# OPERATION RESERCH

COMPUTER BASED OPTIMIZATION METHODS

1-MARK

1. The scientific method in OR study generally involves ------------ phases

a)      Two

b)      Three

c)      Four

d)     Many

Ans. b

2. A LPP with Three decision variables -----be solved graphically

a)      can

b)      cannot

c)      usually

d)     none of the above

Ans. b

3. Name of the second algorithm is

a)      Branch and bound

b)      Land and dig

c)      Gomory

d)     None of the above

Ans. a

4. The given IPP is modified by inserting a new constrained called

a)      Secondary constraint

b)      Gomory constrained

c)      Land constrained

d)     Both a) and b)

Ans. d

5. In the queuing theory there is ----- maximization and minimization of an objective function.

a)      A

b)      No

c)      Both

d)     None

Ans. b

6. The average rate at which customers arrive called

a)      Arrival pattern

b)      Service facility

c)      Both a) and b)

d)     None of the above

Ans. a

7. After adding the secondary constraints the problem is then solved by

a)      Simplex method

b)      Dual simplex method

c)      All of the above

d)     None of the above

Ans. b

8. n’ means

a)      Number of equation

b)      Number of variables

c)      All of the above

d)     None of the above

Ans. b

9. Sometimes the problem may be infeasible indicating that no --------- of the problem exists

a)      Solution

b)      Feasible

c)      Feasible solution

d)     All of the above

Ans. c

10. The objective function may have to be maximized when it expressed the --------

a)      Profit

b)      Contribution

c)      Cost

d)     Both a) and b)

Ans. d

11. To each of the constraint equations add a new variable called an

a)      Slack variable

b)      Surplus variable

c)      Artificial variable

d)     None of the above

Ans. c

12. The variables which have assigned value zero initially are called

a)      Slack variable

b)      Surplus variable

c)      Artificial variable

d)     Non basic variables

Ans. d

13. If one or more values of the basic variables are also zero valued then solution of the system is said to

a)      Non degenerate

b)      Degenerate

c)      Variable

d)     Non variable

Ans. b

14. In modern warfare the defense operations are carried out by ------ components

a)      2

b)      4

c)      5

d)     3

Ans. d

15. The first and the most important requirement is that the

a)      Define alternatives

b)      Choose alternatives

c)      Root problem should be identified and understood

d)     All of the above

Ans. c

. 16. A common method for testing the validity of a model is to compare its performance with some ------ data available for the actual system

a)      Present

b)      Future

c)      Past

d)     All of the above

Ans. c

. 17. In linear programming problems may have

a)      A unique optimal solution

b)      Many number of optimal solution

c)      An unbounded solution

d)     No solution

e)      All of the above

Ans. e

.18. The transportation problem studies

a)      Maximization of profit

b)      Minimization of cost

c)      Both a) and b)

d)     None of the above

Ans. b

. 19. The Vogels Appropriation method takes into account not only the least cost Cij but also the cost that

a)      Just less Cij

b)      Just exceeds Cij

c)      Both a) and b)

d)     None of the above

Ans. b

20. A row or column difference indicates the

a)      Maximum unit penalty

b)      Minimum unit penalty

c)      Both a) and b)

d)     None of the above

Ans. b

21. If the No. of persons is the same as the no. of jobs, the assignment problem is said to be

a)      None

b)      Balanced

c)      Right

d)     Wrong

Ans. b

22. In assignment problem Minimize the

a)      Cost

b)      Time

c)      Both a) and b)

d)     None of the above

Ans. c

23. Assignment model is mostly used in

a)      Industry

b)      Govt.

c)      Planning

d)     None of the above

Ans. c

24. A loop is the sequence of cells in the -------

a)      Transportation table

b)      Feasible solution

c)      Optimum solution

d)     All of the above

Ans. a

25. In the transportation problem it is assumed that the total supply and the total demand are ---

a)      Equal

b)      Non equal

c)      Both a) and b)

d)     None of the above

Ans. a

26. The random number could be selected by any ---------

a)      Past data

b)      Imputing subjective values

c)      Present data

d)     Random process

Ans. d

27. Expand PERT

a)      Project evaluation and review technique

b)      Planning evaluation and review technique

c)      Project evaluation and revise technique

d)     None of the above

Ans. a

28. The game theory prominence only after

a)      1928

b)      1944

c)      1922

d)     1940

Ans. b

29. Competitive situations occur when two or more parties ---------- operate

b)      Interest

c)      Conflicting interest

d)     None of the above

Ans. c

30. In a competitive game the no. of players is

a)      Three

b)      Four

c)      Two

d)     Finite

Ans. d

31. In a typical pricing problem, the management cannot risk changing the price of the product without evaluating the various ----

a)      Samples

b)      Past data

c)      Alternatives

d)     All of the above

Ans. c

32. Simulation is often referred to as -------

a)      Peter berg analysis

b)      Monte Carlo analysis

c)      Both a) and b)

d)     None of the above

Ans. b

33. The transportation algorithm is the -------method

a)      Mathematical

b)      Scientific

c)      Simplex

d)     Graphical

Ans. c

34. Any feasible solution satisfying

a)      m+n+1

b)      m+n-1

c)      m-n-1

d)     none of the above

Ans. b

35. The expression may be traced by

a)      Von Neumann

b)      Ulan

c)      Both a) and b)

d)     None of the above

Ans. c

36. The game is said to be played when each player adopts one of his

a)      Course of action

b)      Move

c)      Both a) and b)

d)     None of the above

Ans. c

37. A game in which two players participate is called

a)      n – person game

b)      two- person game

c)      all of the above

d)     none of the above

Ans. b

38. Expand CPM

a)      Critical Project method

b)      Critical path method

c)      Crucial path method

d)     None of the above

Ans. b

39. In PERT – CPM there are basic phase is

a)      One

b)      Two

c)      Three

d)     Four

Ans. c

40. Basic disadvantages of the mid square method is

a)      Generated numbers may start cycling after a short set of random no. is obtained

b)      Generated numbers may start circling after a long set of random no. is obtained

c)      Both a) and b)

d)     None of the above

Ans. a

2-MARKS

41. All constraints are equations except for the -------------- condition which remain inequalities----------- only.

a)      Non negativity, (≥, 0)

b)      Negativity, (≥, 0)

c)      Non negativity, (≤,0)

d)     All of the above

Ans. a

42. All variables are -------

a)      Negative.

b)      Non negative

c)      Both a) and b)

d)     None of the above

Ans. b

43. The output or the -------------- subject to the set of ------

a)      Problem, constraints

b)      Objective function, constraints

c)      Constraints, objective function

d)     None of the above

Ans. b

44. In aij  i=---------

a)      1,2,3

b)      1,2,3------n

c)      1,2,3,-------m

d)     All of the above

Ans. c

45. Characteristics of canonical forms is

a)      All decision variables are non negative

b)      All constraints are of ≤ type

c)      The objective function is of the maximization type

d)     All of the above

Ans. d

46. The ultimate goal of all such decision is to either maximize the --------- and minimize the ---------------

a)      Benefit, effort required

b)      Effort, benefit

c)      Profit, benefit

d)     None of the above

Ans. a

47. In defense operations there is a necessity to ----------- the activities of various components which gives maximum benefit to the organization as a ---------

a)      Ordinate, whole

b)      Ordinate, separate division

c)      Co- ordinate, whole

d)     Co – ordinate, separate division

Ans. c

48. The cost Cij transporting one units of product from the Ith ------- to the jth -------- is given for each I and j

a)      Destination, source

b)      Destination, objective

c)      Source, destination

d)     None of the above

Ans. c

49. An analysis of the process is made usually with the help of a flow diagram and an attempt is made to identify the points which restrict service or the characteristics which indicate scope for improvement this study is done in a

a)      Exploration of the various alternatives

b)      Preliminary study

c)      Both a) and b)

d)     None of the above

Ans. b

50. Last step of a typical investigation of a queuing system is

a)      Collection of data

b)      Data analysis

c)      Evaluation of alternatives

d)     Implementation

Ans. d

51. Method of choosing a customer for service from amongst those waiting for service is called

a)      Arrival pattern

b)      Service facility

c)      Queue discipline

d)     All of the above

Ans. c

52. The transportation algorithm is the simplex method specialized to the formal of table it involves

a)      Finding an integral basic feasible solution

b)      Testing the solution for optimality

c)      Improving the solution, when it is not optimal

d)     All of the above

Ans. d

53. The business environment is always ------and any decision useful at one time many not be so ------- some time later

a)      Changing, good

b)      Same, good

d)     None of the above

Ans. a

54. An equation can be replaced by two inequalities in opposite direction for example 2x1+3x2 = 5 can be written as

a)      2x1+3x2 ≤5 and 2x1+3x2 ≥5

b)      2x1+3x2 ≤-5 and 2x1+3x2 ≥-5

c)      2x1+3x2 ≤5 and -2x1-3x2 ≥-5

d)     Both a) and c)

Ans. d

55. The remaining characteristics are achieved by using the elementary transformation introduced with the ---------

a)      Mathematical form

b)      Feasible solution

c)      Canonical form

d)     All of the above

Ans. c

56. Von Neumann and Ulan, who in the late 1940’s found a problem in the field of ------

a)      Nuclear physics

b)      Physics

d)     None of the above

Ans. a

57. In 78466 “even” digits signify a Head and the “odd” digits represent a tail. Then H and T in it is

a)      3,2

b)      4,1

c)      1,4

d)     2,3

Ans. b

58. The growing complexities of today’s projects had demanded more ------ and ------- with the objective of optimizing the efficiency of executing the project.

a)      Planning, budget

b)      Systematic, planning

c)      Systematic, more effective planning techniques

d)     All of the above

Ans. c

59. Efficiency in Project planning means

a)      Utmost reduction in the time required to complete the project

b)      Economic feasibility of using available resources

c)      Both a) and b)

d)     None of the above

Ans. c

60. The approach adopted for solving a problem in gambling can be extended decision making in business where --------- is a common feature.

a)      Stock

b)      Capital

c)      Risk

d)     Stationary

Ans. c

4-MARKS

61. State True of False for characteristics of a competitive game

1. The no. of players is infinite
2. Each player has finite no. of courses of moves
3. the game is said to be played when each player plan a strategy
4. The game is played once
5. The corresponding combination of courses of action leads to a transaction to each player
6. The payment is called gain

A)    1-T,2-T,3-T,4-T,5-T,6-F

B)    1-T,2-F,3-T,4-F,5-T,6-F

C)    1-F,2-F,3-T,4-T,5-T,6-F

D)    1-F,2-T,3-F,4-F,5-T,6-T

Ans. d

62. Match the following

Set - 1

1. Project planning
2. scheduling
3. project control

Set - 2

a)      Developing a network diagram showing the sequential inter relationships between the various activities

b)      Refers to revaluating actual progress against the plan

c)      Estimating the durations of activities, taking into considerations the resources required for these execution in most economic manner.

A)    1-a,2-c,3-b

B)    1-a,2-b,3-c

C)    1-c,2-a3-b

D)    None of the above

Ans. a

63. For solving games if we use dominance then the procedure is

a)      In the pay off matrix if each pay off in the rth row is grater then the corresponding pay off in the sth row, Ar dominates As. And so As is deleted

b)      In the pay off matrix, if each pay off in the pth column is less than the corresponding pay off in the qth column, Bp dominates Bq, and so Bq is deleted

c)      The above steps are repeated in succession until the saddle point is reached and hence the solutions is written down

A)    1,2,3

B)    2,1,3

C)    3,1,2

D)    None of the above

Ans. a

64. Match the following

Set - 1

1. PERT
2. CPM

Set - 2

a)      Developed in connection with R and D

b)      Cope with the uncertainties

c)      Developed in connection with construction project

d)     Event oriented network

f)       Used for projects involving activities of non repetitive nature

g)      Used for projects involving activates of repetitive nature

A)    1-a,c,d,f, 2-b,e,g

B)    1-a,b,e,f, 2-c,d,g

C)    1-a,b,d,f, 2-c,e,g

D)    1-b,d,f, 2-a,c,e,g

Ans. c

65. It is essential for the -------- to have a understanding of the -------- so that he will consider the right ------ and formulate the correct model

a)      Executive, process, alternatives

b)      Staff, process, alternatives

c)      Executive, Model, alternatives

d)     None of the above

Ans. a

66. Ships arrive at a port at a rate of one in every 3 hours, with a negative exponential distribution of interracial times. The time a ship occupies a berth for unloading and loading has a negative exponential distribution with an average of 12 hours. If the average delay of ships waiting for berths is to be kept below 6 hours, how many berths should there be at the port.

a)      1

b)      5

c)      8

d)     6

Ans. d

67. In case only some of the variables are restricted to take integral value and rest (n – k) variables are free to take any non negative values, then the problem is knows as

a)      All integer programming problem

b)      Pure integer programming problem

c)      Mixed integer programming problem

d)     Integer programming problem

Ans. c

68. Four jobs are to be done on four different machines. The cost is in ( Rs.) of producing Ith on the Jth machine is given below

Machines

 M1 M2 M3 M4 J1 15 11 13 15 J2 17 12 12 13 J3 14 15 10 14 J4 16 13 11 17

A. In the above question Job 1 to machine

a)      1

b)      2

c)      3

d)     4

Ans. a

B. Job 4 to machine

a)      1

b)      2

c)      3

d)     4

Ans. c

69. State true or false for the basic techniques for getting the optimum solution

1.      Determining the net evaluations for the non – basic variables

2.      Determining the entering variable

3.      Determining the leaving variable

4.      Computing a better basic feasible solution

5.      Repeating steps (1) to (4) until an optimum solution has been obtained

a.       All are true

b.      All are false

c.       Only 1234 are true

d.      Only 1345 are true

Ans. A

70. Use simplex method to solve the LPP

Maximize Z = 2x1 + 4 X2 + X3 + X4

Subject to         x1 + 3 X2 + X4 ≤ 4

2x1 + x2 + ≤ 3

X2 + 4X3 + X4 ≤ 3

x1 ,X2 , X3 , X4 ≥ 0

Is all elements of the last row are -------

a)      Negative

b)      Non – negative

c)      Multipliers

d)     None of the above

Ans. b

71. Objective of operation research is to provide a --------- basis to the ----------- for solving the problems involving the interaction of various ------------ of organization, by employing a team of -------------- from different disciplines, all working -------- for finding a solution which is the best in the interest of the organization as a whole.

a)      Scientific, businessman, components, scientists, together

b)      Scientific, Decision -maker, components, scientists, separately

c)      Scientific, Decision -maker, components, scientists, together

d)     Scientific, Decision -maker, components, staff, together

Ans. c

72. State True or False for OR method in the can be applied in the field of

1. Production
2. Inventory control
3. Marketing
5. Transportation
6. Competitive strategies

A)    All are True

B)    All are False

C)    Only 1,2,3,4,5 are true

D)    Only 2,3,4,5,6 are true

Ans. a

73. Match the following

SET -1

1. Planning
2. Agriculture
3. Hospital
4. Transportation
5. Research and Development

SET -2

a)      There is need for increase output. But this cannot be done arbitrarily.

b)      Product Introduction, Planning etc.

c)      Waiting problems

d)     It is necessary for every government

e)      To regulate the arrivals and processing time

A)    1-c,2-b,3-a,4-e,5-d

B)    1-d,2-a,3-c,4-e,5-b

C)    1-b,2-a,3-d,4-c,5-e

D)    1-c,2-a,3-b,4-d,5-e

Ans. b

74. Decision making can be considered as a general systematic process that steps is

a)      Define the problem, select the alternative, determine the model to be used, evaluate the alternative, choose the one

b)      Define the problem, select the alternative, determine the model to be used, choose the one, define the alternative

c)      Select the problem, define the alternative, determine the model to be used, evaluate the alternative, choose the one

d)     Any of the above

Ans. a

75. Match the following

SET -1

1.      Decision variables

2.      Objective function

3.      Constraints

SET -2

b)      The unknowns to be determined from the solution of model

c)      This defines the measure of effectiveness of the system as a mathematical function of its decision variables

d)     To account for the physical limitations

A)    1-c,2-b,3-a

B)    1-b,2-a,3-c

C)    1-a,2-b,3-c

D)    None of the above

Ans. c