NutriStar produces a line of vitamins and nutritional supplement
1. Draw a network diagram for this project. Identify all the paths through the network diagram.2. Simulate the completion of this project 1000 times assuming that activity times follow a triangular distribution. Estimate the mean and standard deviation of the project completion time.
3. Develop a histogram to summarize the results of your simulation.
4. Calculate the probability that the project can be completed within 30 months. What is the probability that the project will take longer than 40 months? What is the probability that the project will take between 30 and 40 months?
MINI CASE
NutriStar produces a line of vitamins and nutritional supplements. It recently introduced its Nutri-Sports Energy Bar, which is based on new scientific findings about the proper balance of macronutrients. The energy bar has become extremely popular among elite athletes and other people who follow the diet. One distinguishing feature of the Nutri-Sports Energy Bar is that each bar contains 50 milligrams of eicosapentaenoic acid (EPA), a substance strongly linked to reducing the risk of cancer but found in only a few foods, such as salmon. NutriStar was able to include EPA in its sports bars because it had previously developed and patented a process to refine EPA for its line of fish-oil capsules. Because of the success of the Nutri-Sports Energy Bar in the United States, NutriStar is considering offering it in Latin America. With its domestic facility currently operating at capacity, the President of NutriStar has decided to investigate the option of adding approximately 10,000 square feet of production space to its facility in Latin America at a cost of $5 million.
1 Approved Answer
Maulik P answered on January 29, 2021
2.7 Ratings,(9 Votes)
Answers:
1. Draw a network diagram for this project. Identify all the paths through the network diagram.
First of all, we have to calculate expected time of completion of each task and variance.
The table below shows the calculations. For simplicity of calculation, the tasks are given task IDs.
Task ID
Activity
Optimistic
Most Likely
Pessimistic
Expected time
Variance
1
Concept Development
3
12
24
12.50
12.25
2
Plan Definition
2.1
Define project scope
1
2
12
3.50
3.36
2.2
Develop broad schedule
0.25
0.5
1
0.54
0.02
2.3
Detailed cost estimates
0.2
0.3
0.5
0.32
0.00
2.4
Develop staffing plan
0.2
0.3
0.6
0.33
0.00
3
Design and Construction
3.1
Detailed engineering
2
3
6
3.33
0.44
3.2
Facility construction
8
12
24
13.33
7.11
3.3
Mobilization of employees
0.5
2
4
2.08
0.34
3.4
Procurement of equipment
1
3
12
4.17
3.36
4
Start-up and Turnover
4.1
Pre-start-up inspection
0.25
0.5
1
0.54
0.02
4.2
Recruiting and training
0.25
0.5
1
0.54
0.02
4.3
Solving start-up problems
0
1
2
1.00
0.11
4.4
Centerlining
0
1
4
1.33
0.44
Now, based on this, we can produce network diagram as follows:
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2. Simulate the completion of this project 1000 times assuming that activity times follow a triangular distribution. Estimate the mean and standard deviation of the project completion time.
The simulation is done in the ‘Simulation’ sheet in the attached excel file
For each of the activity, a random variable is taken for each simulation,
and using optimistic, most likely and pessimistic times a triangular distributed activity time is generated each time
By appropriately summing up the activity times according to precedence chart, the project completion time can be calculated for each simulation
Repeating this for 1000 times, we get 1000 project completion times
The mean completion time according to simulations = 36.09
The Standard deviation of the completion time = 3.98
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3. Develop a histogram to summarize the results of your simulation.
The Histogram is shown in the ‘histogram’ sheet in the attached excel file.
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4. Calculate the probability that the project can be completed..
For this, we will consider project completion time as normal distribution
Hence, the probability of completing project at any months can be calculated using norm.dist function.
within 30 months.
The probability of project completion in <30 months is 7.20%
longer than 40 months?
The probability of project completion >40 months is 13.11%
between 30 and 40 months?
The probability of project completion between 30 and 40 is 79.69%
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