Discuss the following:
Q1: What is the enumeration approach to solving assignment problems? Is it a practical way to solve a 5 row X 5 column problem? A 7X7 problem? Why?
Q2: The hardrock concrete company has plants in three locations and currently working on 3 major construction projects, each located at a different site. The shipping cost per truckload of concrete, daily plant capacities, and daily plant requirements are provided in the table
|
from/to
|
PROJECT A
|
PROJECT B
|
PROJECT C
|
Plant capacities
|
|
PLANT 1
|
10
|
4
|
11
|
70
|
|
PLANT 2
|
12
|
5
|
8
|
50
|
|
PLANT 3
|
9
|
7
|
6
|
30
|
|
PROJECT REQUIREMENTS
|
40
|
50
|
60
|
150
|
- Formulate an initial feasible solution to hardrock's transportation problem using the northwest corner rule. Then evaluate each unused shipping route by computing all improvement indices. Is this solution optimal? Why
- Is there more than one optimal solution to this problem? Why?
Q3: Ashley's Auto Top Carriers currently maintains plants in Atlanta and Tulsa that supply major distribution centers in Los Angeles and New York. Because of an expanding demand, Ashley has decided to open a third plant and has narrowed the choice to one of two cities-New Orleans or Houston. The pertinent production and distribution costs, as well as the plant capacities and distribution demands, are shown in the table.
|
from/to
|
LA
|
NY
|
NORMAL PRODUCTION
|
UNIT PRODUCTION
|
|
|
|
ATLANTA
|
8
|
5
|
600
|
6
|
|
|
|
TULSA
|
4
|
7
|
900
|
5
|
|
|
|
NEW ORLEANS
|
5
|
6
|
500
|
4
|
ANTICIPATED
|
|
HOUSTON
|
4
|
6
|
500
|
3
|
ANTICIPATED
|
|
FORECAST DEMAND
|
800
|
1200
|
2000
|
|
|
|
Which of the new possible plants should be opened?
Q4: The state of Missouri had three major power-generating companies (A, B, and C). During the months of peak demand, the Missouri Power Authority authorizes these companies to pool their excess supply and to distribute it to smaller independent power companies that do not have generators large enough to handle the demand. Excess supply is distributed on the basis of cost per kilowatt hour transmitted. The following table shows the demand and supply in millions of kilowatt hours and the cost per kilowatt hour of transmitting electric power to four small companies in cities W, X, Y, and Z:
|
from/to
|
W
|
X
|
Y
|
Z
|
EXCESS SUPPLY
|
|
A
|
12
|
4
|
9
|
5
|
55
|
|
B
|
8
|
1
|
6
|
6
|
45
|
|
C
|
1
|
12
|
4
|
7
|
30
|
|
Unfilled power demand
|
40
|
20
|
50
|
20
|
150
|