Download JNTUH MCA 2nd Sem R13 2019 December 812AK Operations Research Question Paper

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Code No: 812AK

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

MCA II Semester Examinations, December - 2019

OPERATIONS RESEARCH

Time: 3 Hours Max. Marks: 60

This question paper contains two parts A and B.

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Part A is compulsory which carries 20 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 8 marks and may have a, b, c as sub questions.

PART - A 5 x 4 Marks = 20

1. a) What are the main characteristics of OR? Explain with suitable examples. [4]
2. b) Show that assignment model is a special case of transportation model. [4]
3. c) What are the various simplifying assumptions made while dealing with sequencing problems? [4]

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4. d) Explain Saddle point, Value of the game, Two-person zero-sum game and strategy. [4]
5. e) Given average arrival rate = 8 /hour, average service time = 5 minutes, calculate
   1. i) utilization factor
   2. ii) Idle time
   3. iii) Probability that a customer arriving at the service counter will have to wait
   4. iv) Probability that the number of customers in the system is 2. [4]

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PART-B 5 x 8 Marks = 40

1. a) Solve the L.P.P. by the simplex method:
   Maximize Z = 40x₁ + 35x₂,
   Subject to 2x₁ + 3x₂ = 60,
   

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   4x₁ + 5x₂ = 96
   x₁, x₂ = 0.
2. b) Use graphical method to solve
   Maximize Z = 6x₁ + 8x₂,
   Subject to 5x₁ + 10x₂ = 60
   

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   4x₁ + 4x₂ = 40
   x₁, x₂ = 0. [4+4]
   OR
   Use the two-phase method to solve the problem:
   Minimize Z = x₁ - 2x₂ - 3x₃ ,
   

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   Subject to -2x₁ + x₂ + 3x₃ = 2,
   2x₁ + 3x₂ + 4x₃ = 1,
   x₁, x₂, x₃ = 0. [8]
3. a) A factory has three warehouses W1, W2 and W3 which supply to four stores S1, S2, S3 and S4. Monthly capacities of the warehouses are W1 = 100 units, W2 = 40 units and W3 = 60 units. Monthly demands at the stores are S1 = 30 units, S2 = 50 units, S3 = 65 units and S4= 55 units. The shipping cost in terms of rupees from warehouses to stores is as given below:
   

   Warehouses	S1	S2	S3	S4
   W1	14	16	12	20
   W2	12	14	10	8
   W3	10	16	8	15

   
   

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   The problem here is to determine the optimum distribution for the factory to minimize shipping costs. [4+4]
   OR
   A department store has leased a new store and wishes to decide how to place four departments in four locations so as to maximize total profits. The table below gives the profits, in thousands of Rupees, when the departments are allocated to the various locations. Find the assignment that maximizes total profits.
   

   	1	2	3	4
   Shoes	20	16	22	18
   Toys	25	22	18	28
   Auto	27	20	26	23
   Housewares	24	22	23	22

4. b) A travelling salesman, named Rolling Stone plans to visit five cities 1, 2, 3, 4 & 5. The travel time (in hours) between these cities is shown below:
   

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   From	1	2	3	4	5
   1	0	5	8	4	5
   2	5	0	7	4	5
   3	8	7	0	8	6
   4	4	4	8	0	8
   5	5	5	6	8	0

   
   How should Mr. Rolling Stone schedule his touring plan in order to minimize the total travel time, if he visits each city once a week? [4+4]
5. a) Shahi Export House has to process five items through two stages of production, Viz, cutting & sewing. Processing times are given in the following table:
   

   Items	Cutting	Sewing
   	Time In Hours
   A	7	4
   B	3	8
   C	11	9
   D	5	10
   E	12	6

   
   Determine an order in which these items should be processed so as to minimize the total processing time.

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6. b) Two jobs are to be performed on five machines A, B, C, D, and E. Processing times are given in the following table. Use graphical method to obtain the total minimum elapsed time. [4+4]
   

   Machine
   Job 1 Sequence	A B C D E
   Time	4 5 3 7 3
   Job 2 Sequence	B C A D E
   Time	6 5 4 3 7

   
   OR
   The failure rates of transistors in a computer are summarized in Table
   Failure rates of Transistors in computers
   

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   End of the week	1	2	3	4	5	6	7
   Probability of failure to date	0.07	0.18	0.30	0.48	0.68	0.89	1

   
   The cost of replacing an individual failed transistor is Rs. 9. If all the transistors are replaced simultaneously, it would cost Rs. 3.00 per transistor. Any one of the following two options can be followed to replace the transistors:
   a) Replace the transistors individually when they fail (individual replacement policy).
   b) Replace all the transistors simultaneously at fixed intervals and replace the individual transistors as they fail in service during the fixed interval (group replacement policy).
   Find out the optimal replacement policy, i.e. individual replacement policy or group replacement policy. If group replacement policy is optimal, then find at what equal intervals all the transistors should be replaced. [8]

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7. Resolve the reliability problem using the following data. Total capital available = 100
   

   Components	1	2	3
   ri	0.70	0.60	0.80
   ci	4	2	3
   Ri	0.75	0.80	0.65
   Ci	5	5	6

   
   OR
   Two firms are competing for business under the conditions such that one firm’s gain is another firm’s loss. Firm A’s payoff matrix is given below. Suggest optimal strategies for the two firms and the net outcome thereof.
   

   Airline B	Does nothing special	Advertises special rates	Advertises special features (i.e., movies, fine food)
   Airline A Advertises special rates	275	-50	5
   Advertises special features (i.e., movies, fine food).	125	130	-65

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8. a) Solve the following game by reducing them to 2 x 2 games by graphical method [4+4]
   

   	B
   A	3 4 0 1 2 -1 5 -2 2 3

9. b) A textile mill buys its raw material from a vendor. The annual demand of the raw material is 9000 units. The ordering cost is Rs. 100 per order and the carrying cost is 20% of the purchase price per unit per month, where the purchase price per unit is Rs. 1.
   Find
   1. i) Economic order quantity
   2. ii) Total cost w.r.t. EOQ

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   3. iii) Number of orders per year
   4. iv) Time between consecutive two orders.
10. A company manufactures refrigeration units in batches. The estimated demand is 12,000 units/year. It costs Rs. 100 to setup the manufacturing process and the carrying cost is Rs. 0.75 per unit per year. Once the production process has been setup, 90 units can be manufactured daily. The demand during the production day has been 65 units per day. How many units should the company produce in each batch? How long will the production cycle last? [4+4]
    OR
    

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    The arrival rate of customers at a banking counter follows Poisson distribution with a mean of 45 per hour. The service rate of the counter clerk also follows Poisson distribution with a mean of 60 per hour.
    1. 1) What is the probability of having 0 customers in the system?
    2. ii) What is the probability of having 5 customers in the system?
    3. iii) What is the probability of having 10 customers in the system?
    4. iv) Find L_s, L_q, W_s, and W_q [8]

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