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 use five basics elements:  Stock Variable;  Flow Variable;  Information Flow;  Material Flow; and  Time Delay

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 Flow Variable Material Flow Information Flow Stock Variable 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

Control Material Flaw to Stock Add New information Send information from the Stock Control Material Flaw from Stock Stock Basic elements

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:

Mathematical Background Re-arranging terms In the limits as Δt goes to zero, the difference equation becomes the differential equation:

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) iThink Stella ModelMaker Vensim Powersim Dynamo

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