Transcript Special Stocks - Foundation Coalition

Operations Management
using System Dynamics
Part I
Learning Objective
After this class the students should be able to:


Understanding how System Dynamics can be
used to understanding the dynamic of
operation
Drawing a simple model using the basic
elements of System Dynamics
Time management

The expected time to deliver this module is 50
minutes. 20 minutes are reserved for team
practices and exercises, 30 minutes for lecture.
System Dynamics

an approach developed to understand how the
interaction between policies and structure of a
organization determine its behavior.

It is used to show how interaction between structures
of the systems and the policies used to control them
can explain their behaviors.

Dynamic models are those that try to reflect changes
in real or simulated time and take into account that
the model components are constantly evolving as a
result of previous actions.
Basic elements
 This
methodology
elements:
Stock Variable;
Flow Variable;
Information Flow;
Material Flow; and
Time Delay
use
five
basics
Stock & Flow


Stock variables are also called state variable. They
indicate the status of our system through time. They
represent stocks, that is, accumulations. They
collect whatever flows into them, net of whatever
flows out of them.
Flow variables are also called control variables. They
are the ones that directly change the stocks. They
can increase or decrease the stocks through time.
Birth (per time period) or water inflow (to a reservoir)
or heat flow from a hot body are examples
Delays and Converter

Delays are Interruptions between actions and their
consequences

Transforming or converting variables are sources of
information used to change the control variables.
Such a variable might be the result of an equation
based on still other transforming variables or
parameters. The birth rate, the evaporation rate, or
the heat loss coefficient are examples of
transforming variables.
Graphical Representation
Material Flow
Flow Variable
Stock Variable
Information Flow
Converter
Interdependent stocks
 We
can understand the industrial
environment as a set of stocks and
activities linked by flow of information
and flow of material, submitted to time
delays.
 For example, we can represent a
company as a set of aggregates stocks.
(See figure in next slide)
Complexities
of a simple
stock
acquisition
system are
cleared
expressed
through a
diagram built
using the
element of
system
dynamics
methodology
Basic elements
Control
Material Flaw
to Stock
Control
Material Flaw
from Stock
Stock
Send information
from the Stock
Add New
information
Mathematical Background

In terms of Calculus, flows represents time
derivatives; stocks are integrals; and converter is
auxiliary variable that contain the micro-logic of
flows. The diagram placed before (anterior slide) can
be mathematical represented as:
Stockt   Stockt  dt  Flow  dt or
Stockt  Stockt t  t * Flow
Mathematical Background

Re-arranging terms
Stockt  Stockt t * t  Flow

In the limits as Δt goes to zero, the difference
equation becomes the differential equation:
d ( Stock )
 Flow
dt
Stock   flow dt
or
Software

There are several software based on System Dynamics, which
can be used to teach operation management. These software
are object oriented, so you do not need special ability in
computer programming to use them. They have a friendly
interface and as you build the model using their object, they
build the differential equation system. When you run the model
they solve the equation system using numerical integration
methods such as: Euler’s Method and Runge-Kutta.
Software (examples)
Dynamo
Vensim
Powersim
iThink
Stella
ModelMaker
Exercise

Consider a store where people enter, receive some
service, then move to the cash register and have to
wait in a checkout line before they can pay and
leave. Only one person can be served at a time, and
initially one person is already at the service center
being served. It takes 5 minutes to be served and 1
minute to get from the service center to the checkout
line. There are already 8 people waiting in the
checkout that last 2 minutes, and one person is
currently being served. One customer arrives every 4
minutes and the first customer arrives in the third
minute after we began the analysis
Exercise

people enter,

receive some service, then

move to the cash register and

have to wait in a checkout line before they can pay
and leave.
Exercise

The teams are invited to sketch a diagram of the
question using the language of System Dynamics. In
other words, using the basic elements presented in
this class.

The teams have 20 minute for drawing the model.
They can improve the model at home and present in
next class.
Reference

Modeling Dynamic Economic System.
Ruth, M. & Hannon, B. Springer, 1997,
Chapter 1 and Chapter 4