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Operation Research (Elective I) (April 2010)

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Total No. of Questions : 6] [Total No. of Pages : 4 P1312 [3764]-139 B.E. (Mechanical) OPERATION RESEARCH (402045) (2003 Course) (Sem. - I) (Elective - I) Time : 3 Hours] [Max. Marks : 100 Instructions to the candidates : 1) 2) Answers to the two sections should be written in separate books. Figures to the right indicate full marks. 3) Use of calculator is allowed. 4) Assume suitable data, if necessary. SECTION - I Q1) Two animal feeds A and B are available in the market. One kg of A contains 0.1 kg of x1, 0.1 kg of x3 and 0.2 kg of x4 and 1 kg of B contains 0.1 kg of x2, 0.2 kg of x3 and 0.1 kg of x4 (x1, x2, x3, x4 are different ingredients). A feed mixing operation can be described in terms of two activities. The daily per head requirement is of at least 0.4 kg of x1, 0.6 kg of x2, 2.0 kg of x3 and 1.8 kg of x4. Feed A can be bought for Rs. 0.07 per kg and feed B for Rs. 0.05 per kg. The availabilities, requirements and costs are summarised in the following table : Ingredient A (kg) B (kg) Requirement (kg) x1 0.1 0 0.4 x2 0 0.1 0.6 x3 0.1 0.2 2.0 x4 0.2 0.1 1.8 Cost Rs. 0.07/kg, Rs. 0.05/kg. Determine the quantities of feeds A and feed B in mixture so that the total cost is minimum. [16] OR P.T.O. Q1) Using the dual, solve the following linear programming problem. [16] Zmax = 2x1 + 2x2 + 4x3 Subjected to, 2x1 + 3x2 + 5x3 2 3x1 + x2 + 7x3 3 x 1 + 4x 2 + 6x 3 5 x1, x2, x3 0 Q2) Consider a firm having two factories. The firm is to ship its products from the factories to three retail stores. The number of units available at factories X and Y are 200 and 300 respectively, whose those demanded at retail stores A, B and C are 100, 150 and 250 respectively. Rather than shipping directly from factories to retail stores, it is added to investigate the possibility of trans-shipment. The transportation cost (in Rupees) per unit is given below : Factory Retail store X B C 0 8 7 8 9 Y 6 0 5 4 3 A 7 2 0 5 1 B 1 5 1 0 4 C Retail store A X Factory Y 8 9 7 8 0 Find the optimal shipping schedule. [16] OR Q2) a) Using VAM Approximation Method to obtain an initial feasible solution of the transportation problem. [8] A B C [3764]-139 D 11 16 21 200 EFG 13 17 14 18 14 10 24 13 10 250 300 400 225 275 250 -2- b) Solve Assignment 1 I 2 II 4 III 7 IV 3 problem. 2 3 3 4 5 6 8 9 5 8 [8] 4 5 7 8 4 Q3) Write short notes (Any Three) : a) EOQ model with Finite Replenishment Rate. b) Dynamic programming. c) Non-linear programming. d) Static inventory model. [18] SECTION - II Q4) a) Describe a two-persons zero-sum game. [4] b) Explain the iterative method of getting an approximate solution to a game problem. [4] c) Solve the game by L.P. Method. [8] B 3 1 3 A 3 3 1 4 3 3 OR Q4) The following mortality rates have been observed for a certain type of light bulbs. [16] Week % failing by end of week 1 2 3 4 5 10 25 50 80 100 There are 1000 bulbs in use and it costs Rs. 2 to replace an individual bulb which has burnt out. If all bulbs were replaced it would cost 50 paise per bulb. It is proposed to replace all bulbs at fixed intervals whether or not they have burnt out. At what interval should all the bulbs be replaced? Q5) Explain Kendall s notation for single-channel Poisson arrivals with exponential service, infinite population model [M/M/1 : FCFS| | ]. [16] OR [3764]-139 -3- Q5) a) Using graphical method, determine the optimal sequence needed to process job 1 and 2 on five machines A, B, C, D, E. For each machine find the job which should be done first also find total time needed to complete both the jobs. [8] Sequence : A B C D E Job 1 Time (hrs) : 1 2 3 5 1 Sequence : C A D E B Job 2 Time (hrs) : 3 4 2 1 5 [8] b) Explain Monte Carlo simulation. Q6) Find the optimum solution for the following network. Activity A B C D E F G H I Succeeding Activity B, C D, E I G F H F Normal duration 8 4 4 3 6 9 5 7 8 Crash durat 8 3 3 3 4 6 4 5 5 [18] Normal cost 500 1000 800 750 1500 2500 500 800 3000 Crash cost 500 750 500 750 800 1600 400 600 1500 Indirect cost = Rs. 150/- per day. OR Q6) a) Given below is the information regarding a project. [8] Activity A B C D E F G H Preceding Activity - - - A, B B B F, C B Duration (days) 3 4 2 5 1 3 6 4 Activity I J K L E, H E, H C, D, F J, K 4 2 1 5 Preceding Activity Duration Draw network find critical path and its duration. b) Write difference between PERT and CPM. c) Explain types of floats. [3764]-139 rrrr -4- [5] [5]

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Additional Info : 2003 Course
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