D-4761-1 Guided Study Program in System Dynamics System Dynamics in Education Project System Dynamics Group MIT Sloan School of Management1 Assignment #24 Reading Assignment: Please read the following paper:• Generic Structures: Exponential Material Delays, by Stephanie Albin (D-4614-E) Also read the following: • Industrial Dynamics,3 by Jay W. Forrester, Chapter 9 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-4761-1 Exercises: 1. Generic Structures: Exponential Material Delays and Industrial Dynamics, Chapter 9: Representing Delays Please read the paper and work through the exercises. Then read the chapter and answer the following questions: A. Tom has just created a new consulting company and hired five consulting rookies. Given that a rookie needs to be trained for an average of eight months before she becomes experienced, how many of the five rookies will become experienced consultants after 12 months? In your assignment solutions document, please include the model diagram, documented equations, and a graph of model behavior. Hint 1: Although all rookies are hired at once, their transition into experienced workers should not be viewed as a discrete process (that is, in eight months, all five workers will suddenly become experienced). Consultants do not suddenly and discontinuously go from inexperienced rookies to experienced consultants. There is a gradual transition in the tasks that they can do, so their gaining experience is a continuous process. Hint 2: Model the hiring decision as a pulse of 5 workers at time 0. B. Because Tom did not realize the long time delay between hiring consultants and training them, he was unable to work on enough consulting projects, and his company went bankrupt. Tom therefore decides to start another company, but this time, he at first recruits 60 workers who already have consulting experience and do not need to be trained. He knows, however, that about six of his workers will retire or quit the company every year, so he makes a decision to also hire six rookies every year. What happens to the number of experienced consultants? Why? Again, in your assignment solutions document, please include the model diagram, documented equations, and a graph of model behavior. Hint: You may wish to change the time horizon over which you simulate the model. C. Tom now realizes that instead of having a constant retiring rate of 6 workers, a constant fraction, approximately 10%, of his consultants leave the company every year. Reformulate the retiring rate equation to reflect this situation. How does the model behavior change compared to part B? In your assignment solutions document, please include the model diagram, documented equations, and a graph of model behavior. Hint: Again, you may want to increase the time horizon of your model. 2. Independent Modeling Exercise As you may have heard, in September 1998, an MIT freshman died of acute alcohol intoxication. An article in the MIT Observer clarified the science behind the effects of alcohol poisoning. The following paragraphs are excerpts taken from that article. “Alcohol is a depressant: it slows down the transmission of neural activity, which in turn lowers blood pressure, decreases heart rate, and slows down breathing. In the case Page 2D-4761-1 of acute alcohol intoxication, or alcohol poisoning, the imbiber’s heart stops and he ceases to breathe. As he suffocates, the bloodstream carries less oxygen to the brain, and brain cells die. According to Professor of Toxicology Peter Dedon, when someone drinks alcohol, it descends into the intestines where it is absorbed into the bloodstream and body water and into the liver. In the liver, alcohol is first metabolized by alcohol dehydrogenase into acetaldehyde and then metabolized into non-toxic acetic acid, commonly known as vinegar. The liver is only able to metabolize approximately 7 grams of alcohol every hour. In the meantime, the alcohol in the bloodstream and body water reacts with receptors in the brain to slow down the transmission of impulses across neurons. [...] “The delayed transmission of neural activity affects trained behavior and learning. It amplifies emotions, loosens inhibitions, and causes feelings of euphoria. These symptoms are characteristic of the “buzz” commonly experienced after a few drinks, when the blood alcohol content reaches approximately 0.02 grams of alcohol per deciliter of blood. As the level of alcohol in the bloodstream continues to rise, however, the mid-brain also becomes affected. In the mid-brain area, the retarded neural activity brings about a loss of motor coordination and dulls responses to external stimuli. These symptoms translate into a loss of coordination, delayed reflex time, and clouded judgment. The State of Massachusetts defines a person with a blood alcohol content of 0.08 grams per deciliter or more to be “legally drunk.” As the blood alcohol content continues to increase, the drinker begins to slur his speech and has difficulty swallowing. The epiglottic closure and the constricting muscles that protect the airway become sluggish. At the same time, the alcohol activates a center in the brain which stimulates vomiting. Alcohol irritating the lining of the stomach will also induce vomiting. A drinker is then at risk to die from aspiration: inhaling his own vomit. If inhaled, the bacteria in the oral cavity may cause an acute infection in the respiratory system, particulate matter may block the victim’s airways, and the highly-acidic gastric contents of the stomach may sear the lungs with a chemical burn. Drinkers will typically loose consciousness when their blood alcohol content reaches approximately 0.15 grams per deciliter. At that point, they are particularly at risk of suffering from aspiration. The use of alcohol also becomes deadly when the abated neural activity begins to affect the medulla, the inner core of the brain. There the sedative begins to affect body temperature, blood pressure, heartbeat, and breathing. Alcohol not only slows down the muscles that control breathing, but also inhibits the body’s response to the carbon dioxide, so a victim of acute alcohol poisoning will not realize that he is suffocating. Half of the