Stock and flow diagram

• • • 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. Both diagrams belong to the chapter System Dynamics. System dynamics is an approach to understanding the behaviour of complex systems over time. It deals with internal feedback loops and time delays that affect the behaviour of the entire system. What makes using system dynamics different from other approaches to studying complex systems is the use of feedback loops and stocks and flows. It depicts the structural understanding of a system - the causal structures that produces the observed behavior. It reveals information about the rates of change of system elements and the measures of the variables of the system.[z]

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

• 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

Flow rate

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	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

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

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

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

There are a lot of software designed for modeling System Dynamics. An extensive list of programs can be found to be on this Wiki page. But the most used software are these:

• Vensim
• Powersim
• IThink/Stella

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 [z] [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