|
ISE 303 Operations Research 1 Exam 1 Sample
- The Ministry of Health maintains three blood banks in
Khobar.
In a particular day, five public and private hospitals have requested
quantities of blood bags of type A-. The blood supplies from the banks,
requested blood bags by the hospitals, and the cost of blood per bag are
shown in the following table:
|
|
|
Hospitals |
|
|
|
|
1 |
2 |
3 |
4 |
5 |
Supply |
|
Blood banks |
1 |
8
|
6
|
3
|
7
|
5
|
20 |
|
2 |
5
|
M
|
8
|
4
|
7
|
30 |
|
3 |
6
|
3
|
9
|
6
|
8
|
30 |
|
|
|
|
|
|
|
|
|
Demand |
|
25 |
25 |
20 |
10 |
20 |
|
In this particular
day, bank 2 cannot deliver blood to hospital 2, hence the cost of
transportation per blood bag is set to M (very large number) to signify
a very large cost.
Apply the least cost method to find a suitable starting basic solution
for this problem.
- Helwani Bros Co. has contracted to supply one kind of
tahina to 4 hotels in Khobar. Tahina is packed in a container of 1000
kg. Helwani operates three storehouses in the city, where all their
products are stored. In one particular day, the availability of tahina
in each storehouse is as:
| Storehouse |
Quantity |
| 1 |
60 |
| 2 |
80 |
| 3 |
40 |
The contract requires
the supply of the following quantities to the four hotels:
| Hotel |
Quantity |
| 1 |
35 |
| 2 |
65 |
| 3 |
25 |
| 4 |
55 |
Helwani
Bros has applied an incentive scheme to new customers (hotels) by giving
discounted prices on tahina. The table below gives the selling price
(riyal) per unit for each combination of storehouse-hotel:
|
|
|
Hotel |
|
|
|
1 |
2 |
3 |
4 |
|
Storehouse |
1 |
8 |
7 |
5 |
2 |
|
2 |
5 |
2 |
1 |
3 |
|
3 |
6 |
4 |
3 |
5 |
As a profit-driven
company, Helwani Bros seeks to meet its contractual agreement and make
the largest money it can collect from the hotels.
Without solving the problem, construct the transportation tableau
equivalent to the problem faced by Helwani Bros.
- Eastern Region Municipality has three kinds of horizontal drilling
machines. The municipality has four construction areas to supply water
to new housing lands. The cost of operating a machine depends on the
type of land being drilled. The equivalent transportation problem is
illustrated in the following transportation tableau:
|
|
|
Destination |
|
|
|
|
1 |
2 |
3 |
4 |
Supply |
|
Source |
1 |
3 |
7 |
6 |
4 |
5 |
|
2 |
2 |
4 |
3 |
2 |
2 |
|
3 |
4 |
3 |
8 |
5 |
3 |
|
Demand |
|
3 |
3 |
2 |
2 |
|
The costs are in
riyal per hour of operation (assuming all the machines work the same
hours).
Starting from the northwest corner method, find the optimal solution for
the transportation problem. Calculate the total cost of the optimal
solution.
- Zain, being a new mobile operator in the Kingdom, has to construct its mobile
network. To serve its anticipated customers in King Abdul Azziz
airbase, KFUPM, and Saudi Aramco, Zain operation department has, as an
initial stage, decided to erect 4 mobile towers in Dhahran area. Four
construction companies have applied for the construction tasks. Since
the constructions have to be started at the same time, a construction
company can work on only one construction task. The construction costs
in hundred thousand riyals are as follows:
|
|
|
Company |
|
|
|
1 |
2 |
3 |
4 |
|
Tower |
1 |
4 |
6 |
5 |
5 |
|
2 |
7 |
4 |
5 |
6 |
|
3 |
4 |
7 |
6 |
4 |
|
4 |
5 |
3 |
4 |
7 |
Use the appropriate method to find the best assignment and calculate the
corresponding total cost.
Dr
Muhammad Al-Salamah
2008
Industrial Engineering
King Fahd University of Petroleum and Minerals |