Econ 434: Operations Research Question Paper

Econ 434: Operations Research

Course:Bachelor Of Science In Economics And Statistics

Institution: Chuka University question papers

Exam Year:2013

CHUKA

UNIVERSITY

UNIVERSITY EXAMINATIONS

FOURTH YEAR EXAMINATION FOR THE AWARD OF DEGREE OF
BACHELOR OF SCIENCE (ECONOMICS AND STATISTICS)

ECON 434: OPERATIONS RESEARCH

STREAMS: B.SC. (ECON & STATS) Y4S1 TIME: 2 HOURS

DAY/DATE: MONDAY 12/8/2013 2.30 P.M. – 4.30 P.M.
INSTRUCTIONS:

Answer questionone any other two questions.
Do not write on the question paper.

Question ONE (30 Marks)

Discuss the characteristics of operations research. [6 marks]

Discuss any five operations research techniques used in Kenya. [5 marks]

Define models as used in operations research and give five qualities of a good model.
[5 marks]
Using suitable examples differentiate between the

Course of action and the state of nature
Decision making under risk and decision making under uncertainty. [4 marks]

A company with four employees has four different jobs to be done. The cost of each employee doing a particular job is as follows.

Employee Job
A B C D
1 15 20 18 24
2 12 17 16 15
3 14 15 19 17
4 11 14 12 13
Using the Hungarian method find the assignment that minimizes the total costs. [10 marks]
Question TWO (20 Marks)

Give any three differences between CPM and PERT method of project management.
[6 marks]

The following information relates to a project to be implemented.

Activity Completion time

Optimistic Most likely Pessimistic

1-2 4 8 12
2-3 1 4 7
2-4 8 12 16
3-5 3 5 7
4-5 0 0 0
4-6 3 6 9
5-7 3 6 9
5-8 4 6 8
7-9 4 8 12
8-9 2 5 8
0-10 4 10 16
6-10 4 6 8

Draw the PERT network for the project
Determine the critical path
Prepare the activity schedule for the project
If a 48 days deadline was imposed, what is the probability that the project will be finished within the time limit? [14 marks]

Question THREE (20 Marks)

Explain the terms re-order level and economic order quantity. [4 marks]

The following information relates to a material in XYZ Co. Ltd.

Annual production demand 50000 units
Ordering cost Sh. 150 per order
Carrying cost 20%
Price per unit Sh.200

Calculate the economic order quantity and the number of orders per year. [6 marks]

The following data relates to compound k10

Maximum monthly usage 300 units
Minimum monthly usage 200 units
Lead time maximum 6 months
Lead time minimum 2 months
Reorder quantity 750 units

Calculate:

The reorder level, minimum stock, maximum stock and average stock. [10 marks]

Question FOUR (30 Marks)

You are given the following Leontief inverse:

(I-A)-1 = ¦(1.15&0.01&0.05@0.05&1.00&0,05@0.15&0.20&0.10)¦(0.25@0.00@0.10)
¦(0.30&0.05&0.30)¦(1.30&)

If the required final demand is

D = ¦(5@10@15)
¦(20&)

Find the level of X that will make this possible. [6 marks]

Discuss the assumptions of linear programming as an optimization technique.
[6 marks]

A manufacturer has two products P1 and P2 both of which are produced in two steps by machines M1 and M2. The process times per hundred for the products on the machine are:
M1 M2 Contribution (per 100 units)
P1 4 5 10
P2 5 2 5
Available hours 100 80

The manufacturer is in a market upswing and can sell as much as he can produce of both the products.

Formulate the mathematical model and
Discuss the shortcoming of using simplex method for optimizing. [8 marks]

Question FIVE (20 Marks)

Differentiate between

Balking and Reneging customer behaviour in queues
Batching and Failures server behaviour in queues [4 marks]

A policeman takes 3 minutes to inspect a lorry. Lorries mean arrival rate at the police check is 15 Lorries per hour. Determine

Who is the server and who is the customer.
Interarrival time and interservice time.
Probability that there is a customer in the queue. [6 marks]

Consider the two-person zero-sum game with the following pay off matrix.

Player B

B1 B2 B3

A1 5 4 6
Player A A2 2 3 7
A3 4 3 0

Determine the optimal pure strategy for both the players and find the values of the game.
[6 marks]

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