## Operations Research Multiple Choice Questions

1. The main objective of OR is to provide a ___, ___ to the decision-makers.

2. OR employs a team of ___ from ___ ___.

3. Mention two applications of OR.

4. How can a hospital benefit from the application of OR methods?
Answer: To solve waiting for problems

5. OR ___ inter-disciplinary approach.

6. OR increases the effectiveness of ___ ability.

7. OR gives a qualitative solution

8. One of the OR phases is the Action phase

9. Diagram belongs to the physical model

10. Allocation problems are represented by the iconic model

11. OR methodology consists of definition, solution and validation only.

12. The interaction between the OR team and Management reaches peak level in the implementation phase.

13. OR imbibes ___ team approach.

14. Linear programming is the tool of ___.

15. The three phases of OR are ___.
Answer: Judgement phase, Research phase & Action phase

16. To solve any problem through the OR approach the first step is ___.

17. ___ represents a real-life system.

18. ___ represents the controlled variables of the system

19. Both the objective function and constraints are expressed in ___ forms.

20. LPP requires existence of ___, ___, ___ and ___.
Answer: An alternate course of action

21. Solution of decision variables can also be ____.

22. One of the characteristics of canonical form in the objective function must be of maximisation.

23. 2x – 3y ≤ 10 can be written as -2x + 3y ≥-10

24. The collection of all feasible solutions is known as the ___ region.

25. A linear inequality in two variables is known as a ___.

26. The feasible region is a convex set

27. The optimum value occurs the anywhere infeasible region

28. We add a surplus variable for “≤” of constraint.

29. The right-hand side element of each constraint is non-negative.

30. A basic solution is said to be a feasible solution if it satisfies all constraints.

31. If one or more values of the basic variable are zero then the solution is said to be degenerate.

32. The right-hand side element of each constraint is non-negative.

33. The key column is determined by Zj – Cj row.

34. Pivotal element lies on the crossing of the key column and key row.

35. The negative and infinite ratios are considered for determining key row.

36. The value of artificial value is “M”.

37. Artificial variables enter as basic variables.

38. Dual LPP always reduces the amount of computation.

39. It is possible to reverse the dual LPP to primal LPP

40. The coefficients of decision variables in the objective function become quantities on the right-hand side of ___.

41. “≤” constraints changes to ___ type in dual LP.

42. For every LPP, there exists a unique ___ problem.

43. Dual variables represent the worth or unit of a resource.

44. Optimality is reached when the resources are not fully utilised.

45. At the optimum level the relationship holds as a strict equation

46. Sensitivity analysis is carried out on ___ simplex table.

47. It helps us to study the effect of changes in ___ ___ in the objective function.

48. The results of sensitive analysis establish ___ and ___ ___ for input parameters value.

49. Transportation problems are a special type of ___.

50. The number of rows and columns need not always be ___.

51. Transportation problem develops a schedule at ___ and ___.

52. In transportation problems, ∑ai = ∑bj is a sufficient and necessary condition for getting a feasible solution.

53. Transportation problems can also be solved by the simplex method.

54. Matrix-minima method gives the optimum solution.

55. In matrix-minima method, you start allocating from the left-top cell of the table.

56. In Vogel‟s approximation method, you first construct penalty and then start allocating.

57. North-west corner rule gives the optimum solution.

58. Vogel‟s approximation method gives a solution near to the optimum solution.

59. All the values of ΔCij – ui – vj should be ___ or ___ for the solution to be optimum.

60. In unbalanced transportation problem ∑ai is ___ ___ to ∑bj.

61. If the number of allocation is less than ___ then it is said to be a degenerate transportation problem.
Answer: m + n – 1

62. In an AP, the constraints are of equality type.

63. The number of facilities should be equal to the number of resources.

64. The decision variables can take on any value.

65. In the Hungarian method, you prepare the row-reduced matrix.

66. The number of assignments should be equal to the number of rows for an optimum solution.

67. There can be more than one allocation in a row.

68. In unbalanced AP, the number of rows ___ to the number of columns.

69. Hungarian method cannot be applied directly to ___ problem.

70. If some jobs cannot be assigned to some machines, then it is called ___ assignment problem.

71. In the travelling salesman problem, the objective is to visit each city ___ ___.

72. Salesman has ___ different sequences if n is the number of cities to be visited.
Salesman

73. Integer programming is applied to problems that involve discrete variables.

74. If some variables take on non-negative values, then it is known as pure IPP.

75. An optimum solution to IPP is first obtained by using ___.

### Operations Research MCQs

1. Operations research is the application of ____________methods to arrive at the optimal Solutions to the problems.

1. economical
2. scientific
3. a and b both
4. artistic

2.    In operations research, the ——————————are prepared for situations.

1. mathematical models
2. physical models diagrammatic
3. diagrammatic models

3.    Operations management can be defined as the application of ————-to a problem within a system to yield the optimal solution.

1. Suitable manpower
2. mathematical techniques, models, and tools
3. Financial operations

4.   Operations research is based upon collected information, knowledge and advanced study of various factors impacting a particular operation. This leads to more informed —-

1. Management processes
2. Decision making
3. Procedures

5.    OR can evaluate only the effects of ————————————————–.

1. Personnel factors.
2. Financial factors
3. Numeric and quantifiable factors.

6 Which of the following is not the phase of OR methodology?

1. Formulating a problem
2. Constructing a model
3. Establishing controls
4. Controlling the environment

7 – The  objective  function  and  constraints  are  functions  of  two  types  of  variables,

_______________ variables and ____________ variables.

1. Positive and negative
2. Controllable and uncontrollable
3. Strong and weak
4. None of the above

8 – Operations research was known as an ability to win a war without really going in to ____

1. Battle field
2. Fighting
3. The opponent
4. Both A and B

9 – Who defined OR as scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control?

1. Morse and Kimball (1946)
2. P.M.S. Blackett (1948)
3. E.L. Arnoff and M.J. Netzorg
4. None of the above

10 – OR has a characteristics that it is done by a team of

1. Scientists
2. Mathematicians
4. All of the above

MCQ on Operations Research

11 – A solution can be extracted from a model either by

1. Conducting experiments on it
2. Mathematical analysis
3. Both A and B
4. Diversified Techniques

12 OR uses models to help the management to determine its _____________

1. Policies
2. Actions
3. Both A and B
4. None of the above

13 What have been constructed from OR problems an methods for solving the models that are available in many cases?

1. Scientific Models
2. Algorithms
3. Mathematical Models
4. None of the above

14 -Which technique is used in finding a solution for optimizing a given objective, such as profit maximization or cost reduction under certain constraints?

1. Quailing Theory
2. Waiting Line
3. Both A and B
4. Linear Programming

15 -What enables us to determine the earliest and latest times for each of the events and activities and thereby helps in the identification of the critical path?

1. Programme Evaluation
2. Review Technique (PERT)
3. Both A and B
4. Deployment of resources

16 – OR techniques help the directing authority in optimum allocation of various limited resources like_____

1. Man and machine
• money
• material
• all of the above

17 -The Operations research technique which helps in minimizing total waiting and service costs is

1. ueuing Theory
2. Decision Theory
3. Both A and B
4. None of the above

18 .What is the objective function in linear programming problems?

1. A constraint for available resource
2. An objective for research and development of a company
3. A linear function in an optimization problem
4. A set of non-negativity conditions

19 – .Which statement characterizes standard form of a linear programming problem?

1. Constraints are given by inequalities of any type
2. Constraints are given by a set of linear equations
3. Constraints are given only by inequalities of >= type
4. Constraints are given only by inequalities of <= type

20 – Feasible solution satisfies __________

1. Only constraints
2. only non-negative restriction
3. [a] and [b] both
4. [a],[b] and Optimum solution

MCQ on Operations Research

21 – In Degenerate solution value of objective function _____________.

1. increases infinitely
2. basic variables are nonzero
3. decreases infinitely
4. One or more basic variables are zero

22 – Minimize Z = ______________

1. maximize(Z)
2. maximize(-Z)
3. maximize(-Z)
4. none of the above

23 -In graphical method the restriction on number of constraint is _________

1. 2
2. not more than 3
3. 3
4. none of the above

24 -In graphical representation the bounded region is known as _________ region.

1. Solution
2. basic solution
3. feasible solution
4. optimal

25 -Graphical optimal value for Z can be obtained from

1. Corner points of feasible region
2. Both a and c
3. corner points of the solution region
4. none of the above

26 -In LPP the condition to be satisfied is

1. Constraints have to be linear
2. Objective function has to be linear
3. none of the above
4. both a and b

27 – Identify the type of the feasible region given by the set of inequalities

x – y <= 1

x – y >= 2

where both x and y are positive.

1. A triangle
2. A rectangle
3. An unbounded region
4. An empty region

28 -Consider the given vectors: a(2,0), b(0,2), c(1,1), and d(0,3). Which of the following vectors are linearly independent?

1. a)  b, and c are independent
2. a, b, and d are independent
3. a and c are independent
4. b and d are independent

Q29 – Consider the linear equation

x1 + 3 x2 – 4 x3 + 5 x4 = 10

How many basic and non-basic variables are defined by this equation?

1. One variable is basic, three variables are non-basic
2. Two variables are basic, two variables are non-basic
3. Three variables are basic, one variable is non-basic
4. All four variables are basic

30 – The objective function for a minimization problem is given by

z = 2 x1 – 5 x2 + 3 x3

The hyperplane for the objective function cuts a bounded feasible region in the space (x1,x2,x3). Find the direction vector d, where a finite optimal solution can be reached.

1. d(2,-5,3)
2. d(-2,5,-3)
3. d(2,5,3)
4. d(-2,-5,-3)

MCQ on Operations Research

31 – In game theory, the outcome or consequence of a strategy is referred to as the

1. payoff.
2. penalty.
3. reward.
4. end-game strategy.

32-  Operations Research approach is?

1. multi-disciplinary
2. scientific
3.  intuitive
4.  collect essential data

33 – Operation research approach is typically based on the use of _____

1. physical model
2.  mathematical model
3.  iconic model
4.  descriptive model

34 – Mathematical model of linear programming problem is important because ________

1. it helps in converting the verbal description and numerical data into mathematical expression
2. decision makers prefer to work with formal models
3.  it captures the relevant relationship among decision factors
4.  it enables the use of algebraic technique

35 –  In Program Evaluation Review Technique for an activity, the optimistic time 2, the pessimistic time is 12 and most-likely time is 4. What is the expected time?

1. 0
2.  1
3.  5
4. 6

36 – Graphical method of linear programming is useful when the number of decision variable are __________.

1. 2
2.  6
3. finite
4. infinite

37 – A feasible solution to a linear programming problem _______________.

1. must satisfy all the constraints of the problem simultaneously
2.  need not satisfy all of the constraints, only some of them
3.  must be a corner point of the feasible region.
4.  must optimize the value of the objective function

38 – Utilization factor is also known as ___________.

1. Traffic intensity
2. Kendals notation
3. Row minima method
4. Unbalanced assignment problem

39 –  While solving a linear programming problem in feasibility may be removed by _________.

3.  removing a constraint
4. removing a variable

40 –  In the optimal simplex table, Zj-Cj=0 value indicates _____________.

1. alternative solution
2.  bounded solution
3.  infeasible solution
4.  unbounded solution

MCQ on Operations Research

41 –  If all aij values in the entering variable column of the simplex table are negative, then ___________.

1. there are multiple solutions
2.  there exist no solution
3.  solution is degenerate
4.  solution is unbounded

42 –  If an artificial variable is present in the basic variable column of optimal simplex table, then the solution is ___________.

1. alternative
2. bounded
3. no solution
4. infeasible

43 – For any primal problem and its dual ______________.

1. optimal value of objective function is same
2. primal will have an optimal solution iff dual does too
3.  both primal and dual cannot be infeasible
4.  dual will have an optimal solution iff primal does too

44 – Principle of complementary slackness states that ____________.

1. primal slack*dual main=0
2.  primal main+dual slack=0
3. primal main+dual surplus=0
4.  dual slack*primal main not equal to zero

45 – If primal linear programming problem has a finite solution, then dual linear programming problem should have ____________.

1. finite solution
2.  infinite solution
3. bounded solution
4.  alternative solution

46 – The initial solution of a transportation problem can be obtained by applying any known method. How-ever, the only condition is that __________.

1. the solution be optimal
2.  the rim conditions are satisfied
3.  the solution not be degenerate
4. the few allocations become negative

47 -The dummy source or destination in a transportation problem is added to ______.

1. satisfy rim conditions
2. prevent solution from becoming degenerate
3. ensure that total cost does not exceed a limit
4.  the solution not be degenerate

48 – Which of the following methods is used to verify the optimality of the current solution of the transportation problem ____________.

1. Modified Distribution Method
2. Least Cost Method
3.  Vogels Approximation Method
4.  North West Corner Rule

49 – An optimal assignment requires that the maximum number of lines which can be drawn through squares with zero opportunity cost be equal to the number of ________.

1. rows or coloumns
2. rows and coloumns
3. rows+columns- 1
4. rows-columns

50 –  Maximization assignment problem is transformed into a minimization problem by ________.

1. adding each entry in a column from the maximum value in that column
2.  subtracting each entry in a column from the maximum value in that column
3. subtracting each entry in the table from the maximum value in that table
4.  adding each entry in the table from the maximum value in that table

MCQ on Operations Research

51 –  To proceed with the MODI algorithm for solving an assignment problem, the number of dummy allocations need to be added are ___________.

1. n
2.  n-1
3.  2n-1
4.  n-2

52 – An artificial variable leaves the basis means, there is no chance for the ________ variable to enter once again.

1. slack
2.  surplus
3. artificial
4. dual

53 –  Simplex method was designed by ___________.

1. Dantzig
2.  A.Charnes
3.  Lemke
4. Hungarian

54 – Dual Simplex Method was introduced by ____________.

1. Dantzig
2.  A.Charnes
3. Lemke
4.  Hungarian

55 – The cell with allocation can be called ___________ .

1. Cell
2.  Empty cell
3.  Basic cell
4. Non-basic cell

56 – The cell without allocation is called __________.

1. Basic cell
2.  Non-basic cell
3. Empty cell
4. Basic solution

57 – Service mechanism in a queuing system is characterized by ___

1. customers behavior
2.  servers behavior
3.  customers in the system
4.  server in the system

58 – The problem of replacement is felt when job performing units fail ____

3.  suddenly

59 – Least Cost Method is also known as __________.

1. North West Corner Method
2.  Matrix Minima Method
3.  Row Minima method
4. Coloumn Minima method

MCQ on Operations Research

60 – The objective of network analysis is to ___________.

1. minimize total project duration
2.  minimize total project cost
3.  minimize production delays, interruption and conflicts
4.  maximize total project duration

61 – A activity in a network diagram is said to be __________ if the delay in its start will further delay the project completion time.

1. forward pass
2. backward pass
3.  critical
4. non critical

62 – A strategy that is best regardless of what rival players do is called

2. a Nash equilibrium strategy.
3. tit-for-tat.
4. a dominant strategy.

63 – A game that involves interrelated decisions that are made over time is a

1. sequential game.
2. repeated game.
3. zero-sum game.
4. nonzero-sum game.

64 – A game that involves multiple moves in a series of identical situations is called a

1. sequential game.
2. repeated game.
3. zero-sum game.
4. nonzero-sum game.

65 – Sequential games can be solved using

1. tit-for-tat.
2. dominated strategies.
3. backward induction
4. risk averaging.

66 – A firm that is threatened by the potential entry of competitors into a market builds excess production capacity. This is an example of

1. a prisoners’ dilemma.
2. collusion.
3. a credible threat.
4. tit-for-tat.

67 – What is the fundamental purpose of game theory?

1. To analyse decision-making
2. To analyse strategic interactions
3. To predict decision outcome
4. To predict firm behaviour

68 – An assignment problem is considered as a particular case of a transportation problem because

1. The number of rows equals columns
2. All xij= 0 or 1
3. All rim conditions are 1
4. All of the above

69 – An optimal assignment requires that the maximum number of lines that can be drawn through squares with zero opportunity cost be equal to the number of

1. Rows or columns
2. Rows & columns
3. Rows + columns –1 d.
4. None of the above

70 – While solving an assignment problem, an activity is assigned to a resource through a square with zero opportunity cost because the objective is to

1. Minimize total cost of assignment
2. Reduce the cost of assignment to zero
3. Reduce the cost of that particular assignment to zero
4. All of the above

MCQ on Operations Research

71 – The method used for solving an assignment problem is called

1. Reduced matrix method
2. MODI method
3. Hungarian method
4. None of the above

72 – The purpose of a dummy row or column in an assignment problem is to

1. Obtain balance between total activities &total resources
2. Prevent a solution from becoming degenerate
3. Provide a means of representing a dummy problem
4. None of the above

73 – Maximization assignment problem is transformed into a minimization problem by

1. Adding each entry in a column from the maximization value in that column
2. Subtracting each entry in a column from the maximum value in that column
3. Subtracting each entry in the table from the maximum value in that table
4. Any one of the above

74 – If there were n workers & n jobs there would be

1. n! solutions
• (n-1)! solutions
• (n!)nsolutions
• n solutions

75 -An assignment problem can be solved by

1. Simplex method
2. Transportation method
3. Both a & b
4. none of above

76 – The assignment problem

1. Requires that only one activity be assigned to each resource
• Is a special case of transportation problem
• Can be used to maximize resources
• all of the above

Q77 – An assignment problem is a special case of transportation problem, where

1. Number of rows equals number of columns
2. All rim conditions are 1
3. Values of each decision variable is either 0 or 1
4. All of the above

78 – Every basic feasible solution of a general assignment problem, having a square pay-off matrix of order, n should have assignments equal t

1. 2n+1
2. 2n-1
3. m+n-1
4. m+n

79 – To proceed with the MODI algorithm for solving an assignment problem, the number of dummy allocations need to be added are

1. n
2. 2n
3. n-1
4. 2n-1

80 – The Hungarian method for solving an assignment problem can also be used to solve

1. A transportation problem
2. A travelling salesman problem
3. A LP problem
4. Both a & b

MCQ on Operations Research

81  An optimal solution of an assignment problem can be obtained only if

1. Each row & column has only one zero element
• Each row & column has at least one zero element
• The data is arrangement in a square matrix
• None of the above

82 – Which method usually gives a very good solution to the assignment problem?

1. northwest corner rule
• Vogel’s approximation method
• MODI method

d) stepping-stone method

83 – The northwest corner rule requires that we start allocating units to shipping routes in the: middle cell.

1. Lower right corner of the table.
2. Upper right corner of the table.
3. Highest costly cell of the table.
4. Upper left-hand corner of the table.

84 – The table represents a solution that is:

1. an initial solution
• Infeasible
• degenerate.
• all of the above

85 – Which of the following is used to come up with a solution to the assignment problem?

1. MODI method
2. northwest corner method
3. stepping-stone method
4. Hungarian method

86 – What is wrong with the following table?

• The solution is infeasible.
• The solution is degenerate.
• The solution is unbounded.
• The solution is inefficient in that it is possible to use fewer routes.

87 –  The solution presented in the following table is

• infeasible.
• degenerate.
• unbounded.
• Optimal.

88 – The solution shown was obtained by Vogel’s approximation. The difference between the objective function for this solution and that for the optimal is

• 40
• 60
• 80
• 100

89 – Optimal solution of an assignment problem can be obtained only if

1. Each row & column has only one zero element
2. Each row & column has at least one zero element
3. The data is arrangement in a square matrix
4. None of the above

90 – In assignment problem of maximization, the objective is to maximise

1. Profit
2. optimization
3. cost
4. None of the above

MCQ on Operations Research

91 – What is the difference between minimal cost network flows and transportation problems?

1. The minimal cost network flows are special cases of transportation problems
2. The transportation problems are special cases of the minimal cost network flows
3. There is no difference
4. The transportation problems are formulated in terms of tableaus, while the minimal cost network flows are formulated in terms of graphs

92 – With the transportation technique, the initial solution can be generated in any fashion one chooses. The only restriction is that

1. the edge constraints for supply and demand are satisfied.
2. the solution is not degenerate.
3. the solution must be optimal.
4. one must use the northwest-corner method

93 – The purpose of the stepping-stone method is to

1. develop the initial solution to the transportation problem.
2. assist one in moving from an initial feasible solution to the optimal solution.
3. determine whether a given solution is feasible or not.
4. identify the relevant costs in a transportation problem.

94 – The purpose of a dummy source or dummy destination in a transportation problem is to

1. prevent the solution from becoming degenerate.
2. obtain a balance between total supply and total demand.
3. make certain that the total cost does not exceed some specified figure.
4. provide a means of representing a dummy problem.

94 – Which of the following is NOT needed to use the transportation model?

1. the cost of shipping one unit from each origin to each destination
2. the destination points and the demand per period at each
3. the origin points and the capacity or supply per period at each
4. degeneracy

95 – Which of the following is a method for improving an initial solution in a transportation problem?

1. northwest-corner
2. intuitive lowest-cost
3. southeast-corner rule
4. stepping-stone

96 – The transportation method assumes that

1. there are no economies of scale if large quantities are shipped from one source to one destination
2. the number of occupied squares in any solution must be equal to the number of rows in the table plus the number of columns in the table plus 1.
3. there is only one optimal solution for each problem.
4. the number of dummy sources equals the number of dummy destinations.

97 – An initial transportation solution appears in the table.

• Yes, this solution can be improved by \$50.
• Yes, this solution can be improved by \$100.
• No, this solution is optimal.
• Yes, the initial solution can be improved by \$10.

98 – What is the cost of the transportation solution shown in the table?

• \$1350
• \$1070
• \$1150
• \$1230

99 – Which statement regarding this transportation table is best?

1. The solution is degenerate.
2. This solution can be improved by shipping from C to X.
3. This solution would be improved by shipping from B to W.
4. This solution was developed using the northwest corner rule.

100 – Which of these statements about the stepping-stone method is best?

1. A dummy source and destination must be added if the number of rows plus columns minus 1 is not equal to the number of filled squares.
2. Only squares containing assigned shipments can be used to trace a path back to an empty square.
3. An improvement index that is a net positive means that the initial solution can be improved.
4. Only empty squares can be used to trace a path back to a square containing an assigned shipment

MCQ on Operations Research

101 – In  a  transportation  problem,  we  must  make  the  number  of  _______  and______ equal.

1. destinations; sources
2. units supplied; units demanded
3. columns; rows
4. positive cost coefficients; negative cost coefficients

102 – _________ or __________ are used to “balance” an assignment or transportation problem.

1. Destinations; sources
2. Units supplied; units demanded
3. Dummy rows; dummy columns
4. Large cost coefficients; small cost coefficients

103 – The net cost of shipping one unit on a route not used in the current transportation problem solution is called the __________.

1. change index
2. new index
3. MODI index
4. Improvement index

104 – The procedure used to solve assignment problems wherein one reduces the original assignment costs to a table of opportunity costs is called __________.

1. stepping-stone method
2. matrix reduction
3. MODI method
4. northwest reduction

105 – The method of finding an initial solution based upon opportunity costs is called__________.

1. the northwest corner rule
2. Vogel’s approximation
3. Johanson’s theorem
4. Flood’s technique

106 – An assignment problem can be viewed as a special case of transportation problem in which the capacity from each source is _______ and the demand at each destination is________.

1. 1; 1
2. Infinity; infinity
3. 0; 0
4. 1000; 1000

107 – _______ occurs when the number of occupied squares is less than the number of rows plus

1. Degeneracy
2. Infeasibility
3. Unboundedness
4. Unbalance

108 – Both transportation and assignment problems are members of a category of LP problems called ______.

1. shipping problems
2. logistics problems
3. generalized flow problems
4. network flow problem

109 – The equation Ri + Kj = Cij is used to calculate __________.

1. an improvement index for the stepping-stone method
2. the opportunity costs for using a particular route
3. the MODI cost values (Ri, Kj)
4. the degeneracy index

110 – In case of an unbalanced problem, shipping cost coefficients of ______ are assigned to each created dummy factory or warehouse.

1. very high positive costs
2. very high negative costs
3. 10
4. zero

MCQ on Operations Research

111 – The initial solution of a transportation problem can be obtained by applying any known method. However, the only condition is that

1. The solution be optimal
2. The rim conditions are satisfied
3. The solution not be degenerate
4. All of the above

112 – The dummy source or destination in a transportation problem is added to

1. Satisfy rim conditions
2. Prevent solution from becoming degenerate
3. Ensure that total cost does not exceed a limit
4. None of the above

113 – The occurrence of degeneracy while solving a transportation problem means that

1. Total supply equals total demand
2. The solution so obtained is not feasible
3. The few allocations become negative
4. None of the above

114 – An alternative optimal solution to a minimization transportation problem exists whenever opportunity cost corresponding to unused route of transportation is:

1. Positive & greater than zero
2. Positive with at least one equal to zero
3. Negative with at least one equal to zero
4. None of the above

115 – One disadvantage of using North-West Corner rule to find initial solution to the transportation problem is that

1. It is complicated to use
2. It does not take into account cost of transportation
3. It leads to a degenerate initial solution
4. All of the above

116 – The solution to a transportation problem with ‘m’ rows (supplies) & ‘n’ columns (destination) is feasible if number of positive allocations are

1. m+n
2. m*n
3. m+n-1
4. m+n+1

117 – If an opportunity cost value is used for an unused cell to test optimality, it should be

1. Equal to zero
2. Most negative number
3. Most positive number
4. Any value

118 – During an iteration while moving from one solution to the next, degeneracy may occur when

1. The closed path indicates a diagonal move
2. Two or more occupied cells are on the closed path but neither of them represents a corner of the path.
3. Two or more occupied cells on the closed path with minus sign are tied for lowest circled value
4. Either of the above

119 – The large negative opportunity cost value in an unused cell in a transportation table is chosen to improve the current solution because

1. It represents per unit cost reduction
2. It represents per unit cost improvement
3. It ensure no rim requirement violation
4. None of the above

120 – The smallest quantity is chosen at the corners of the closed path with negative sign to be assigned at unused cell because

1. It improve the total cost
2. It does not disturb rim conditions
3. It ensure feasible solution
4. All of the above

MCQ on Operations Research

121 – When total supply is equal to total demand in a transportation problem, the problem is said to be

1. Balanced
2. Unbalanced
3. Degenerate
4. None of the above

122 – Which of the following methods is used to verify the optimality of the current solution of the transportation problem

1. Least cost method
2. Vogel’s approximation method
3. Modified distribution method
4. All of the above

123 – The degeneracy in the transportation problem indicates that

1. Dummy allocation(s) needs to be added
2. The problem has no feasible solution
3. The multiple optimal solution exist
4. a & b but not c

124 – In a transportation problem, when the number of occupied routes is less than the number of rows plus the number of columns -1, we say that the solution is:

1. Unbalanced.
2. Infeasible.
3. Optimal.
4. Degenerate.

125 – The only restriction we place on the initial solution of a transportation problem is that: we must have nonzero quantities in a majority of the boxes.

1. all constraints must be satisfied.
2. demand must equal supply.
3. we must have a number (equal to the number of rows plus the number of columns minus one) of boxes which contain nonzero quantities.
4. None of the above

126 – The initial solution of a transportation problem can be obtained by applying any known method. However, the only condition is that

1. the solution be optimal
2. the rim condition are satisfied
3. the solution not be degenerate
4. all of the above

127 – The dummy source or destination in a transportation problem is added to

1. satisfy rim condition
2. prevent solution from becoming degenerate
3. ensure that total cost does not exceed a limit
4. all of the above

128 – The occurrence of degeneracy while solving a transportation problem means that

1. total supply equals total demand
2. the solution so obtained is not feasible
3. the few allocations become negative
4. none of the above

129 – An alternative optimal solution to a minimization transportation problem exists whenever opportunity cost corresponding to unused routes of transportation is:

1. positive and greater than zero
2. positive with at least one equal to zero
3. negative with at least one equal to zero
4. all of the above

130 – One disadvantage of using North-West Corner Rule to find initial solution to the transportation problem is that

1. it is complicated to use
2. it does not take into account cost of transportation
3. it leads to degenerate initial solution
4. all of the above