AMS 341 (Fall, 2023) Operations Research I: Deterministic Models Homework Set # 8
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AMS 341 (Fall, 2023)
Operations Research I: Deterministic Models
Homework Set # 8
Due on BrightSpace by noon (12 pm), Friday, November 17, 2023.
Read Chapter 7 Sections 3,5 and Chapter 8 Section 4 (Critical Path Method)
Submit the following three problems:
(1). Consider the following Balanced Transportation problem and the given BFS. Supposed variable x14 enters the basis. Which variable(s) leaves the basis?
|
|
|
|
|
|
supply |
|
|
100 |
|
|
|
100 |
|
|
50 |
|
50 |
|
100 |
|
|
|
|
80 |
|
80 |
|
|
|
50 |
20 |
100 |
170 |
|
demand |
150 |
50 |
150 |
100 |
|
(2). The following is an assignment problem, rows correspond to people and columns to jobs that must be performed. Our goal is to minimize the cost of the assignment.
|
job |
1 |
2 |
3 |
4 |
5 |
|
person 1 |
0 |
4 |
3 |
0 |
5 |
|
person 2 |
0 |
5 |
3 |
4 |
2 |
|
person 3 |
0 |
1 |
0 |
0 |
0 |
|
person 4 |
0 |
6 |
2 |
0 |
6 |
|
person 5 |
0 |
0 |
0 |
0 |
0 |
(a) What is the smallest number of lines are enough to cover all zeros?
(b) The smallest uncovered element is:
(3). The following is a list of tasks that have to be completed as soon as possible.
|
Activity |
Predecessors |
Time (hours) |
|
A |
- |
5 |
|
B |
- |
9 |
|
C |
- |
6 |
|
D |
B,C |
5 |
|
E |
A,B |
10 |
|
F |
C |
2 |
|
G |
D,F |
6 |
|
H |
B |
8 |
(a) What are the critical activities for this project?
(b) How soon can the project be completed?
(c) What is the total loat of activity F?
(d) If activity D is made shorter by 1 hour, would the project take less time to complete? Explain briely (e) If activity E is made shorter by 1 hour, would the project take less time to complete? Explain briely
Additional practice problems - do not turn these in:
Use the transportation simplex method to solve Problem 1 Section 7-1 (page 371). Practice by starting with all 3 methods to ind an initial BFS.
Consider a Balanced Transportation Problem. The number of basic variables found by Vogel’s method must be the same as the number of basic variables found by the Northwest Corner method. True or False? Explain.
Consider a Balanced Transportation Problem. The cost of a BFS found by the Min Cost method must be at least as good as the cost of a BFS found by the Northwest Corner method. True or False? Explain.
Problem 1 Section 7-5 (page 398).
Problem 5 Section 8-4 (page 447). No need to calculate free loat.
Consider a project network that has a unique critical path. Suppose task A on the critical path is shortened by 10 days, and task B on the critical path becomes 10 days longer. Does the project completion time remain the same?
2023-12-25