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# Periyar University 2009 B.B.A -INTRODUCTION TO OPERATION RESEARCH-II-4thsemester - Question Paper

Sunday, 27 January 2013 06:35Web

(7 pages) S.No. 2140

(For the candidates admitted from 2006-2007 onwards) B.B.A. DEGREE EXAMINATION, APRIL/MAY 2009.

06 UBA 09

Fourth Semester INTRODUCTION TO OPERATIONS RESEARCH II Time : Three hours    Maximum : 100 marks

PART A (10 x 2 = 20 marks)

Define two-person zero-sum game.

3: \5#lat do you mean by queue?

/Define service rate.

______r-

is meant by network diagram?

Define dummy activity.

7.(What    is the optimal replacement policy?

8.    What do you mean by staff replacement?

9.    Define Economic Order Quantity.

PART B (5 x 4 = 20 marks)

11.    Jjjy Describe the basic rules for solving games.

Or

(b) What are the steps required to detect a saddle point?

12.    (a) What /are the characteristics of queuing moctels? /

Or

(b) People arrive at a theatre ticket booth in a Poisson distributed arrival rate of 25 per hour. Service time is constant at 2 minutes. Calculate :

(i)    The mean number in the waiting line.

(ii)    The mean waiting time.

13.    (a) What are the rules of network construction?

Or

(bVThe following table gives the activities of a constedction project and duration :

Activity:    1-2 1-3 2-3 2-4 3-4 4-5

Duration (days): 20 25 10 12 6 10

(i)    Draw the network for the project.

(ii)    Find the critical path.

2    S.No. 2140

14. (a) Explain the various types of replacement policies.

Or

(b) A machine costs Rs. 500. Operation and mai    :e costs are zero for the first year and ;e

increase by Rs. 100 every year. If money is worth 5% every year, determine the best age at which the machine should be replaced. The resale value of the machine is negligibly small. What is the weighted average cost of owning and operating the machine?

15. (a) What are the deterministic inventory problems? Or

las to supply 20,000 units per day. He can produce 30,000 units per day. The cost of holding a unit in stock is Rs. 3.00 per year and the set-up cost per run is Rs. 50.00. How frequently, and of what size, the production runs be made?

PART C (5 x 12 = 60 marks)

16. (a) Reduce the following game by dominance and find the game value :

Player B

Player A

 i II III IV I 3 2 4 0 n 3 4 2 4 m 4 2 4 0 IV 0 4 0 8

Or

b)Determine the optimum strategies and the value of the game :

Player B

Player A

 I II III IV V I 16 4 0 14 -2 II 10 8 6 10 12 III 2 6 4 8 14 IV 8 10 2 2 0

S.No. 2140

[P.T.O.]

17. Arrivals at a telephone booth are considered to be Poisson, with an average time of 10 minutes between one arrival and the next. The length of a phone is assumed to be distributed exponential, with near 3 minutes.

(i)    What is the probability that a person arriving at the booth will have to wait?

(ii)    Find the average number of units in the

system.

Or

(b) Consider a self service store with one cashier. Assume Poisson arrivals and exponential service times. Suppose that nine customers arrive on the average every 5 minutes and the cashier can serve 10 in 5 minutes. Find:

(i)    The average number of customers queueing for service.

(ii)    Average time a customer spends in the

system.

(iii)    Average time a customer waits before being served.

18. (a) Tasks A, B, C........I constitute a project. The

notation X < Y means that the task X must be finished before Y can begin. With this notation.

A<D;A<E;B<F;D<F;C<G;C<H; F < I; G < I.

Draw a network diagram and find the minimum time of completion of the project.

Or

/

(b) rA small project is composed of seven activities whosetime estimates are listed below :

Activity Estimated duration (weeks)

i-j Optimistic Most likely Pessimistic

 1-2 1 1 7 1-3 1 4 7 1-4 2 2 8 2-5 1 1 1 3-5 2 5 14 46 2 5 8 5-6 3 6 15

(i)    Draw the project network,

(ii)    Find the expected duration and variance of each activity.

6    S.No. 2140

19. (a) Machine A costs Rs. 9,000. Annual operating costs are Rs. 200 for the first year and then increases by Rs. 2,000 every year. Determine the best age at which to replace the machine. If the optimum replacement policy is followed, what will be the average yearly cost of owning and operating the machine?

Or

considering replacement of a machine, whose cost price is Rs. 12,200 and the scrap value Rs. 200. The running (maintenance and operating) costs in Rs. are found from experience to be as follows:

8

Year:

Running cost: 200 500 800 1200 1800 2500 3200 4000 When should the machine be replaced?

20.    aircraft company uses rivets of an

approximates customer rate of 2,500 kg. per year. The rivets cost/Rs. 30 per kg and the company personnel estimate that it costs Rs. 130 to place an order and the inventory carrying cost is 10% per year. How frequently should orders for rivets be placed and what quantities should be ordered?

Or

(b) The demand of an item is uniform at a rate of 20 units per month. The fixed cost is Rs. 10 each time a production run is made. The production cost is Re. 1 per item and the inventory carrying cost is Re. 0.25 per item per month. If the shortage cost is Rs. 1.25 per item per month, determine how often to make a production run and of what size should be?

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