D-4758-1 Guided Study Program in System Dynamics System Dynamics in Education Project System Dynamics Group MIT Sloan School of Management1 Assignment #21 Reading Assignment: • Industrial Dynamics,3 by Jay W. Forrester, Chapter 2: An Industrial System 1 Copyright © 1999 by the Massachusetts Institute of Technology. Permission granted to distribute for non-commercial educational purposes. 3 Forrester, Jay W., 1961. Industrial Dynamics. Waltham, MA: Pegasus Communications. 464 pp. Page 1D-4758-1 Exercises: 1. Industrial Dynamics Please read chapter 2 of Industrial Dynamics. The chapter shows and explains the behavior of a simple model of a distribution system, similar to the system simulated in the “Beer Game.” Please let us know if you have any questions. You do not need to submit anything for this reading assignment. 2. Modeling Exercise In this exercise, you are going to build a simple model of inventory ordering. We will continue to expand on this model in later assignments to eventually build a full model of the “Beer Game.” In New England, USA, a certain town is home to many prestigious colleges. The rowdy students in these centers for higher learning spend their evenings nestled in front of their computers with mugs of herbal tea. All of the students go to a local shop, The Tea Pot, to buy many varieties of tea, among them the well-loved Heavenly Seasonings brand, a caffeine-free, 100% natural herbal tea. Richard, the manager at The Tea Pot, displays some boxes of tea on his shelves, but keeps most of his tea in large crates in his supply room. These crates constitute his inventory of tea. Richard has hired you as a consultant to help him study the fluctuations of his inventory of Heavenly Seasonings tea. Step 1: Inventory Every week, The Tea Pot sells the contents of four crates of Heavenly Seasonings tea to the college students in the area. Today, Richard counted exactly twelve crates of Heavenly Seasonings tea in his supply room. In order to always have plenty of herbal tea on hand, Richard receives four crates of Heavenly Seasonings tea from his supplier every week. A. Start building a model by representing the stock of the inventory of Heavenly Seasonings tea that Richard has in his supply room, along with the inflow and outflow to the stock. In your assignment solutions document, include the model diagram and documented equations. B. Draw a reference mode for the behavior of the stock over a period of fifty weeks. Simulate the model. In your assignment solutions document, include a graph of the model behavior. What happens to the inventory of herbal tea? Why? C. Consider the scenario in which demand for Heavenly Seasonings tea is higher due to the introduction of a new flavor: Strawberry Kiwi Delight. Now college students are buying four and a half crates worth of Heavenly Seasonings tea a week. Richard is not Page 2D-4758-1 sure that the new craze will last, so he continues receiving only four crates a week. Draw a reference mode for the behavior of The Tea Pot’s inventory over the next fifty weeks. Then simulate the model. In your assignment solutions document, include a graph of model behavior in this scenario. What happens to the stock of inventory? Why? We need to improve the model to take into account the fact that Richard may not always be able to satisfy the demand for Heavenly Seasonings tea. He can only sell tea if he has it on hand, in his supply room. As long as the inventory is above a certain fraction of the inventory that Richard desires to keep, sales will equal demand. As students deplete his inventory of tea, however, Richard starts to ration the tea. Richard would most likely not sell all of his Heavenly Seasonings tea to the first people who came into his store; he would probably keep a few boxes aside for employees or for his favorite customers. Hence, as The Tea Pot’s inventory declines further, the inventory shortage will start having an effect on sales, and sales will fall below demand. When the ratio of the remaining to desired inventory drops to zero, the effect of inventory shortage will prevent any sales from taking place. D. From the above description, improve the model to reflect Richard’s inability to sell tea that he does not have. In your assignment solutions document, include the modified model diagram and documented equations. Hint: You will need to use a lookup function. You will also want to create a variable, sales, and set the outflow of the stock of inventory equal to those sales. E. Draw a new reference mode for the behavior of the stock of inventory in the Strawberry Kiwi Delight scenario. Simulate the model over a period of fifty weeks. In your assignment solutions document, include a graph of model behavior. What happens now to the stock of inventory? Why? Step 2: Unfilled Orders If Richard receives four crates of Heavenly Seasonings tea every week, it is because he placed orders for that tea with his supplier several weeks earlier. Now, Richard orders tea to replace the tea that he sells every week. In a notebook, Richard keeps a log of all of his transactions. He keeps track of how many orders he places every week and how many orders are filled every week when the delivery truck arrives. Today, Richard has unfilled orders for 16 cases of herbal tea. A. Create a stock of “Unfilled Orders.” What are the inflows and outflows to the stock? From the above description, formulate the equations driving the flows to the stock. In your assignment solutions document, include the new model diagram and documented equations. Hint 1: The two stocks, “Inventory” and “Unfilled Orders” represent two different concepts and hence there cannot be a flow from one to the other. Hint 2: Do not connect any flows to each other. Instead, formulate identical equations for the two flows if you wish them to have the same values. Page 3D-4758-1 B. Draw reference modes for the two stocks under the original scenario (college students demand four crates worth of herbal tea a week) and then simulate the model over a period of fifty weeks. In your assignment solutions document, include graphs of the behavior of both stocks. What are the equilibrium values of the two stocks? Why? C. Draw reference modes for the two stocks under the Strawberry Kiwi Delight scenario. Simulate the model under this scenario over a period of fifty weeks. In your assignment solutions