Homework 4 SOLUTION Out: April 18, 2014 LOOKUP and IF-THEN-ELSE Functions

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1 I.E. 438 SYSTEM DYNAMICS SPRING 204 Dr.Onur ÇOKGÖR Homework 4 SOLUTION Out: April 8, 204 LOOKUP and IF-THEN-ELSE Functions Due: May 02, 204, Learning Objectives: In this homework you will use LOOKUP and IF-THEN-ELSE functions for modeling by using the VENSIM PLE software; (VENSIM PLE software MUST BE used for this homework.) Assignment Using a lookup-function it is easy to define any kind of behavior between too variables. Build a simple model with positive feedback to model the interest of bank savings. If the savings are below 0000 TL the interest rate is 6%, if the savings are between 0000 and TL the interest rate is 9% and if the savings exceed TL the interest rate is %. interest INTEREST LOOKUP Build a model presented above. Select the INTEREST LOOKUP -variable with the equation-tool and choose Lookup as the type of the variable. Click the As Graph -button that appears next to the Help-button. A pop-up window will appear. Insert the Input- Output pairs to form a graph. Define the I/O pairs so that they fulfill the given demands. Write the equation for interest as: INTEREST LOOKUP () Initially there is 00 TL in the bank. The simulation parameters are: FINAL TIME=00, TIME STEP=0.25 and Units for Time=Year. Answer following questions: a) How much savings there are at 50th year and at the end of the simulation? Show all your steps, graphs and document all equations. b) How would the situation change if the interest rate would always be 6%. Create another model, where interest rate is fixed 6% and examine how it will affect to the 50 th year value and final value of savings. Again, show all your steps, graphs and document all equations. c) Do the same model by using condition equation (IF-THEN-ELSE-function) instead of LOOKUP-function; and specify again how much savings there are at the 50 th year and at the end of the simulation? Again, show all your steps, graphs and document all equations. (For condition equation, you don t need any auxiliary variable, you can enter the condition equation directly to the rate equation; check for the help of Vensim PLE for the usage of IF THEN ELSE function).

2 SOLUTION: a) Build an interest model shown in the exercise sheet. Create the model. interest INTEREST LOOKUP Select the INTEREST LOOKUP variable and create a Lookup- table. Choose Lookup as the type of the variable and click the As Graph button.

3 Write equations and copy the document all output; () FINAL TIME = 00 The final time for the simulation. (2) INITIAL TIME = 0 The initial time for the simulation. (3) interest= INTEREST LOOKUP()* (4) INTEREST LOOKUP( [(0,0)-(2e+006,0.2)],(0,0.06),(9999,0.06),(0000,0.09),(99999,0.09),(200000,0.),(2e+006,0.)) /Year (5) SAVEPER = TIME STEP The frequency with which output is stored. (6) = INTEG ( interest, 00) (7) TIME STEP = 0.25 The time step for the simulation. Simulate: 80,000 60,000 TL 40,000 20, Time (Year) : Current are TL at the year 50. are TL at the end of simulation.

4 b) Create another model, where interest rate is fixed 6% and examine how it will affect to the final value of savings. interest (fixed rate) INTEREST RATE Write equations and copy the document all output; () FINAL TIME = 00 The final time for the simulation. (2) INITIAL TIME = 0 The initial time for the simulation. (3) "interest (fixed rate)"= INTEREST RATE* (4) INTEREST RATE= 0.06 /Year (5) SAVEPER = TIME STEP The frequency with which output is stored. (6) = INTEG ( "interest (fixed rate)", 00) (7) TIME STEP = 0.25 The time step for the simulation. Simulate: 40,000 30,000 TL 20,000 0,000 0 are TL at the year 50. are TL at the end of simulation. are substantially smaller when using fixed interest rate at the end of simulation, however no change at 50 th year Time (Year) : Current

5 c) Create same model as in Lookup model except auxiliary variable, but this time using IF THEN ELSE-function. interest (if then else) Write equations and copy the document all output; () FINAL TIME = 00 The final time for the simulation. (2) INITIAL TIME = 0 The initial time for the simulation. (3) "interest (if then else)"= IF THEN ELSE(<0000, 0.06*, IF THEN ELSE(<=200000, 0.09 *, 0.*)) (4) SAVEPER = TIME STEP The frequency with which output is stored. (5) = INTEG ( "interest (if then else)", 00) (6) TIME STEP = 0.25 The time step for the simulation. Simulate: 80,000 60,000 TL 40,000 20, Time (Year) : Current are TL at the year 50. are TL at the end of simulation.

6 We have obtained same results with lookup function. Lookup function can be replaced with condition equation (IF- THEN-ELSE), but usually condition equations are quite confusing, hard to handle and very time-consuming to build, at least when situation is more complex than in our example. Instead Lookup functions are easy to use, just make sure you are doing them right.