ࡱ> M bjbj== WWlfffz*-*-*-8b-~-zw.(F.L...FNGGvvvvvvv$x z"vf/GAF/G/GvG..vGGG/G:8.f.vG/GvGvGHmNfjv.. dNz&*-iG:jtjv,v0wt~ |G |jvGzzTUTORIAL: Introduction to System Dynamics and VENSIMa Tool for Characterizing Project Dynamics Perhaps no tool in the history of humankind has had so great an impact on the understanding of complex processes and problems. In this section we provide a brief tutorial on how to build system dynamics models. Such models can be a substantial problem-solving aid in coping with the problems of project management. We shall be concentrating on a specific software package called VENSIM. While several packages could potentially be chosen for use here, our focus is on VENSIM because there is a robust version of it that is free for students to use as a learning tool. More than that, VENSIM does what it does as least as well or better than its competition. For higher education, it has to be the tool of choice. VENSIM Tutorial VENSIM is one of several commercially available programs that facilitate the development of continuous simulation models known as system dynamics models. Compared with competing programs, VENSIM is extraordinarily powerful yet inexpensive. Its developer, Bob Eberlein, vends the tool as shareware. This gives students an opportunity to learn the tool and evaluate it before actually buying it. The Personal Learning Edition (PLE) of VENSIM can be downloaded for free from the www.VENSIM.com web site. Once downloaded, VENSIM must be installed. It comes with a substantial array of prefabricated models that can be readily used or re-used. When creating a new model the user will click on File on the main menu and then New. The following dialog box pops up. Figure 6a.1 VENSIM Time Bounds box in upper right corner This is called the time bounds box. In this box, you specify the starting time, the ending time, the time step and the units on time. The time step should create at least 500 steps between the starting time and the ending time. For example, if the starting time is 2010 and the stopping time is 2060, then you should use a time step that is no larger than .1 year. Units on time can be smaller than a second and larger than a year. Once you click OK, you exit the time bounds box and are shown the main screen. You can always return to the time bounds box by clicking on Model and then Time bounds. The main screen presents a drawing canvas and an additional tool palette. You can use this canvas and palette for drawing causal loop diagrams and stock and flow diagrams. However, only stock and flow diagrams can be translated into running simulations. VENSIM adds a fourth row of iconic tools below the tool bar. These icons are used to delineate the diagrams. For causal loop diagrams, only the variable tool and the connector tool are used. Try creating the following causal loop diagram: Figure 6a.2. Casual Model for population Use the tool just to the right of the arrow on the bottom row of iconic tools to create the variable names net growth rate normal, population net growth rate, and population. You can tell which tool is the variable tool by resting the cursor on the icon. This will cause a prompt to popup. For the variable tool, the popup reads Variable Auxiliary/Constant. Next, add the connections or edges. Use the fourth tool from the left on the bottom row of icons; the one labeled Arrow when the cursor is rested on it. To attach an edge from one variable to another you must first select the Arrow tool. Then click on a variable and then click again at the approximate point where you want the edge to curve. Finally click on the destination or target variable. You can also click on the origination variable and then directly on the destination variable, but this will produce a straight line connection which is somewhat less aesthetic than the curved connector or edge. From causal Loop Diagram to Stock and Flow Diagram The transition from causal loop diagram to stock and flow diagram has to be performed manually by the user. So far, no such software exists to perform this function for model builders. To accomplish the transition, every variable and edge in the causal loop diagram must be identified as to type. There are three variable types and two edge-types in VENSIM. The variable types are Auxiliary/Constant, stock (also called box or level or state), and the rate variable. The edge types are information (which is represented as a connector edge of the type used in the causal loop diagram) and flow. The variable types are exhibited below  The variable delineations above dont tell us anything about the character of the variables themselves. For example, a stock variable represents a point where content can accumulate and deplete, like the holding tank on the back of a toilet or a sink, a bath tub, a gas tank and so forth. A The edge types are exhibited below.  To translate a causal loop diagram to a stock and flow diagram, you must simply identify all of the variables and edges. However, frequently when we do this we discover that things (variables, edges) are missing and that we must add variables/edges to create a relevant stock and flow diagram. The reason this is the case is because causal loop diagrams are created for a variety of different reasons, not just to be translated into stock and flow diagrams. Often causal loop diagrams are created to efficiently delineate causal relationships without regard to what structure is necessary to expedite transitions to stock and flow diagrams. When this happens rate variables are left out, frequently. So you must accomplish the transition from causal loop diagrams to stock and flow diagrams manually. Once youve done that you can delineate the stock and flow diagram onto the VENSIM canvas. Lets see how this works for the simple population growth model we were discussing earlier. Before we can do that we need a few rules. For example, in any causal loop diagram involving a pair of variables in a loop (technically, a cycle), one of those variables must be a rate and one must be a stock. The loop is created by a pair of edges. One of those edges must be an information edge and the other is a flow edge. The question is, which is which. 6A-1 An Example: Population Dynamics. As an example of the synthesis procedure, consider a simple model of a population system, such as an ant hill or bee hive. For simplicity we assume an infinite food supply and a limitless environment conducive to population growth. Thus the growth of population is unhindered and the model need embrace only the population itself. The quantities to be subsumed by the boundary B are listed in Table 6.2 together with the units associated with each quantity. Quantity Name Units P Population capita BR Birth rate births/time unit DR Death rate deaths/time unit BRN Birth rate normal births/(capita-time unit) DRN Death rate normal deaths/(capita-time unit) Table 6A.1 A List of Quantities in the Population Model This list is sufficient to accomplish steps 1 and 2 of the methodology. Next, the couplings between the various quantities are specified. The details necessary to accomplish this step will be taken up later. Once the couplings between the quantities are determined, a graph showing the interconnections between the quantities can be drawn. We call this graph a causal diagram. The casual diagram for the simple population model is shown below in Figure 6.1.  + + BRN BR P DR DRN + + + + Figure 6A.3: Causal Diagram for a Simple Population Model An arrow directed from one quantity to another is referred to as a coupling. If the sign associated with the coupling is positive, then the quantity from which the coupling is directed is said to have a positive affect on the quantity toward which the coupling is directed. The reader should convince himself that Figure 6a.3 is correct from an intuitive stand-point. From the casual diagram model the analyst proceeds to develop the schematic or flow diagram model, involving steps 5 and 6 of the methodology. In order to do this, it is necessary that the analyst have well in mind the distinguishing characteristics of each of the quantity and coupling types.  As previously mentioned, states are represented by rectangles , rates by valves     auxiliaries by circles , and parameters by small circles . There are two types of couplings flow couplings and information couplings. Flow couplings are represented by solid lines and information couplings by dashed lines. Once all quantities and couplings are classified, the resultant schematic model can be delineated as shown in Figure 6A.4.  Figure 6A.4: Schematic (Flow) Diagram of a Simple Population Model From the schematic diagram, the analyst is able to write equations for each of the variables and parameters of the model. The parameter values are established from observations and measurements made on the system directly. For example, assume that 4 births per 100 capita per time unit were observed, as were 2.8 deaths per 100 capita per time unit. Then BRN = .04 , and DRN = .028 . The other three equations are provided here without justification. P(t+(t) = P(t) + (t*(BR-DR) (6A.1) P(0) = 1.65E9 BR = P*BRN (6A.2) DR = P*DRN Using these equations the analyst is ready to code a simulation computer program or use packaged software that will accomplish the task. An appropriate program is shown in Figure 6A.3 where a time-step of .2 time units is used , a time-domain of 50 time units is specified and an initial population of 1000 capita is assumed. The variables are printed every simulated time unit. BRN = .05 DRN = .03 P = 1000. T = 0. DT = .2 FOR I = 1,1251 BR = P*BRN DR = P*DRN PRINT T,P,BR,DR P = P + DT*(BR - DR) T = T+DT NEXT STOP END Figure 6A.5: A BASIC Simulation Computer Program for the Simple Population Problem However, we can avail ourselves of a different tack, namely use VENSIM. To do so, we click on the equation tool on the toolbarthe right-most icon on the lower-most toolbar with the symbol Y=x 2 on it. VENSIM will highlight all variables that require equation-related information to be specified. When you click on any of these variables, VENSIM brings up its equation editor dialog box. It will then require you to enter information into white, boxed areas of this dialog box. Once youve done what it needs it will allow you to close the box and proceed to another variable. Once all of the equations are specified, you can press the runner icon or go to the menu bar and click on Model and then Simulate under that. VENSIM will run the simulation. It is now possible for you to specify a figure like that in Figure 6A.4 that enables you to view the results.. The results are plotted in Figure 6A.6 where it is observed that population, birth rate, and death rate all exhibit exponential growth.  Figure 6A.6. Behavior Exhibited by the Exponentially Growing Population Model A One-Sector Inventory Model Consider the following situation. Sonya Magnova is a television retailer who wishes to maintain a desired inventory equal to DI television sets so that she doesnt have too sell her demonstrator and show models. She is currently experiencing moderately constant demand of D units per month. Sonyas ordering policy is quite simple adjust actual inventory toward desired inventory so as to force these to conform as closely as possible. Currently, the inventory is low Io units are left. The time required for inventory t be received once it is ordered at AT, the adjustment time. Sonyas order rate in terms of units per month can be approximated by the equation OR = (DI - I)*AT.  Figure 6A.7. Flow diagram for a simple inventory adjustment problem. Sonyas order rate equation contains four essential components: A desired condition, DI An actual condition I A measure of the discrepancy (DI-I) A way to express action based on the discrepancy  EMBED Equation.2  Most rate equations that express deliberate managerial control of a certain flow contain these four basic components [7]. It should be apparent that the only flow in this case is television sets. This flow is accumulated into and depleted from a state or level called inventory. The flow diagram for this model appears in Figure 6a.7. The structure appears similar to the population model examined earlier. The behaviors, however, are quite different, due to the differences in the information infrastructures in the two models. These differences cause the actual equations used for the two rates to be quite different. For the inventory model, these are  EMBED Equation.2  (6A.3) and I(t + (t) = I(t) + (t ( OR (6A.4)   DI Io Figure 6a.8. Plotted behavior of the simple, one-sector inventory model. By comparing equations (6.3) and (6.4) with equations (6.1) to (6.2), it becomes increasingly apparent how these two models differ from each other. The inventory model produces a behavior like that shown in Figure 6.6. This behavior is called exponential goal seeking. Clearly, an actual condition or state is being driven toward some goal or desired condition. The discrepancy between the desired and actual condition decreases, but never quite get to zero, assuming (as in this problem) that the desired condition remains constant. If the desired condition varies, then the actual condition will attempt to follow the desired condition. Towards a Model of Project Dynamics Projects begin with a huge block of uncompleted work. Eventually, all of this work gets completed. The rate at which uncompleted work gets finished and thus enters the realm of completed work is called the work rate. Obviously, the work rate would be a function of the number of workers, the efficiency with which they work and so forth. Based on this short scenario, evidently there are two stock variables, places where work in this case can deplete and accumulateuncompleted work and completed work. There is one rate variable, the work rate. This rate depletes the stock uncompleted work and adds to the stock variable completed work. We must decide what units to use for all of this. We pick hours for each of the two stock variables and hours/month for the rate variable.  Figure 6a.9. Simple Stock and Flow Model of Uncompleted vs. Completed Work To create this diagram, we click on the box variable icon and then on n the canvas where we want the box variable (stock or state) positioned. VENSIM opens up with a text field in which it expects the user to enter a name for this stock. We enter Uncompleted work and hit . We do this again for Completed work, except we do this to the right of the Uncompleted work box. Next, we select the rate tool by clicking on it. Then, we click on the stock Uncompleted work and again on the other stock Completed work. VENSIM again responds with a text field in which we enter the text work rate followed by . VENSIM will then delineate a flow from Uncompleted work to Completed work with a rate symbol representing a rate variable that controls the flow between the two. The diagram is done. Assume for the moment that 10,000 hours of uncompleted work are determined to comprise a project, whose work rate is 100 hours per month. Initially, there are no hours of completed work. It should be clear that 100 months will be required to complete the project. Once the figure above is created on the VENSIM canvas, the next step is to specify equations for the model. This is accomplished by clicking on the Y=x2 tool. VENSIM then displays all of the variables that require an explicit equation. In general, stocks require, as a minimum, an initial defining condition. For example, click on Uncompleted work. The equation editor dialog box pops up with the cursor in the initial value field. We enter the number 10000. This is all we have to do because VENSIM understands that Uncompleted work is depleted by the rate work rate and has already set up an equation for that in the topmost field of the editor box. We click on OK to close the box. We do the analogous thing for Completed work; namely, we click on it to bring up the equation editor dialog box. Then we enter 0 in the initial value field and click on OK to close the box. Notice now that neither of these two entities (Uncompleted work and Completed work) are highlighted. VENSIM is satisfied with what it knows about these variables. Only one variable remains highlightedwork rate. As before, we click on it and once again, the equation editor box pops up with the cursor positioned in the equation field. Since we said the work rate was 100 hours per month, we enter 100 and click on OK to close the box. Now, there should be no variables that are not highlighted. We have one more thing to do before running the simulation. We have to specify a data name for the data file that VENSIM will create and store on the hard drive during the time in which the simulation is running. This is done by entering a filename in the white text field at the top of the VENSIM display in the tool bar row immediately below the menu bar. We enter WORK1. Now we can click on the Runner tool next to the white text field, and the simulation runs almost instantaneously. The behavioral result is exactly what we would expect. The Uncompleted work is depleted to zero in 100 months exactly. At which point in time, all of the work is done. We see this because completed work ekes upward until all 10,000 hours are accumulated within it. The behavior of both variables is entirely linear. Figure 6a.10. Work: From YET TO BE DONE to ALREADY COMPLETED The above model is unrealistic because we would expect to hire several people to work on the project, where as the above model seems to assume only one person at 5/8 time. Typically, there are 160 hours in a month, assuming a 40-hour work-week. Lets assume that one person gets hired a month for each of the first five months. Now, how long will it take to complete the project? Certainly, it will take less than 100 months. If all five persons were available at the very beginning, then 160*5 or 800 hours would be available each month. The project would be complete in 12.5 months. However, each person is brought on gradually because the project manager, the one who is hired first, can only train one at a time. His training time is built into the 10000 hour estimate. Assume also that the first month of each persons time on the job is productive at half of the normal rate; that is, 80 hours of productive time is all that is derived from each team-members first month on the job. These considerations give rise to the following work rate function: Work rate = 160 * time if time<=5 and 800 if time is greater than 5. We use an IFTHENELSE() function to model this in VENSIM, as follows: IF THEN ELSE(time<=5,160*time, 800) Here, the first argument of the IFTHENELSE function is the conditional expression time<=5. The second argument is the result the function will return if the expression is true, while the third argument is the result the function will return if the expression is false. We will build this expression into our model by clicking on the equation editor icon or tool Y=x2 on the second toolbar at the top. In place of 100, we type or paste in the above expression exactly as it appears above. When we click on OK, VENSIM comes back with the following remark; The following inputs were not expected (but are used): Time Do you want to update the input list? Your response to the query should be Yes. So, click on Yes. Figure 6a.11. VENSIM Delineation of the Uncompleted to Completed Work Model VENSIM closes the equation editor dialog box and returns you to the model formulation canvas, which should look like this, after you have used the pointer to move the time up above the variable work rate.  Since we expect this project to now be done in twenty months, we reset the duration to twenty months as follows. On the menu bar, we click on Model and then on the menu item Time Bounds The time bounds dialog box comes up and we reset the final time to 20 months and the time step to .125 months. Next, we change the data name to Work3 because a new data name is needed for storage on the hard drive of the data that will be generated during the simulation run. Now we press the runner icon. The plotted results appear below. Figure 6a.12. Plot of Uncompleted work vs. Completed work for a 29 month period Something isnt quite right in this picture because Uncompleted work gets drained to a negative 3950 man-months in the twenty-month period. In other words, the project ran much longer than it needed to because it was unable to detect when all of the work was completed. Rather than using cut and try techniques of trying to estimate when the project will be throughobviously, somewhere between 12.5 months and 20 months, we choose instead to pass information about Uncompleted work to the rate work rate. To do this we use the connector tool . We click on the connector tool to select it. Then we click on Uncompleted work and again on work rate, to indicate that we want information about Uncompleted work passed to work rate. Finally, we must once again change the equation for work rate as follows: IF THEN ELSE(Uncompleted work>0, IF THEN ELSE(time<=5,160*time, 800), 0) This will force the work rate to zero when the amount of uncompleted work is zero. We change the data name to Work4 and click on the runner. The result appears in the figure below.  Figure 6a.13. Revised Plot of Uncompleted work vs. Completed work for a 20 month period Clearly, it took longer than 12.5 months to complete the project. In fact, the project is complete in roughly 15 months time. Now, by passing information about Uncompleted work to work rate we have been able to construct an equation that will set work rate to zero when Uncompleted work is zero, as indeed it should be. It should also be clear that we can nest the IF THEN ELSE function within itself. Suppose that the 10000 hours of uncompleted work is just the first of three major phases that make up a project and that the second and third phases, themselves also each 10000 hours long, cannot start until the first phase is complete. Furthermore, assume these phases must use a startup policy identical to that of the first phase; namely, a new person is brought on-board each month. To accomplish this we can establish focus on the entire structure so far by rubber-banding it with our cursor, copying it and then pasting it back twice. First, we make sure the cursor is selected. Then, we mark a position to the left and above the structure, hold down the left mouse button and drag the cursor down to a point below and to the right of the structure. Make certain all of the structure is within the rectangular area with a dashed line for a border. When we release the left mouse button, the whole structure is highlighted, indicating all of it has been selected. We then select (click on) Edit and then Copy (or hit -C) to copy the entire structure onto the clipboard. Next we select Edit and then Paste (or hit -V) to paste the entire structure back onto the canvas. VENSIM has a question about what we are doing. It wants to know if this is to be replicated structure. We answer Yes. The pasted structure is highlighted and needs to be moved off of the structure it was cloned from. VENSIM has changed the names by adding a 0 after each name. Since we need two of these structures, one for each of phases two and three, we need to paste the structure onto the canvas again. We do this the shortcut way by hitting -V and once again, we get the question about replication from VENSIM. As before, we answer with Yes and a replicated structure is pasted over the structure that was cloned. We pull it over to a portion of the canvas that is unused. Next, we use the connector to pass information about Completed work to work rate 0 and work rate 1. The end result should appear as shown below.  Figure 6a.14. Plot of Several Tasks linked together We must now adjust the equations for work rate 0 and work rate 1. We click on the equation editor and just these two variables are highlighted, indicating VENSIM thinks these two variables are the only ones whose equations require any modification. We agree. We click on work rate 0 and establish the following relationship: IF THEN ELSE(Completed work>9999,IF THEN ELSE(Uncompleted work 0>0, IF THEN ELSE(Time<=5,160*Time, 800), 0),0) This is just the earlier relationship for work rate with the another IF THEN ELSE added. That prevents work rate 0 from being anything other than 0 until the previous phase involving Completed work is 99.99% finished. We do the same for Work Rate 1. Then we adjust the time bound on the model (click on Model and then Time Bounds) to set a Final Time of 35. (We think it will take approximately 30 months, but we want to leave some extra time to see what happens after all of the work is completed. We get the following result:  Figure 6a.15. Plot of Completed work for a succession of two tasks in which the second task cannot start until the first task is finished There are no surprises in the figure above. The follow-on phases start immediately after the first phase is complete and run until they are themselves complete.  Figure 6a.16. Plot of Uncompleted work Depletion for a Succession of Two (Three) tasks Exercises 1. A certain project requires 100 experienced professionals to complete it. An estimated 8000 man-months of work is to be done. Currently, there are five rookies and five experienced people on the project. New hires are brought-on to the project as rookies at the rate of 8 a month. It takes six months for a rookie to become experienced. (Every month, 1/6 of the rookie group flows into the experienced group.) The rate at which experienced people quit and take on other jobs is 2% of the existing cadre of experienced professionals each month. The rate at which work is being completed each month is measured in man-months/month and is simply the number of experienced people on the project at any given time. Work flows from work undone to work completed. The purpose of the model is to determine how long in actuality it will take to complete the project assuming everything goes according to plan. What units will you use on time? Hint: there are at least four states (stocks) in your model. 2. Suppose, in 1 above, that work completed is found to be 10% defective, resulting in a flow back into work undone Suppose also, that rookies leave the company at a rate of 3% a month. Add these constructs to the model you developed above. 3. Suppose in 1 above, you are interested in determining total project cost. Rookies are paid $45 per month, while professionals are paid $65 per month. What is the total project cost? 4. A project initially has 2000 months of work entailed in it. Assume there are 50 people working on the package, i.e., the work rate is 50. After 40 months the project is expected to be completed. Determine a structure that will characterize work remaining and work accomplished for a 40 month period. Delineate variables, a causal loop diagram and a stock-and-flow diagram. 5. THE END-OF-SEMESTER CRUNCH. A student is having trouble coping with the end of semester crunch as assignments, test preparations, and term projects compete for less and less time. For convenience, we shall refer to all of these time consuming activities as school work. As more and more school work gets assigned or becomes due, the backlog of uncompleted school work begins to build up. The only way to reduce the backlog is to get the work done. This we shall refer to as the work completion rate. The real problem is the work pressure that builds up. Certainly, a larger assignment backlog contributes to more work pressure, but there are other contributors as well such as time remaining to complete the work (or just time remaining). Time remaining is the difference between the current calendar date and the due date of the assignments and projects, and the test dates. The grad student copes with this work pressure in two ways. By working longer hours (more hours per week), the student can increase the work completion rate. Doing a skimpier job by taking short cuts on the assignments, test preparations, and projects also speeds up the work completion rate as effort devoted to each assignment is reduced. Both of these strategies have their down sides, as we shall see. Can you think of any other strategies for coping with this problem? Consider the strategy of working long hours. This deprives the student of sleep, resulting in burnout, ultimately After a week or two of long hours, the student begins to suffer from burnout and productivity begins to drop. A drop in productivity reduces the work completion rate. Consider the strategy of reduced effort in which the student takes short cuts. Reduced effort strategies result in reduced grades which are also undesirable (in some students minds at least). Actually, what happens is that reduced effort reduces the quality of the work which results in reduced grades. But reduced grades taken in relation to a grades standard will result in increased effort devoted to work. a. What are the major variables? b. Are there tautologies that need to be eliminated? c. How do these variables change over time? d. What does your work backlog look like over the course of a semester? 6. A work package initially has 1000 months of work entailed in it. Assume there are 100 people working on the package, i.e., the work rate is 100. After 10 months the package is expected to be completed. Determine a structure that will characterize work remaining and work accomplished for a twenty-four month period. Delineate variables, a causal loop diagram and a stock-and-flow diagram. A certain project requires up to 100 experienced information technology professionals to complete it. The project consists of two major tasks in a finish start relationship; that is, task two cannot commence until task one is complete. For both tasks, there is a flow from work undone to work completed. An estimated 10,000 man-hours of work is to be done for each task. All of the available professionals will be applied to the first task and then to the second. Currently, there are ten professionals on the project. New hires are brought-on to the project at the rate of 5% of the professionals on the project a month. The rate at which people quit and take on other jobs is 2% of the existing cadre of professionals each month. The rate at which work is being completed each month is measured in man-months/month and is simply the number of professionals on the project at any given time. Work flows from work undone to work completed for the first task. Once the first task is complete, an identical second structure involving work undone and work completed is needed for the second task. The purpose of the model is to determine how long in actuality it will take to complete the project assuming everything goes according to plan. What units will you use on time? 8. A certain project requires experienced information technology professionals to complete it. The project consists of two major tasks. The second task begins in month four and bears no relationship to task one, except that the two tasks will share resources 50-50. Task one gets all of the human resources (professionals) until the start of month four, after which each task gets half. For both tasks, there is a flow from work undone to work completed. An estimated 1,000 man-months of work is to be done for each task. Currently, there are ten professionals and five new hires on the project. The hiring rate for new hires is 6% of the professionals on the project. The maturation time for new hires is six months, so every month one sixth of the new hires flow into the professional category. After the total number of professionals reaches 50, hiring is stopped. The rate at which professionals quit and take on other jobs is 2% of the existing cadre of professionals each month. The rate at which work is being completed each month is measured in man-months/month and is simply the number of professionals on the project at any given time. Work flows from work undone to work completed for both tasks. The purpose of the model is to determine how long in actuality it will take to complete the project assuming everything goes according to plan. What units will you use on time? Hint: there are at six stocks and three flows in your model. 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