Download Linear Programming MSIS 651 Homework 4

Linear Programming
MSIS 651
Homework 4
Instructor: Farid Alizadeh
Due Date: Friday December 12, 2002
(Slip under my door in Ackerson 200m)
last updated onDecember 5, 2002
1. Do problem 13.9 parts a-d.
2. AMPL project: Do problems 14.9 all parts. Then model it as an AMPL
project and enter the data given at the beginning of the problem in the
.dat file and solve. Report both primal and dual values in the output.
3. Does Dijkstra’s algorithm work if some arc costs are negative? Discuss
your answer. (Hint: Note that id there is a direct cycle of total negative
length in a network, then the shortest path problem is unbounded because
we can go through this problem as many times as we wish and reduce the
“length” indefinitely.)
4. Find a dual feasible solution to the network flow problem on the next
page. As usual numbers on the arcs are costs. Numbers next to nodes
are supplies if they are positive and demands if they are negative (Note:
This is the opposite of the convention used in your text.) Those nodes
without any number next to them are transshipment nodes.
1
MSIS 651, Fall 2002
Homework 4
1
4
1
6
D
3
1
6
−9
A
12
5
1
−6
B
5
C
1
3
E
−9
2
−4
F
7
2
9
2
H
6
G
10
15
2
13
I
13
Due date: 12/12/02