Operations Management using System Dynamics

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Operations Management using System Dynamics

• Part I

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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

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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.

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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.

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Basic elements

• This methodology use five basics elements
• Stock Variable
• Flow Variable
• Information Flow
• Material Flow and
• Time Delay

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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

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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.

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Graphical Representation
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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)

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Complexities of a simple stock acquisition system
are cleared expressed through a diagram built
using the element of system dynamics methodology
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Basic elements
Control Material Flaw to Stock
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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

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Mathematical Background

• Re-arranging terms

• In the limits as ?t goes to zero, the difference
  equation becomes the differential equation

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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 Eulers Method and Runge-Kutta.

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Software (examples)
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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

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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.

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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.

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Reference

• Modeling Dynamic Economic System. Ruth, M.
  Hannon, B. Springer, 1997, Chapter 1 and Chapter 4