1. Draw a network diagram for this project. Identify all the paths through the network diagram — Simulate completion 1000 times assuming that activity follow triangular

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?

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.

SOLUTION

The following abbreviations will be used for the activities.

Activity Description	Abbreviation
Concept Development	A
Plan Development
Define project scope	B
Develop broad schedule	C
Detailed cost estimates	D
Develop staffing plan	E
Design and Construction
Detailed engineering	F
Facility construction	G
Mobilization of construction Employees	H
Procurement of equipment	I
Start-up and Turnover
Pre-startup inspection	J
Recruiting and training	K
Solving start-up problems	L
Centerlining	M

Using these abbreviations and the information provided in the case, the following AOA network diagram can be constructed.

B F

G

A C H I J K

D

L M

E

There are 32 paths through the network as follows

A, B, F, G, J, K, M A, D, F, G, J, K, M

A, B, F, G, J, L, M A, D, F, G, J, L, M

A, B, F, I, J, K, M A, D, F, I, J, K, M

A, B, F, I, J, L, M A, D, F, I, J, L, M

🔒

Unlock the complete assignment

You are viewing the free preview. Purchase this assignment once to reveal the complete resource.

$9.99 USD

Secure checkout is completed by Stripe.

A, B, H, G, J, K, M A, D, H, G, J, K, M

A, B, H, G, J, L, M A, D, H, G, J, L, M

A, B, H, I, J, L, M A, D, H, I, J, L, M

A, C, F, G, J, K, M A, E, F, G, J, K, M

A, C, F, G, J, L, M A, E, F, G, J, L, M

A, C, F, I, J, K, M A, E, F, I, J, K, M

A, C, F, I, J, L, M A, E, F, I, J, L, M

A, C, H, G, J, K, M A, E, H, G, J, K, M

A, C, H, G, J, L, M A, E, H, G, J, L, M

A, C, H, I, J, K, M A, E, H, I, J, K, M

A, C, H, I, J, L, M A, E, H, I, J, L, M

Prior to simulating the project, the mean and standard deviation for each activity must be calculated. The spreadsheet shown below was developed to calculate these parameters.

Next, the actual spreadsheet to simulate the completion of the project can be developed. As demonstrated in the textbook, one approach is to dedicate a column to each activity and then generate random activity times. Thus, in the spreadsheet developed for this case, columns A - M were dedicated to activities A - M, respectively. Then random numbers were generated for the activities using Crystal Ball and defining cells A3:M3 as Assumption Cells. A portion of the simulation model is shown below.

After generating the random numbers in the Assumption Cells, one column is dedicated to each path and formulas are entered to calculate the path completion time based on the random activity times generated. Entering the formulas is very straightforward since the letters used to label the activities correspond directly to the column labels. To illustrate, the formula for path A - B - F- G - J - K - M in row three is: =A3+B3+F3+G3+J3+K3+M3.

To determine the time to complete the project, a final column was entered that calculates the maximum path completion time across all paths in the spreadsheet. Then, summary statistics for this column were calculated. One simulation of 1,000 replications of the project yielded an average project completion time of 35.85 months with a standard deviation of 4.69 months. The maximum completion time was 50.83 months and the minimum completion time was 19.52 months.

This histogram created by Crystal Ball is shown below.

The probability of completing the project in 30 months or less is 10.2%:

The probability of the project taking more than 40 weeks is 19.0%:

The probability of the project taking 30 to 40 months is 70.8%: