System Dynamics Stocks and Flows

System Dynamics Stocks and Flows - Transcript

System Dynamics
Stocks and Flows





STOCKS FLOWS AND ACCUMULATION
Causal loop diagrams are wonderfully useful in many situations They are well suited to represent interdependencies and feedback processes They are used effectively at the start of a modeling project to capture mental models both those of a client group and your own They are also used to communicate the results of a completed modeling effort
One of the most important limitations of causal diagrams is their inability to capture the stock and flow structure of systems





STOCKS FLOWS AND ACCUMULATION
Stocks are accumulations

They characterize the state of the system and generate the information upon which decisions and actions are based





STOCKS FLOWS AND ACCUMULATION
The inventory of a manufacturing firm is the stock of product in its warehouses

The number of people employed by a business is a stock

The balance in your checking account is a stock Stocks are altered only by inflows and outflows Yet despite everyday experience of stocks and flows all too often people fail to distinguish clearly between them





STOCKS FLOWS AND ACCUMULATION





STOCKS FLOWS AND ACCUMULATION
Equivalent representations of stock and flow structure

Stock and Flow Diagram

Integral Equation
Stock t

t

Inflow s Outflow s ds Stock t 0
t0





Identifying Stocks and Flows
Units of Measure in Stock and Flow Networks The units of measure can help you distinguish stocks from flows Stocks are usually a quantity such as widgets of inventory people employed or Yen in an account The associated flows must be measured in the same units per time period The Snapshot Test Stocks characterize the state of the system To identify key stocks in a system imagine freezing the scene with a snapshot Stocks would be those things you could count or measure in the picture


Identifying Stocks and Flows
Any flow into or out of a stock can be either positive or negative The direction of the arrow defines the sign convention for the flow





Identifying Stocks and Flows
The determinants of rates include not only stocks but any constants and exogenous variables These too are stocks Constants are state variables that change so slowly they are considered to be constant over the time horizon of interest in the model Exogenous variables are stocks you have chosen not to model explicitly and are therefore outside the model boundary For example in a model of the demand for a new video game the size of the potential market might depend on the population between say ages 4 and 20 The product life cycle will last a few years at most Over this time horizon the population between 4 and 20 years of age is not likely to change significantly and can reasonably be assumed constant

Identifying Stocks and Flows
Mathematical description of a system requires only the stocks and their rates of change For ease of communication and clarity however it is often helpful to define intermediate or auxiliary variables





Identifying Stocks and Flows
For example a population model might represent the net birth rate as depending on population and the fractional birth rate fractional birth rate in turn can be modeled as a function of food per capita

The auxiliary variables Fractional Birth Rate and Food per Capita are neither stocks nor flows They are functions of the stocks and exogenous inputs in this case Food





Identifying Stocks and Flows
Population participates in two feedback loops A positive loop more people more births more people and a negative loop more people less food per person lower fractional net birth rate fewer births The inclusion of the auxiliary variables distinguishes the two loops and allows unambiguous assignment of link and loop polarities





Identifying Stocks and Flows
The auxiliaries can always be eliminated and the model reduced to a set of equations consisting only of stocks and their flows By substituting the equation for Food per Capita into the equation for Fractional Birth Rate and then substituting the result into the equation for Net Birth Rate you can eliminate the auxiliaries reducing the model to one with only Net Birth Rate and Population Ideally each equation in your models should represent one main idea





Exercises


Beginner modleing exercises