SCHOOL OF MECHANICAL ENGINEERING
FINAL ASSESSMENT TEST – Model Question Paper
Course: MEE1024 Operations Research
Time: Three Hours Max. Marks: 100
Faculty: Dr. S. Narayanan / Dr.P.A.Jeeva
Part – A (5 x 5 = 25 Marks)
Answer any FIVE questions
1. A company sells two different products A and B. The company makes a profit of Rs.40
and Rs.30 per unit on products A and B respectively. The two products are produced in a
common production process and are sold in two different markets. The production
process has a capacity of 30000 man-hours. It takes three hours to produce one unit of A
and one hour for produce one unit of B. The market has been surveyed and company
officials feel that the maximum number units of A that can be sold is 8000 and those of B
is 12000 units. Subject to these limitations, the products can be sold any convex
combination. Formulate the above problem as a L.P.P.
2. Solve the following assignment problem.
Machines
1 2 3 4
A 1 4 6 3
Operators B 9 7 10 9
C 4 5 11 7
D 8 7 8 5
3. A factory has five jobs, each of which should go through two machines A and B, in the
order AB. Processing time in hours for the jobs are given below.
Job: J1 J2 J3 J4 J5
Machine A: 5 1 9 3 10
Machine B: 2 6 7 8 4
Determine the optimal sequence for performing the jobs that would minimize the total
elapsed time.
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4. The following table gives the activities in construction project and time duration.
Activity Preceding activities Normal time (days)
1-2 - 20
1-3 - 25
2-3 1-2 10
2-4 1-2 12
3-4 1-3, 2-3 5
4-5 2-4, 3-4 10
Draw the activity network of the project and find critical path of the project.
5. The demand for a particular item is 18000 units per year. The holding cost per unit is
Rs.1.20 per year and the cost of one order is Rs.400. No shortages are allowed and the
replacement rate is instantaneous. Determine the optimum order quantity and number of
orders per year.
6. Discuss the significance of Monte-Carlo simulation in manufacturing company.
7. The maintenance cost and resale value per year of a machine whose purchase price is
Rs.7000 are given below
Year : 1 2 3 4 5 6 7 8
Maintenance cost (Rs): 900 1200 1600 2100 2800 3700 4700 5900
Resale value (Rs) : 400 2000 1200 600 500 400 400 400
When should the machine be replaced?
Part – B (15 x 5 = 75 Marks)
Answer any FIVE questions
8. Solve the following LPP using two-phase method
Maximize 6x1+3x2
subject to 2x1+3x2 30
3x1+2x2 = 4
x1+x2 1
x1,x2 0
9. Find the optimal solution of the following transportation problem. Suppose that penalty
costs per unit of unsatisfied demand are 5, 3 and 2 for destination P, Q and R.
Destinations
P Q R Supply
A 5 1 7 10
B 6 4 6 80
Sources
C 3 2 5 15
Demand 75 20 50
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10. The following table gives data on normal time and cost and crash time and cost for a
project. Indirect cost is Rs.50 per week.
Activity Normal Crash
Time Cost(Rs.) Time Cost(Rs.)
1-2 3 300 2 400
2-3 3 30 3 30
2-4 7 420 5 580
2-5 9 720 7 810
3-5 5 250 4 300
4-5 0 0 0 0
5-6 6 320 4 410
6-7 4 400 3 470
6-8 13 780 10 900
7-8 10 1000 9 1200
(i) Draw the network and identify the critical path
(ii) What is the normal project duration and the associated cost.
(iii) Crash the relevant activities systematically and determine the optimal project
completion time and cost.
11. (a) Explain the various costs related to inventory. (3Marks)
(b) A shopkeeper has a uniform demand of an item at the rate of 50 items per month. He
buys from supplier at a cost of Rs.6 per item and the cost of ordering is Rs.10 per time. If
the stock holding costs are 20% per year of stock value, how frequently should he
replenish his stocks? Now, suppose the supplier offers a 5% discount on orders between
200 and 999 items and a 10% discount on orders exceeding or equal to 1000. Can the
shopkeeper reduce his costs by taking advantage of either of these discounts? (12Marks)
12. (a) State three applications of waiting line theory in manufacturing enterprise. (3Marks)
(b) A computer center is equipped with three digital computers, all of the same type and
capability. The number of users in the center at any time is equal to 10. For each user, the
time for writing and inputting a program is exponentially distributed with mean rate 0.5
per hour. The execution time per program is exponentially distributed with mean rate 2
per hour. Assuming that the center is in operation on a full-time basis, and neglecting the
effect of computer downtime, find the following
i. The probability that a program is not executed immediately upon receipt at the
center
ii. The average number of programs awaiting execution
iii. The expected number of idle computers
iv. The average percentage of idleness per computer (12Marks)
13. Customers arrive randomly at a three-clerk post office. The inter arrival time is
exponential with mean 5 minutes. The service time is also exponential with mean 10
minutes. All arriving customers form one waiting line and are served by free clerks on a
FIFO basis. Simulate the system and run the simulation for the purpose of determining
the average number of waiting transactions and average busy time of system.
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14. (a) Describe a two-persons zero-sum game. (3Marks)
(b) Use graphical method in solving the following game.
Player B
1 4 -2 -3
Player A
2 1 4 5
(12Marks)
15. The following mortality rates have been observed for a certain type of light bulbs:
End of week : 1 2 3 4 5 6
Probability of
Failure data : 0.09 0.25 0.49 0.85 0.92 1.00
There are 1000 such bulbs which are to be kept in working order. If a bulb in service, it
costs Rs. 3 to replace but if all the bulbs are replaced in the same operation, it can be done
for only Rs.0.70 a bulb. It is proposed to replace all bulbs at fixed intervals whether or not
they have burnout, and to continue replacing burnt out bulbs as they fail
(i) What is the best interval between group replacements?
(ii) At what group replacement price per bulb, would a policy of strictly individual
replacement become preferable to the adopted policy?
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