Assignment 1 (Due at 11:59 pm)
Instructions:
- Please answer the assignment questions in this docx file and save once you’re satisfied. Assignment 1 covers the lectures slides for Week 1 and Week 2.
- There are three assignment problems. Please follow the instructions given at the end of each question if any.
- To submit your assignment, go to “Assignments” on the left panel of the course homepage. Then
- Click on the bold link “Assignment 1” to open;
- Go down to Section 2 “Assignment Materials” on the webpage you’re directed to;
- Click the button “Browse My Computer” in Section 2 and upload your document;
- Scroll down to the bottom of the webpage and click the grey button “Submit” in Section 3 “Submit” to complete the submission.
- To resubmit your assignment, simply click to open “Assignment 1” again and click the grey button “Start New Submission” on the upper right corner of the “Review Submission History” webpage you’re directed to. You can make as many submissions as you like before the due time. Only the last submission will be graded.
Assignment Problems (120 points in total):
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| Resources | |
| Labor | 400 hours per day @ $20 per hour |
| Raw Materials | 20,000 pounds per day @ $2 per pound |
| Energy | $10,000 per day |
| Capital | $8,000 per day |
(a) What is the capital productivity? Please provide the formula for calculating productivity, at least one step of calculation, and the correct answer for full credit. (6 points)
(b) What is the total productivity in this problem? Please provide the formula for calculating productivity, at least one step of calculation, and the correct answer for full credit. (6 points)
- Suppose a project consists of the following activities.
| Activity | Immediate Predecessors | Time (Days) | |
| A | None | 5 | |
| B | None | 8 | |
| C | A | 4 | |
| D | B, C | 6 | |
| E | B, C | 4 | |
| F | D | 6 | |
| G | E, F | 4 | |
(a) Draw the activity-on-node (AON) project network based on the table above. Only nodes and directed arrows are required in the network for full credit. (10 points)
(b) Listall the paths in the network and calculate the completion time of each path for full credit. (10 points)
(c) What is the project completion time? Please give the reason for full credit. (4 points)
- The following represents a project that should be scheduled using PERT.
| Activity | Immediate Predecessor(s) | Times (Days) | ||
| a | m | b | ||
| A | None | 1 | 3 | 5 |
| B | None | 1 | 2 | 3 |
| C | A | 1 | 2 | 3 |
| D | A | 2 | 3 | 4 |
| E | B | 3 | 4 | 11 |
| F | C, D | 3 | 4 | 5 |
| G | D, E | 1 | 4 | 6 |
| H | F, G | 2 | 4 | 5 |
(a) Draw the AON project network. Only nodes and directed arrows are required in the network for full credit. (10 points)
(b) Calculate the expected activity time for each activity. (16 points)
(c) Calculate the variance of the activity time for each activity. (16 points)
(d) List all paths and calculate their expected completion time. (24 points)
(e) What is the critical path? (4 points)
(f) What is the expected project completion time? Please give the reason. (4 points)
(g) What is the variance of the project completion time? Please provide at least one step of calculation and the correct answer for full credit. (4 points)
(h) What is the probability of completing this project within 16 days? Please provide the formula for calculating the z value, at least one step of calculation, and the correct probability for full credit. (6 points)
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