D-4421-2 1 Modeling Exercises Section 1 Prepared for MIT System Dynamics Education Project Under the Supervision of Dr. Jay W. Forrester by Joseph G. Whelan May, 1994 Vensim Examples added October 2001 Copyright © 1994 by the Massachusetts Institute of Technology Permission granted for non-commercial educational purposesD-4421-2 3 Table of Contents Abstract .....................................................................................................5 Introduction ...............................................................................................6 How to Build Models.................................................................................7 Building Models ........................................................................................10 Model 1: An Ecological System......................................................10 Description: ...........................................................................11 Exploration:...........................................................................11 Model 2: A Heating/Cooling System ..............................................13 Description Part A: ................................................................13 Exploration Part A: ................................................................14 Description Part B:.................................................................15 Exploration Part B: ................................................................15 Model 3: A Predator Prey System...................................................16 Description: ...........................................................................16 Exploration:...........................................................................16 Solutions....................................................................................................18 Model 1: An Ecological System......................................................18 Model 2: A Heating/Cooling System ..............................................25 Model 3: A Predator/Prey System...................................................31 Vensim Examples……………………………………………… ................39D-4421-2 6 The exercises in this paper require a Macintosh1 Computer with 2 Mb of RAM if running System 6.0.4 and at least 4 Mb of RAM if running System 7 or higher. Also required is the STELLA2 II software package. If you do not have STELLA, it can be obtained from High Performance Systems: High Performance Systems, Inc. 45 Lyme Road Hanover, NH 03755 (800) 332-1202 Abstract This paper is the first in a series of papers designed to utilize and enhance the modeling capabilities of the reader. This series of papers is part of a project called Road Maps. Road Maps is a self study guide to lead the reader through the process of learning system dynamics. Road Maps is currently being worked on by the System Dynamics in Education Project at MIT under Jay Forrester, the founder of system dynamics. The beginning of this paper outlines the importance and the process of model building. This paper also contains three separate modeling exercises. Each exercise begins with a brief description of the system after which the reader constructs a system dynamics model of the system. The reader then runs the model under varying conditions and answers some questions. This paper is not intended as an introduction to system dynamics or model building. The reader is expected to have prior experience with both. Solutions to all the exercises are included at the end. The modeling exercises are presented approximately in order of difficulty, but need not be done in this sequence. 1Macintosh is a registered trademark of Apple Computer, Inc. 2STELLA is a registered trademark of High Performance Systems, Inc..D-4421-2 7 Introduction Modeling is a crucial element of system dynamics. We use mental models every day of our lives to make decisions without addressing the model being used. Creating and simulating models using STELLA or other modeling software forces us to solidify our mental models and allows us to observe the behavior of complex systems where mental models are inadequate. One drawback of using a computer to simulate systems is that the computer will always do exactly what you tell it to do. Your computer won't say "Hey wait a minute, you can't have a negative population," or "You can't make the number of sick people greater than the total population." You must be the one to generate and verify a valid model. To make system dynamics modeling as useful as possible, a modeler must acquire many skills. Below is a list of some important skills: • Have a general idea of how the system should behave to test the accuracy of the computer simulation. • Generate a valid model of the system to be analyzed. • Enter the model correctly into the computer. • Make the model clear so that others can understand its structure. The exercises you encountered in Road Maps I-IV have prepared you for the task of creating your own models. This paper will allow you to exercise some of the skills you have already learned and enable you to acquire new skills as well. Future parts of Road Maps will contain more sections of the Modeling Exercises series (this is the first section) enabling you to further increase your modeling skills.D-4421-2 8 How to Build Models Building a model can be a very rewarding, yet challenging process. There is no set way to build a model. Each model that you build will be different, and likewise the steps you follow in building your models will vary. In some cases, you may be able to jump directly into STELLA and start mapping. In other cases the modeling process may take a considerable amount of time. Below is a rough guideline for how to go about the process of model building. It is not intended as a "cookbook" for model building but rather as a way to get you started. 1. Define the purpose. What you want to do with your model is entirely up to you. However, you must define the purpose for your model before you can begin to build it. Do you want to explore different management policies for a park? Perhaps you merely wish to teach your third graders about population dynamics. You must have a goal in mind to decide how complex to make your model. This purpose will also guide you in your decisions regarding how much certainty you require in your numbers, where to set your model boundary and