdopters variable and choose Create Data Set from the popup menu. The data set PotentialAdoptersDS will be created. It will store the history of the variable that can be displayed on the chart. Move the data set icon aside like shown on the figure below.

2. Go to the General page of the Properties view. 3. Specify the data set title in the Title edit box: # of potential adopters. It will

be displayed in the legend displayed for this data item in the chart. 4. Clear the Show at Runtime check box to prevent showing the data set icon in the

presentation window at model runtime.

Create one more data set for Adopters

1. Create data set for the Adopters variable in the same way and set up its title: # of adopters.

Draw a time plot displaying adopter and potential adopter population pools

1. Choose the Time Plot element from the Analysis page of the Palette view. 2. Click the place in the graphical editor where you want to place the chart and resize as

shown on the figure.



3. Go to the General page of the Properties view. 4. Set up the chart’s time diapason. In the Time Window edit box, type: 8 (so the chart

will display all the simulation run). 5. Specify data sets to be displayed on the time plot. 6. Add PotentialAdoptersDS data set to be visualized on this plot by clicking the

Add Data Set button and defining settings for the data set in the property section above. Choose PotentialAdoptersDS data set from the Data Set drop-down list. Choose the first option from the Point Style drop-down list to turn off indicating data set values with a marker.

7. Add AdoptersDS data set in the same way. 8. Define how the plot will be updated with new data set values. At the botom of the

properties page, choose Update automatically option and specify the update rate in the Recurrence (in time units) edit box to the right: 0.1.

Now you can run the model and examine the trend of potential adopter and adopter populations over time. You will see classic S-shaped diffusion curves.


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System Dynamics Modeling Tutorial - paginas.fe.up.ptpaginas.fe.up.pt/~ee01260/AnyLogic Models/Bass Diffusion/AnyLogic… · AnyLogic 6 System Dynamics Modeling Tutorial Step 0. Analyzing