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Operations Research Question Paper

Operations Research

Course:Bachelor Of Science In Information Technology

Institution: Masinde Muliro University Of Science And Technology question papers

Exam Year:2010

SECOND YEAR EXAMINATION FOR THE DEGREE OF BACHELOR OF
SCIENCE IN INFORMATION TECHNOLOGY
OPERATIONS RESEARCH
DATE: APRIL 2010 TIME: 2 HOURS
INSTRUCTIONS: Answer question ONE and any other TWO questions
QUESTION ONE
(a) Suggest a suitable Operations Research model, if any, for the following situations:
(i) Deciding the quantities of the three products to be produced per week for a company
you work for.
(ii) Opening another reservation counter at the Railway station.
(iii) Setting minimum stock level of bicycles in a store.
(iv) Deciding the optimal lot size of a product for placing order by a trading company.
(v) Determination of the number of bomb hits to destroy enemy’s nuclear plant.
(vi) Establishing dependency relationships among the activities involved in the manufacture
and marketing of a new product.
(vii) Modification in the design of a new product
(7 Marks)
(b) Explain the role of computers in Operations Research. (4 Marks)
(c) State the four properties which a competitive situation should have if it is to be called a competitive
game (4 Marks)
(d) Discuss the costs associated with Queuing system. In addition explain the concept of optimum service rate and optimum cost. (5 Marks)
(e) Consider the problem of assigning five operators to five machines. The assignment costs in K£ are
given below
Operators
Machines I II III IV V
A 10 5 13 15 16
B 3 9 18 3 6
C 10 7 2 2 2
D 5 11 9 7 12
E 7 9 10 4 12
Assign the operators to different machines so that total cost is minimized (Use the Hungarian
Assignment method) (10 Marks)
QUESTION TWO
(a) Explain any six reasons for maintaining inventory. (6 Marks)
(b) Discuss the various costs associated with inventory control (6 Marks)
(c) A company uses annually 24,000 units of a raw material which costs K£1.25 per unit. Placing each
order costs K£ 22.50 and the carrying cost is 5% per year of the average inventory.
(i) Find the EOQ (3 Marks)
(ii) Total inventory cost (including the cost of material) (5 Marks)
QUESTION THREE
a) (i) List three methods of obtaining an initial basic feasible solution of a Transportation problem.
(ii) Which is the best method among them? Why? (6 Marks)
b) Use the method in a (ii) above to determine an initial basic feasible solution for the transportation
problem below:
Destination
Origin I II III IV V Supply
A 2 11 10 3 7 4
B 1 4 7 2 1 8
C 3 9 4 8 12 9
Demand 3 3 4 5 6
(11 Marks)
c) Find the total transportation cost in (b) above (3 Marks)
QUESTION FOUR
a) In a game of matching coins with two players, suppose A wins one unit of value when there are two heads, wins nothing when there are two tails and looses ½ unit of value when there is a head and a tail. Determine the payoff matrix, the best strategies for each player and the value of the game to player A. (8 Marks)
b) Explain any four advantages to the use of Simulation. (8 Marks)
c) Distinguish between Group replacement and individual replacement policies. (4 Marks)
QUESTION FIVE
The Activity durations for a project are given below.
a) Draw the Network diagram; identify the critical path and the project duration. (10 Marks)
b) Compute the total float and free float for each activity. (4 Marks)
Activity 1-2 1-4 2-3 3-5 3-7 4-7 5-7 7-8
Duration
(days)
4 36 2 15 10 2 9 20
c) A plant manufactures two products A and B. The profit contribution of each product has been
estimated as K£ 20 for product A and 24 for product B. Each product passes through three
departments of the plant. The time required for each product and total time available in each
department are as follows:
Department Hours Required Available Hours
During the
month
Product A Product B
1 2 3 1,500
2 3 2 1,500
3 1 1 600
The company can only supply at most 250 units of product B per month.
Required
Formulate as a Linear Programming model and set up an initial Simplex tableau for this problem.
(6Marks)

Operations Research Question Paper

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