Difference between revisions of "Stock and flow diagram"

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* In general, the formulas for the flows will depend on things that are changing (state)  
 
* In general, the formulas for the flows will depend on things that are changing (state)  
  
−
=Stock Flow Symbols=
+
=Symbols=
  
−
State of the System: Stocks (“Levels”,
+
Each graphical tool for modeling System Dynamics has its own form of symbols, but basics are same in the following points. [x] [y]:
−
“State Variables”, “Compartments”) [x]
+
 
−
* Stocks (Levels) represent accumulations  
+
== Stocks ==
 +
[[File:Stock.JPG]]
 +
 
 +
* In a stock & flow diagram are shown as rectangles
 +
* Stocks (also known as Levels) represent '''accumulations'''
 
– These capture the “state of the system”  
 
– These capture the “state of the system”  
−
– Mathematically, we will call these “state variables”  
+
– Mathematically it can be called as “state variables”
−
• These can be measured at one instant in time  
+
* Are used to represent the real-world processes (e.g. stocks of material, knowledge, people, money)
−
• Stocks start with some initial value & are thereafter  
+
* Stocks can be measured at one instant in time  
−
changed only by flows into & out of them  
+
* Stocks start with some '''initial value''' and are thereafter changed only by '''flows into''' & '''out of them'''
 
– There are no inputs that immediately change stocks  
 
– There are no inputs that immediately change stocks  
−
• Stocks are the source of delay in a system  
+
* Stocks are the source of delay in a system  
−
• In a stock & flow diagram, shown as rectangles
 
  
−
Stocks (also known as levels, accumulations, or state variables) are used to represent the real-world processes (e.g. stocks of material, knowledge, people, money). They change their value continuously over time with the given flows.
 
  
−
Stocks are drawn with rectangles that represent some accumulators containing some amount of contents of the stock.[y]
+
'''The Critical Role of Stocks in System Dynamics:'''
 +
* Stocks determine current state of system
 +
– Stocks often provide the basis for making choices
 +
* Stocks central to most disequilibria phenomena (buildup, decay)
 +
* Lead to inertia
 +
* Give rise to delays
  
  
−
=Examples of Stocks=
+
===Examples of Stocks===
  
−
There is list of common examples of Stocks [x]:
+
There is a list of common examples of Stocks [x]:
  
 
* Water in a tub or reservoir  
 
* Water in a tub or reservoir  
 
* People of different types  
 
* People of different types  
−
**– {Susceptible, infective,immune} people  
+
** {Susceptible, infective,immune} people  
−
**– Pregnant women  
+
** Pregnant women  
−
**– Women between the age of x and y  
+
** Women between the age of x and y  
−
**– High-risk individuals  
+
** High-risk individuals  
 
* Healthcare workers  
 
* Healthcare workers  
 
* Medicine in stocks  
 
* Medicine in stocks  
Line 54: Line 61:
 
* Owned vehicles  
 
* Owned vehicles  
  
−
=Examples of Flows=
 
  
−
There is list of common examples of Flows [x]:  
+
== Flows ==
 +
'''Flow'''
 +
[[File:Material flow2.JPG]]
 +
 
 +
'''Flow rate'''
 +
[[File:Material flow.JPG]]
 +
 
 +
All changes to stocks occur via flows. In turn, stocks in a system determine the values of flows.
 +
* Drawn with an arrow with a valve (denoting the flow rate) in the middle of it
 +
* Always expressed per some unit time: If these flow into/out of a stock that keeps track of things of type X (e.g. persons), the rates are measured in X/(Time Unit) (e.g. persons/year, $/month, gallons/second)
 +
* Typically measure over certain period of time (by considering accumulated quantity over a period of time)
 +
– e.g. Incidence Rates is calculated by accumulating people over a year, revenue is $/Time, water flow is litres/minute
 +
– Can be estimated for any point in time
 +
 
 +
 
 +
===Examples of Flows===
 +
 
 +
There is a list of common examples of Flows [x]:  
 
* Inflow or outflow of a bathtub (litres/minute)  
 
* Inflow or outflow of a bathtub (litres/minute)  
 
* Rate of incident cases (e.g. people/month)  
 
* Rate of incident cases (e.g. people/month)  
Line 76: Line 99:
  
  
 +
== Examples of Stock and flows==
 +
[[File:Stock and flow.JPG]]
 +
 +
<center>
 +
{| border="1"
 +
|align="center"|'''Stock'''
 +
|align="center"|'''Inflows'''
 +
|align="center"|'''Outflows'''
 +
|-
 +
|align="center"|bank balance   
 +
|align="center"|deposits interest
 +
|align="center"|withdrawals
 +
|-
 +
|align="center"|housing stock
 +
|align="center"|housing investment
 +
|align="center"|housing depreciation
 +
|-
 +
|align="center"|CO2 in atmosphere
 +
|align="center"|tons emitted
 +
|align="center"|tons sequestered 
 +
|-
 +
|align="center"|population
 +
|align="center"|births, immigration
 +
|align="center"|deaths,  emigration
 +
|-
 +
|align="center"|fuel tank
 +
|align="center"|refueling
 +
|align="center"|fuel consumption
 +
|}
 +
</center>
 +
 +
 +
== Cloud ==
 +
[[File:Source.JPG]]
 +
 +
Cloud represents either:
 +
 +
* '''Source of the flow''' - when the flow is originated from outside the model
 +
* '''Sink of the flow''' - when the flow sinks
 +
 +
Both sources and sinks are assumed to have infinite capacity and do not impose any limitations on the flows.
 +
Clouds are drawn as the part of the flow element, in case the flow does not flows in/out of some stock.
 +
 +
== Auxiliaries ==
 +
[[File:Variable.JPG]]
 +
 +
Auxiliaries are used to '''define some intermediate concepts'''. Auxiliary can change '''instantaneously''' according to the specified formula.
 +
 +
== Parameters ==
 +
 +
Parameters are commonly used to '''define numeric constants'''.
 +
 +
== Links ==
 +
[[File:Information flow.JPG]]
 +
 +
Link is used to '''define a dependency between elements of a stock and flow diagram'''.
 +
 +
If  some element A is mentioned in the equation or initial value of element B, you should first connect these elements with a link going from A to B and only then type the expression in the properties of B.
  
  

Revision as of 22:33, 23 January 2014

      • IN CONSTRUCTION --Tomyk007 21:12, 22 January 2014 (CET)

Definition

A Stock & Flow Diagram (SFD) is similar to a Causal Loops Diagram (CLD) though provides a more rigourous representation. By explicitly identifying Stocks, reservoirs which change over time, and Flows, which are responsible for changes in Stocks, the resultant insight explicitly depicts the manner in which things change.

Captures

  • Stock
  • Flows
  • Quatified feedback loops

Rules

  • Stocks are always changed by flows
  • In general, the formulas for the flows will depend on things that are changing (state)

Symbols

Each graphical tool for modeling System Dynamics has its own form of symbols, but basics are same in the following points. [x] [y]:

Stocks

Stock.JPG

  • In a stock & flow diagram are shown as rectangles
  • Stocks (also known as Levels) represent accumulations

– These capture the “state of the system” – Mathematically it can be called as “state variables”

  • Are used to represent the real-world processes (e.g. stocks of material, knowledge, people, money)
  • Stocks can be measured at one instant in time
  • Stocks start with some initial value and are thereafter changed only by flows into & out of them

– There are no inputs that immediately change stocks

  • Stocks are the source of delay in a system


The Critical Role of Stocks in System Dynamics:

  • Stocks determine current state of system

– Stocks often provide the basis for making choices

  • Stocks central to most disequilibria phenomena (buildup, decay)
  • Lead to inertia
  • Give rise to delays


Examples of Stocks

There is a list of common examples of Stocks [x]:

  • Water in a tub or reservoir
  • People of different types
    • {Susceptible, infective,immune} people
    • Pregnant women
    • Women between the age of x and y
    • High-risk individuals
  • Healthcare workers
  • Medicine in stocks
  • Money in bank account
  • CO2 in atmosphere
  • Blood sugar
  • Stored Energy
  • Degree of belief in X
  • Stockpiled vaccines
  • Goods in a warehouse
  • Beds in an emergency room
  • Owned vehicles


Flows

Flow Material flow2.JPG

Flow rate Material flow.JPG

All changes to stocks occur via flows. In turn, stocks in a system determine the values of flows.

  • Drawn with an arrow with a valve (denoting the flow rate) in the middle of it
  • Always expressed per some unit time: If these flow into/out of a stock that keeps track of things of type X (e.g. persons), the rates are measured in X/(Time Unit) (e.g. persons/year, $/month, gallons/second)
  • Typically measure over certain period of time (by considering accumulated quantity over a period of time)

– e.g. Incidence Rates is calculated by accumulating people over a year, revenue is $/Time, water flow is litres/minute – Can be estimated for any point in time


Examples of Flows

There is a list of common examples of Flows [x]:

  • Inflow or outflow of a bathtub (litres/minute)
  • Rate of incident cases (e.g. people/month)
  • Rate of recovery
  • Rate of mortality (e.g. people/year)
  • Rate of births (e.g. babies/year)
  • Rate of treatment (people/day)
  • Rate of caloric consumption (kcal/day)
  • Rate of pregnancies (pregnancies/month)
  • Reactivation Rate (# of TB cases reactivating per unit time)
  • Revenue ($/month)
  • Spending rate ($/month)
  • Power (Watts)
  • Rate of energy expenditure
  • Vehicle sales
  • Vaccine sales
  • Shipping rate of goods


Examples of Stock and flows

Stock and flow.JPG

Stock Inflows Outflows
bank balance deposits interest withdrawals
housing stock housing investment housing depreciation
CO2 in atmosphere tons emitted tons sequestered
population births, immigration deaths, emigration
fuel tank refueling fuel consumption


Cloud

Source.JPG

Cloud represents either:

  • Source of the flow - when the flow is originated from outside the model
  • Sink of the flow - when the flow sinks

Both sources and sinks are assumed to have infinite capacity and do not impose any limitations on the flows. Clouds are drawn as the part of the flow element, in case the flow does not flows in/out of some stock.

Auxiliaries

Variable.JPG

Auxiliaries are used to define some intermediate concepts. Auxiliary can change instantaneously according to the specified formula.

Parameters

Parameters are commonly used to define numeric constants.

Links

Information flow.JPG

Link is used to define a dependency between elements of a stock and flow diagram.

If some element A is mentioned in the equation or initial value of element B, you should first connect these elements with a link going from A to B and only then type the expression in the properties of B.


Software tools


Examples

A manufacturing firm

A manufacturing firm maintains an inventory of finished goods from which it ships to customers. Customer orders are filled after a delay caused by order processing, credit checks, etc. Map the stock and flow structure, drawing on the following variables: Inventory, Raw Materials, Production, Order Backlog, Order Rate.



References [x] http://www.cs.usask.ca/~osgood/Classes/CMPT858Spring2011/LectureSlides/Lecture%207%20--%20Stock%20and%20Flows.pdf [y] http://www.anylogic.com/anylogic/help/index.jsp?topic=/com.xj.anylogic.help/html/sd/Stock%20and%20Flow%20Diagrams.html

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