Stock Flow Modeling in Vensim - Assignment Instructions

Upload a single master report file (in pdf format) which should include all your  answers, graphs, diagrams, Vensim stock-flow screen shots, equations, explanations for each question. Make sure you include the names of all group members in the master pdf file. Use Vensim to develop the simulation models for all the questions. Include all the Vensim files related to each question and name them appropriately. The Vensim models (.mdl) files and Excel files should be placed in one single folder. Then compress the folder in .zip or .rar format and upload the compressed file. Do not e-mail me your answers. Follow this instruction strictly otherwise points will be taken off. Late submission will be penalized (5 points/hr).

 
1. Qualitatively, draw the stock variables for the corresponding input flow variables shown in the following figure

2.Suppose two IT firms, x and y, are engaged in a cyber-warfare modeled by the System:

Parameters c and b are the cyber combat effectiveness coefficients of organizations x and y, respectively. They represent the strengths of the respective organizations. Assume that firm y is more powerful than firm x (i.e., b > c).

the value of b really make a difference? Develop a stock-flow model, generate relevant graphs and explain the results.

(b) Create a Causal Loop Diagram for the above scenario.

3.In a software organization, the number of programmers hired is one per $200K of expected revenue per year. Based on this, construct a stock and flow model of staff recruitment, using the stock flow structure, that takes the following into consideration.

– There are three kinds of programmer: Rookie, Experienced and Expert.

– All hires are done at the Rookie level, and programmers progress to Experienced with an average delay of 50 weeks for rookies, and a delay of 150 weeks before experienced become expert.

– On average, there is attrition from each programmer category. This is 5 % for Rookies, 2 % for Experienced and 1 % for Expert (per year).

- Assume annual expected revenue of the company is $50 million.

- Develop a stock-flow model, generate relevant graphs and explain the result.4.

4.Imagine an IT company generates output or revenue though combined inputs of machines (computer hardware) and employees (programmers). The overall output of the company is defined as follows:

Revenue or Output = No. of Programmers * SQRT (No. of Computer)

Question 1

The machines or computers are depreciated at a rate of 0.10 per quarter. The depreciated computers are discarded. i.e., Discard = No. of Computer * Depreciation Rate. A fixed percentage of the output or revenue is reinvested in every quarter to upgrade the existing computers and to purchase more computers. Assume, Investment = Revenue * Reinvestment  Fraction. Also, assume Reinvestment Fraction = 0.02 per quarter and No. of Programmers = 100. Initial no. of Computers = 100. Assume time step is 0.25.

- Develop a stock-flow model to simulate the above scenario. Explain the result and generate relevant graphs. When does the system reach to equilibrium? Is there some critical number of computers that generates equilibrium? (Hint: Only “computer” should be a stock)

5.Consider two IT companies whose survival depends on their mutual cooperation. One simple model of this mutualism is given by the autonomous system:

a) Solve the system of equations numerically using Euler’s Method and implement it in Excel. Upload the Excel file. Assume reasonable values for parameters a, b, m, and n

b) Write down the equations for numerically solving the system using Euler’s method.

c) Interpret the constants a, b, m, and n in terms of the business problem.

d).What are the equilibrium levels? Create a phase plot diagram. 

6.Suppose the employees of a sales division of a hardware company earn commission which is dependent on the growth of sales revenue given by the following dynamics:

(a) Model the sales growth by using stock-flow in Vensim. What is the critical value of c greater than which the sales revenue becomes unsustainable?

(b) Extend the above problem assuming that sales revenue growth is subject to another threshold variable (represented by a).

7.The spread of a computer virus in a network of computers can be modeled by the following equation:

a)Develop a stock-flow model to find the equilibrium points of this model and determine the stability.

b) If 5% of the computer is infected (so V = 0.05) initially, then what fraction of the computers in the network will be infected in the long run?

c)What if the initial fraction of infection is 30%? Generate relevant graphs and explain the result.

8.You gain weight because you eat; you lose weight when you exercise. However, the more you exercise, the greater your appetite is and the more likely you are to eat. Also, the more you weigh, the greater your appetite will be. So, the weight grows and grows. a) Draw a causal loop diagram and develop the corresponding stock-flow simulation model. Can this pattern be changed? b) What do you need to change in this model to make your weight stabilize at a certain level and stay there? Develop a stock-flow model for the modified causal loop. Generate relevant graphs and explain the result.

9.Extend the stock & flow model of Predator-Prey (available in the Blackboard) assuming that there exist two sets of prey (A & B) populations instead of one. In this case, the predator ‘s gains are additive from the both prey populations. Assume that growth rate of A > growth rate of B. Also, assume that prey population growth is constrained by capacity (