Rr411902 Mathematical Modelling And Simulation

RR

Code No: RR411902

IV B.Tech I Semester(RR) Supplementary Examinations, December 2009 MATHEMATICAL MODELLING AND SIMULATION (Electronics & Computer Engineering) Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. (a) State the general rules for converting any primal L. P. P. into its dual.

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(b) What are the useful aspects of duality in L. P. P.

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2. (a) Give an algorithm to solve an “Assignment” problem?

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(b) What is an unbalanced assignment problem? Explain it with at least one example. 3. (a) Derive the E. O. Q. formula for the manufacturing model with shortages

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(b) A manufacturing firm has to supply 3,000 units annually to a customer who does not have enough space for storing the material. There is a contract that if the supplier fails to supply the material, a penalty of Rs. 40 per unit per month will be levied. The inventory holding cost amounts to Rs. 20 per unit per month and the setup cost is Rs. 400 per run. Find the expected number of shortages at the end of each scheduling period. [10] 4. What is the ABC analysis? Why it is necessary? What are the basis steps in implementary it? [16] 5. Consider a self service store with one cashier. Assume poisson arrivals and exponential service times. Suppose that a customer arrive on the average every 5 minutes and the cashier can serve 10 in 5 minutes. Find [16] (a) The average number of customers queuing for service (b) The probability of having more than 10 customers in the system (c) The probability that a customer has to queue for more than 2 minutes If the service can be speeded upto 12 in 5 minutes by using a different cash register, what will be the effect on the quantities (a), (b) and (c) 6. (a) Discuss in brief

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i. Dummy activity ii. Free float iii. Independent float iv. Total float (b) What are the three estimates needed for PERT analysis? How do you use these estimates to compute the expected activity time and the variance in activity time? [8] 7. Discuss any four reasons for solving operations research problems by simulation. [16] 8. Explain the process of calibration and validation of simulation models. ?????

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