COMP SCI / SFWR ENG 4O03 – Operations Research

COMP SCI / SFWR ENG 4O03 – Operations Research
Problem Set 3 – 20 points
Handed out: October 27, 2014
Due date: November 26, 2014
** justify your answers **
1. Tom hates to wait at stop signs, yield signs and traffic signals while driving. To minimize
this aggravation, he has prepared maps of the various regions in which he frequently
drives, and measured the average delay (in seconds) at each of the various intersections
in these regions. He wants to find a route from location 2 to 4 which minimizes his delay
at intersections (regardless of the total distance he has to drive to avoid delays). The
details of his map are listed below:
From
1
1
2
2
2
3
5
To
3
4
1
3
5
4
4
Delay (in seconds)
3
6
2
7
6
5
7
Model it as a shortest path problem, and solve it using Dijkstra algorithm.
6p
2. Consider the following system of difference constraints.
x1 − x2 ≤ 1
x1 − x4 ≤ −4
x2 − x3 ≤ 2
x2 − x5 ≤ 7
x2 − x6 ≤ 5
x3 − x6 ≤ 10
x4 − x2 ≤ 2
x5 − x1 ≤ −1
x5 − x4 ≤ 3
x6 − x3 ≤ −8
Model it as a constraint graph and use Bellman-Ford algorithm to find a feasible solution,
or determine that no feasible solution exists.
7p
3. CFS want to transfer oil from its plant to Calgary. The major challenge in oil transmission
is to prevent pressure loss. So some pumps are used to increase pressure through several
pipelines without any loss if the oil through it is within its capacity. Any oil beyond
its capacity will be lost. Moreover each pipeline among pumps has a certain capacity
too. You are asked to find out the maximum amount of oil that can be transmitted
throughout the network so that no oil loss occurs. The information on the available
pumps and pipes is listed below:
Pump
A
B
C
Capacity 10
20
30
Location CFS CFS CFS
Pipe
A↔B
Capacity
5
A↔C
10
D
40
Calgary
A↔D B↔C B↔D C↔D
13
5
7
20
Model it as a maximum flow problem and solve it using Ford-Fulkerson algorithm. 7p
• Your solution must reach your instructor or the TA by or before the due date.
• You, or your reliable friend must give your work to the TA hand-to-hand or deliver at class to
your instructor.
• You have to sign your assignment; your signature certifies that the assignment is your work.
• If you use some software to reach a solution, provide explanations.