Bdsm-ch6_mapping Stock And Flow

Business Dynamics and System Modeling

Chapter 6: Mapping Stocks and Flows Pard Teekasap Southern New Hampshire University

Outline 1.Stock, Flows, and Accumulation 2.Identifying Stocks and Flows 3.Mapping Stocks and Flows

Diagramming Notation for Stocks and Flows • • • • • • • 

Stock Inflow

Stock Flow Valve (Flow Regulator) Source or Sink (Stocks outside model boundary)

Stock Inflo w

Outflow

O utflow

S to c k O u t fl o w I n f lo w

Stock and Flow

Equivalent representations of stock and flow diagram Hydraulic Metaphor:

Stock and Flow Diagram: Stock Inflow

Outflow

Integral Equation: t

Stock (t ) =

[Inflow (s ) - Outflow (s )]ds + Stock (t 0) t0

Differential Equation: d( St ock) /d t = Net C hange in St ock = Inflow (t ) – O ut flow (t )

Contribution of Stocks to Dynamics • Stocks characterize the state of the system and provide the basis for actions • Stock provide systems with inertia and memory • Stocks are the source of delays • Stocks decouple rates of flow and create disequilibrium dynamics

Stocks and Flows in different disciplines

M

Which one is the stock and which one is the flow? • Units of measure in stock and flow networks • The snapshot test

Unit of measure of stocks and flows • Stocks are usually a quantity e.g. widgets of inventory, people employed, or Dollar in an account • The associated flows must be measured in the same units per time period e.g. the rate at which widgets are added per week to inventory, the hiring rate in people per month

The snapshot test • Freeze the system scene with a snapshot • Stocks would be things you can count or measure in the picture, including psychological states and other intangible variables

Identifying stocks, inflows, outflows • Completing/Assigning/Homework • Brownies in stomach/Eating/Digesting • Expenses/Income/Money in back account • Shrinking/Pinocchio’s nose/Lengthening • Building/Nuclear Weapons/Disarming • Cavities/Developing/Filling

Conservation of Material • The contents of the stock and flow networks are conserved • Items entering into a stock will remain there until they flow out • When an item flows from one stock to another, the first stock loses precisely as much as the second gains

State-determined systems • Stock can change only via its inflows and outflows • Stocks determine the flows Net Rate of Change

State of the System (Stock)

Auxiliary Variables • System requires only stocks and flows. However, for ease of communication and clarity, it is helpful to define intermediate or auxiliary variables • The auxiliaries can always be eliminated and mathematically the same, but it is harder to explain, understand, and modify • The use of auxiliary variables is critical to effective modeling. Ideally, each equation in the models should

Example of using auxiliary variables Population Net Birth Rate + R +

Population Net Birth Rate ? ? +

Fractional Birth Rate

B +

Food per Capita + Food

Food

Stocks change only through their rates Customers Wating for Service

Curstomer Arrival Rate

B- -

-

Customer Departure Rate

In co rre ct

+ Workweek B +

Productivity

Service Staff

Curstomer Arrival Rate

Customers Wating for Service B +

C o rre ct

Customer Departure Rate + + +

Workweek B + Service Staff

Productivity

Should I use mathematical diagram or stock and flow diagram

• Depends on the context of the modeling project you are doing and the background of your client team • If your clients have very little technical training, the bathtub metaphor is often used to good effect

Which detail I should present and which detail I should lump it together

• Usually it is wise to identify the main stocks in a system and then the flows that alter those stocks • It is better to start with a high-level, aggregate representation and add detail if needed to address the purpose • Beginning with detailed process maps often leads to paralysis due to their complexity, data requirements, and rapid

Example of aggregation Production Start Rate Parts in Process Assembly Start Rate

Work in Process Inventory

Assemblies in Process Test Start Rate Product in Testing Production Completion Rate Finished Inventory Shipment Rate

Modifying the Model qModify the diagram to represent the case where units that fail testing are scrapped qModify your diagram to represent the case where items failing testing are returned to assembly for rework

Guideline for aggregation • For activities taking place serially, consider the average residence time of item in each stock. The stock with short residence times relative to the time scale for the dynamics of interest can be omitted or aggregated into adjacent stocks • Parallel activities can be aggregated together if the individual flows are governed by similar decision rules and if the time different items spend

Setting the model boundary • Are the assumptions about the “clouds” reasonable?

Are these two clouds reasonable Source: Unlimited Supply of Material

Production Starts

WIP Production

Finished Inventory Shipments Sink: Unlimited Absorption Capacity

Model Boundary

Extending the model scope Supplier Production Starts Supplier WIP Supplier Production

Supplier Sector

Supplier Inventory Supplier Shipments

Parts Inventory Production Starts Manufacturer Sector

WIP Production

Finished Inventory Shipments

Dealer Stocks

Dealer Sector New Car Sales

Adding the customers Shipments

Dealer Stocks New Car Sales

Cars on the Road Scrap Rate

Dealer Sector

Household Sector