M.Sc. DEGREE EXAMINATION, NOVEMBER/DECEMBER 2017.
Third Semester
OR and SQC
MATHEMATICAL PROGRAMMING II
2 21235 A
Time 3 Hours Max. Marks 70
PART — A
Answer any FIVE questions. 6 30 Marks)
1. Explain
two-person-zero sum game
pay-off matrix
pure and mixed strategies and
dominance property.
2. Explain the graphical method of solving a game.
3. Explain
present value method and
the concept of depreciation with suitable examples.
4. Explain the replacement policy of items that fail when the value of money remains
the same.
5. Explain sequencing problem and its assumptions.
6. Explain the sequencing problem with n jobs and two machines.
7. What is simulation? What are its advantages and disadvantages?
8. Explain Monte-Carlo technique and discuss its uses.

PART — B
Answer ALL questions. 10 40 Marks)
9. State and prove the fundamental theorem of games.
Or
Solve the following game by linear programming:

3 4 3
1 2 2
1 2 1
10. A manual stamper currently valued at Rs. 1,000 is expected last 2 years and
costs Rs. 4,000 per year to operate. An automatic stamper which can be
purchased for Rs. 3,000 will last 4 years and can be operated at an annual
cost of Rs. 3,000. If money carries the rate of interest 10% per annum,
determine which stamper should be purchased?
Or
Discuss the types of replacement policies of items that fail completely.
11. When passing is not allowed solve the following sequencing problem giving an
optimum solution
Job M1 M2 M3 M4 M5
A 9 7 4 5 11
B 8 8 6 7 12
C 7 6 7 8 10
D 10 5 5 4 8
Or
Explain the general n job shop problem. Discuss the branch and bound
algorithm for flow shop scheduling with a suitable example.
3 21235 A
SP 1
12. The material manager of a firm wishes to determine the expected demand for
a particular item in stock during the reorder lead time. The information is
needed to determine how far in advance he should reorder before the stock
level is reduced to zero. However both the lead time (in days) and the demand
per day for the item are random variables described by the probability
distribution given below:
Lead Time 1 2 3
Probability of Occurrence 0.50 0.30 0.20
Demand /Day (units) 1 2 3 4
Probability 0.10 0.30 0.40 0.20
Simulate the problem for 30 reorders to estimate the demand during lead
time.
Or
XYZ company operates an automatic car-wash facility in a city. The manager
is concerned about the long lines of cars that build up while waiting for
service. The service time for the system is machine-paced and thus constant.
The manager has the opportunity to decrease the service time by increasing
the speed of the conveyor that pulls the cars through the system. Of course
the quicker the pace, the lower is the quality of the car-wash. The manager
wants to study the effects of setting the system for a 2-minute car wash. The
following data on customer arrivals have been gathered.
Inter arrival time (minutes) 1 2 3 4 5
Number of occurrences 136 34 102 51 17
Simulate the arrival of 20 customers. The doors open at 8.00 am. Compute
the average waiting time per customer, the average time spent in the system,
the percentage of time the system is ideal and the maximum queue length.
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