52213-mt----operation Research

NR

Code No: 52213/MT

M.Tech. – II Semester Regular Examinations, September, 2008 OPERATION RESEARCH (Power System Control & Automation) Time: 3hours

Max. Marks:60 Answer any FIVE questions All questions carry equal marks ---

1.

Consider following 3 machines and 5 jobs flow shop problem. Using johnson’s rule. Find out optimal schedule and the corresponding makes Job 1 2 3 4 5

2.a) b) 3.

Machine-1 11 13 15 12 20

Machine-2 10 8 6 7 9

Machine-3 12 20 15 19 7

Distinguish unconstrained G.P. and constraint G.P. with ≤ type constraint with examples. Explain steps involved in simulation of simple electrical system. Maximize z = 2 x1 + 2 x2 + 4 x3 2 x1 + x2 + x3 ≤ 2 Subject to 3x1 + 4 x2 + 2 x3 ≥ 8 x1 , x2 x3 ≥ 0 Show that phase I will terminate with zero artificial basic variable. Carry out phase II with zero artificial variable as part of starting basic solution.

4.

Discuss need for dual simplex method and sensitivity analysis with assumed simple example. Discuss the changes effected by variation of constraint, constants and addition or deletion of variables and constraints. Contd…2.,

Code No: 52213/MT

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5.

Apply least cost method to solve following transportation problem

6.

Suppose that you want to invest Rs 4000 at start of years 2,3,4. Interest rate offered is 8%. Compounded annually and bonuses for next 4 years are 1.8%, 1.7%, 2.1% and 2.5% respectively. Second bank offers 7.5% Interest rate but bonus is higher by 0.5%. Maximize accumulated capital at the end of 4 years.

7.

With an assumed nonlinear optimization problem for multi variables, apply any one method for optimal solution.

8.

Two products are manufactured on two sequential machines. Following table gives machining time in minutes per unit for two products. Machining time Machine 1 2

Product1 Product 2 5 3 6 2

Daily production quotas for two products are 80 and 60 units. Each machine runs 8 hrs a day, overtime may be used if necessary to meet production quota. Formulate problem as a goal programming model and solve it. ^*^*^