ISE 421 Operations Research 2 Exam 2 Sample
- The industrial engineer is planning the replacement of a paper
bag making machine. The machine was bought 3 years ago and the
planning horizon is 5 years. The policy of the company prohibits the
removal of any machine that is 3 years old or younger unless it is
the end of the planning horizon, but it must be replaced when it
reaches the age of 5 years. The price of an identical machine
100,000 riyals. The annual operating costs of the machine, the
salvage values, and the annual revenues as a function of the age of
the machine are:
|
Age |
Revenue |
Operating
cost |
Salvage
value |
|
0 |
20,000 |
200 |
- |
|
1 |
19,000 |
600 |
80,000 |
|
2 |
18,500 |
1,200 |
60,000 |
|
3 |
17,200 |
1,500 |
50,000 |
|
4 |
15,500 |
1,700 |
30,000 |
|
5 |
|
|
10,000 |
Find the dynamic programming model of this problem and use it to
find the best replacement policy.
- In a manufacturing process, the packaging stage is the last
operation. The demand for the production is uncertain, but it is
only known with a probability. The industrial engineer wants to find
how many temporary packagers are required to be hired every month
for the coming 3 months. He has found that the costs and profits
associated with the hiring of the temporary workers are the most
critical. Hence, he has decided that the best measure of the best
decision will be the one that will maximize the net income, which is
defined as profit minus unused worker cost minus hiring cost minus
any shortage cost. Shortage happens when the demand for packagers
exceed the hired packagers.
The demand for packagers during the following months with their
probabilities are:
Month 1:
| Packagers |
Probability |
| 2 |
0.3 |
| 3 |
0.5 |
| 4 |
0.2 |
Month 2:
| Packagers |
Probability |
| 5 |
0.1 |
| 6 |
0.6 |
| 7 |
0.3 |
Month 3:
| Packagers |
Probability |
| 1 |
0.2 |
| 2 |
0.7 |
| 3 |
0.1 |
The cost of unused worker is 3,000 riyals per month. The hiring cost has a fixed cost component of 1,500 riyals and a variable cost component of 2,000 riyals per packager. Each packager can generate a monthly profit of 6,000 riyals. Any shortage costs the company 1,500 riyals in lost sales.
Write a dynamic programming model for this problem and use it to find the most economical number of packagers that have to be hired every month.
-
Saudi Air Suspensions Co produces three types of air suspensions for small, medium, and large cars. The production capacity of the plant is limited by 8 machines. The number of machines required for the production of the suspension types and the unit revenues are
| Suspension type |
Number of Machines |
Unit revenue (100 riyals) |
|
1 |
4 |
5 |
|
2 |
3 |
4 |
|
3 |
2 |
2 |
The production has been set up so that the production quantity will be repeated every hour. The industrial engineer needs to find which of the suspension types to produce and how many. Find the optimal production mix using dynamic programming.
Instructor: Dr Muhammad Al-Salamah |