Download OU B.Sc Computer Science 6th Sem Operations Research Important Questions

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Subject Title: Operations Research Prepared by: E.Sukanya

Year: lll Semester: VI Updated on: 25-03-

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Unit - I:

1. Definitions of (i) Operations Research (ii) Deterministic model (iii) Probability model
2. Definitions of (i) Decision Variable (ii) Convex sets (iii) Extreme points of Convex Sets.
3. Definitions of (i) Solution (ii) Feasible solution (iii) Basic Solution (iv) Basic Feasible Solution (v) Degenerate Solution (vi) Non-degenerate Solution (vii) Optimum Solution (viii) unbounded solution.
4. Explain about the Fundamental theorem of LPP.

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5. Describe about the Graphical Method Algorithm.
6. Describe about the Simplex Method Algorithm.
7. Explain the Characteristics of Standard Form of LPP.
8. Solve the following LP problem by Graphical Method: Max z=5x; + 7x,; STC:x; + x, < 4,3x; + 8x, < 24, 10x; + 7x, < 35,x,x, = 0
9. Solve the LP problem by Simplex Method: Maxz=3x, + 5x; + 4x3; STC: 2x1 + 3x, < 8,2x; + 5x3 < 10, 3x; + 2x, + 4x3 < 15 and xq,%x5,x3 =0

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10. Solve the LP problem by Simplex Method: Maxz=x, — 3x, + 2x3 STC: 3xy— X, + 3x3 < 7,—2x; + 4x, < 12,—4x; + 3x, + 8x3 < 10 and xq,%x5,x3 =0

Unit - 1I:

11. Describe the algorithm of Big M or Penalty method.
12. Describe the algorithm of Two Phase Method
13. Describe the algorithm of Duality.

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14. Explain the dual of the Dual is Primal.
15. Definition of (i) Artificial variable (ii) Degeneracy in LPP (iii) Duality of LPP (iv) Primal and Dual pairs.

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16. Solve the following LP problem by Big M method. Max z= x; + 2x, + 3x3 — x4; STC: x; + 2x, + 3x53 = 15; 2x; + x5 + 5x3 = 20; x; + 2x, + x5 + x,=10 and x;, x5, x3,%, = 0
17. Solve the following problem by Two-Phase Simplex Method: Min z=x; + x,; STC:2x; + x, = 4,%, + 7x, =7 and x;,x, = 0

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18. Write the Dual of the following LP problem: Min z=3x; — 2x, + 4x3; STC: 3x, + 5x, + 4x3 = 7,6x1 + X5 + 3x3 = 4; 7x; — 2%, — x3 < 10; X1 — 2%y + 5x3 = 4;4x, + 7x, — 2x3 = 2 and x4, %, %3 = 0.
19. Obtain the dual of the LP problem: Min z=x; + x, + x3; STC: x; — 3%, + 4x3 = 5;x; — 2x, < 3,2X, — X3 = 4,%x1,x, = 0 and x5 is unrestricted.
20. Solve the following problem by Dual Simplex Method: Min z= 2x; + x5; STC: 3x; + x, = 3, 4x; + 3x, = 6,x; + 2x, = 3 and x;,x, = 0

Unit - 1l

21. Definitions of (i) Feasible Solution (ii) Basic Feasible Solution (iii) Degenerate basic feasible solution (iv) Optimum basic feasible solution (v) Transhipment problem

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22. Describe the algorithm of North West Corner Rule (NWCR)
23. Describe the algorithm of Matrix Minima method or Least Cost Method.
24. Describe the algorithm of VAM.
25. State the algorithm of Stepping stone method
26. State The Algorithm Of UV Method or MODI Method

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27. Obtain an Initial Feasible-Solution by NWCR

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28. Obtain an Initial Basic Feasible Solution by Least cost Entry method to the following transportation problem.

29. Obtain an Initial Basic Feasible Solution by using VAM to the following Transportation problem

30. Obtain an Optimum Basic Feasible Solution by using Stepping Stone Method

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31. Solve the following Transportation problem using UV —method/ MODI method

32. Resolve Degeneracy if occurs and solve the following Transportation problem

33. Consider a Transhipment problem with two sources, three destinations, the cost for shipment in rupees are given below. Determine the Optimum Schedule

Unit - IV

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34. Describe the Hungarian method for an assignment problem.
35. Describe the algorithm of Johnson’s algorithm to obtain optimum sequence for n jobs and two machines
36. Describe the algorithm of n jobs through three machines
37. Describe the algorithm of n jobs through K machines
38. A department has four sub ordinates and four tasks have to be performed. Subordinates differ in efficiency and tasks differ in their intrinsic difficulty. Time each man would take to perform each task is given in the effectiveness matrix. How the tasks should be allocated to each person so as to minimize the total man-hours?

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39. The owner of a small machine shop has four machinists available to do jobs for the day.Five jobs are offered with expected profit for each machinist on each job as follows.

Find by using an assignment method, the assignment of machinists to jobs that will result a maximum profit. Which job should be declined:

40. A company has 4 machines on which'to.do 3 jobs. Each job can be assigned to one and only one machine. The cost of each job‘on‘each machine is given in the following table.

What are the job assignment which will minimize the cost?

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41. We have 5 jobs, each of which has to be processed on two machines A and B in the order AB. Processing times are given in the following table (in hours)

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

42. Determine the optimal sequence of jobs that minimizes the total elapsed time base on the given processing times