2019 question bank (with answers) for viva

BORA INSTITUTE OF MANAGEMENT SCIENCES
Question Bank for Viva
Quantitative Techniques in Management (KMB206)
Page 1 of 10
UNIT 1
Introduction to Operations Research
1. Define Operations Research.
Operations research can be defined as a tool employed to increase the effectiveness
of managerial decisions as an objective supplement to the subjective feeling of the
decision-maker.
2. When did operations research evolve?
Major growth in the discipline of operations research took place during World War
II
3. What is a model in OR?
A mathematical model is a quantitative tool that represents systems, processes or
environment in the form of equations.
4. Name any four models you have studied in this subject?
Any four of:
(i) Linear programming
(ii) Transportation model
(iii) Assignment model
(iv) Game theory
(v) Sequencing model
(vi) Queuing theory
(vii) Replacement problem
(viii) Project management
UNIT 2
Linear Programming Problem
5. What is the full form of LPP?
Linear Programming Problem.
6. When did linear programming originate?
Linear programming originated in the 1920s.
7. Give an application of linear programming?
LP finds its application in all areas of management for profit maximisation or cost
minimisation.
8. Name the methods for solving a linear programming problem?
The methods available for solving an LPP are:
(i) Graphical method,
(ii) Trial and error method,
(iii) Algebraic method and
(iv) Simplex method.
9. What are the two parts of a linear programming problem?
Objective function and constraints.
10. Define objective function.
The mathematical function that describes the objective of the problem is known as
the objective function.
11. Define constraint.
The underlying conditions which cannot be violated while achieving the problem’s
objective are called as constraints.

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12. What are explicit constraints?
The constraints that can be derived directly from the information given in the
problem are called the explicit constraints.
13. What are implicit constraints?
The constraints which are not directly mentioned in the problem but can be implied
from the information are the implicit constraints. They are also known as non-
negativity constraints.
14. What is the practical significance of non-negativity constraints?
Non-negativity constraints signify that in OR no variable can ever assume a negative
value.
15. What is feasible area/polygon?
The area within the solution of an LPP lies is known as the feasible area.
16. What is feasible solution?
Any possible solution in the context of an OR problem is called a feasible solution.
17. What is infeasible solution?
A solution that may be mathematically obtainable but practically impossible is known
as an infeasible solution.
18. What is optimum solution?
The best among the feasible solutions is known as the optimum solution.
19. What is unbounded solution?
If in a maximisation LPP, the feasible area is not closed from one side, it is a case of
unbounded solution.
20. On which theorem is the graphical method based?
The graphical method is based on the extreme point theorem.
21. State the extreme point theorem.
The optimum solution to an LPP lies at one of the extremities of the feasible polygon,
provided there exists a solution to the LPP which is unique, finite and optimal.
22. What are iso-profit lines?
The lines on a graph joining the points denoting same profit (or loss) are called as the
iso-profit lines.
23. What is the advantage of the graphical method?
The graphical method is the simplex of all methods of solving LPP.
24. What is the limitation of the graphical method?
The graphical method can be used to solve only two-variable LPPs.
25. Name the three exceptions to the extreme point theorem.
The three exceptions to the extreme point theorem are:
(i) Multiple optimum solutions
(ii) Unbounded solution
(iii) Infeasible solution.
26. What is the implication of multiple optimum solutions for an organisation?
The existence of multiple optimum solutions gives an organisation the flexibility to
consider qualitative factors also while addressing a problem.
27. On which theorem are the trial and error, algebraic and simplex methods based?
All these three methods are based upon the basis theorem.

Page 3 of 10
28. State the basis theorem.
If in a system of equations we have ‘m’ variables and ‘n’ constraints, m being greater
than n, then the solution obtained by putting m–n of the variables as zero results in
a corner point. The solution at the corner point is known as a Basic Solution.
29. What are structural variables?
The variables that constitute the actual structure of a problem are called the structural
variables.
30. What are non-structural variables?
The variables that do not form the actual structure of an LPP are called the non-
structural variables.
31. What is a slack variable?
The non-structural variable added to the LHS of a less than or equal to type
constraint, to convert it into an equation is known as a slack variable.
32. What is a surplus variable?
The non-structural variable subtracted from the LHS of a greater than or equal to
type constraint, to convert it into an equation is known as a surplus variable.
33. Define artificial variables.
The variables that do not have any practical significance but are just introduced to
make the problem solvable are known as the artificial variables.
34. What are basic variables?
The variables that exist in a basic solution are called as the basic variables. They
normally have a non-zero, non-negative value.
35. What are non-basic variables?
The variables that are not a part of a basic solution are known as non-basic variables.
36. What is the value of a non-basic variable?
A non-basic variable is always equal to zero.
37. What is the value of the coefficient of a slack/surplus variable?
The coefficient of a slack/surplus variable is always equal to zero.
38. What is the coefficient of an artificial variable?
The coefficient of an artificial variable is denoted by Big ‘M’ – a very big positive
quantity.
39. Give one advantage of the trial and error method.
The trial and error method can be used for solving LPPS with more than two
variables.
40. Give one disadvantage of the trial and error method.
If the number of variables is large, solving the LPP using the trial and error method
may become unmanageable.
41. Give one advantage of the algebraic method.
The algebraic method systemises the trial and error method so that solution of LPPs
with several variables becomes less cumbersome.
42. Give one disadvantage of the algebraic method.
The algebraic method is quite complex.
43. Who discovered the simplex method?
George Dantzig discovered the simplex method in 1947.

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44. What are the advantages of simplex method?
(i) Can be used to solve LPPs with more than two variables.
(ii) Is simpler than the algebraic method.
45. What is the disadvantage of simplex method?
The method is more complicated than the graphical method.
46. Name one software used for solving OR models.
TORA.
47. What is the full form of TORA?
Temporary-Ordered Routing Algorithm.
48. Name the columns in a simplex table.
(i) Coefficient of the basic variables
(ii) Basic variables
(iii) Solution variables
(iv) One column each for all the variables.
49. Name the rows in a simplex table.
(i) One row each for all the basic variables
(ii) Cj row
(iii) Zj row
(iv) Cj–Zj row.
50. What is simplex criterion 1 used for?
The simplex criterion 1 is used for identifying the incoming basic variable.
51. What is simplex criterion 2 used for?
The simplex criterion 2 is used for identifying the outgoing basic variable.
52. What is optimum column?
The column of the incoming basic variable is known as the optimum column.
53. What is replaced row?
The row of the outgoing basic variable is known as the replaced row.
54. What is the pivot element?
The element of the simplex table lying at the intersection of the optimum column and
the replaced row is known as the pivot element.
55. What is the criterion for optimum solution in case of a maximisation LPP?
In case of a maximisation LPP, if all the elements of the Cj–Zj row are either zero or
negative, it indicates that the optimum solution has been achieved.
56. What is the criterion for optimum solution in case of a minimisation LPP?
In case of a minimisation LPP, if all the elements of the Cj–Zj row are either zero or
positive, it indicates that the optimum solution has been achieved.
57. What is the Big ‘M’ method?
The Big ‘M’ method is a slight modification of the simplex method used to solve an
LPP containing artificial variable(s).
58. How can we identify the case of multiple optimal solutions from the optimum simplex table?
If the Cj–Zj row element in the column of a non-basic variable is equal to zero, it
indicates the presence of multiple optimum solutions.
59. How can we identify the case of infeasible solution from the simplex table?
If all the elements of the optimum column are negative, it is a case of infeasible
solution.

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60. How can we identify the case of unbounded solution from the simplex table?
If the criterion for optimality is satisfied and the basic solution still contains an
artificial variable, it is a case of unbounded solution.
61. What is a degenerate solution?
A degenerate solution is one in which one or more of the basic variable(s) become(s)
equal to zero.
62. What is sensitivity/post-optimality analysis?
Sensitivity analysis is aimed at analysing the effect of a change in any problem
parameter upon the optimum solution.
63. Define duality.
For every LP problem, a corresponding LPP always exists. This is called duality.
64. Give one advantage of duality.
The concept of duality can be used to simplify the process of solving an LPP.
65. Give one application of duality.
Duality can be applied for economic interpretation of the solution of an LPP.
66. If the primal is a maximisation problem, what will be the nature of the dual?
The dual of a maximisation LPP is always a minimisation LPP.
67. How do we determine the number of variables in the dual?
The number of variables in the dual is equal to the number of constraints in the
primal.
68. How do we determine the number of constraints in the dual?
The number of constraints in the dual is equal to the number of variables in the
primal.
69. How do we get the coefficient matrix of the dual constraints?
The coefficient matrix of the dual constraints is given by the transpose of the
coefficient matrix of the primal.
70. How do we get the RHS constants of dual constraints?
The RHS constants of dual constraints are given by the objective function coefficients
of the primal variables.
71. How do we get the objective function coefficients of the dual variables?
The objective function coefficients of the dual variables are equal to the RHS
constants of the dual constraints.
72. While formulating the dual, how do we deal with a primal variable that is unrestricted in sign?
If a primal variable is unrestricted in sign, the corresponding dual constraint is a strict
equality.
73. While formulating the dual, how do we deal with a constraint that is strict equality?
If a primal constraint is strict equality, the corresponding dual variable is unrestricted
in sign.
Transportation Problem
74. Which OR model has been modified to form the transportation model?
The linear programming model has been modified to form the transportation model.
75. How many occupied cells are there in a transportation problem?
The number of occupied cells is equal to m+n–1, where m is the number of rows and
n is the number of columns in the transportation problem.

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76. How can we spot degeneracy in a transportation problem?
If the number of occupied cells is less than m+n–1, it indicates degeneracy.
77. Name the methods for finding the initial solution of a transportation problem.
The methods for finding the initial solution are:
(i) North west corner rule (NWCR)
(ii) Least cost method (LCM)
(iii) Vogel’s approximation method (VAM).
78. Which is the simplest method of finding the initial solution of a transportation problem?
The north west corner rule is the simplest method of finding the initial solution of a
transportation problem.
79. Which is the best method of finding the initial solution of a transportation problem?
The Vogel’s approximation method is the best method of finding the initial solution
of a transportation problem.
80. What is the advantage of Vogel’s approximation method?
The Vogel’s approximation method often results in a solution that is optimum.
81. Name the methods for finding the optimum solution of a transportation problem?
The methods for finding the optimum solution are:
(i) Stepping stone method
(ii) Modified Distribution (MODI) method.
82. What are the rules for forming the closed loop?
The following are the rules for forming the closed loop:
(i) Starting from an unoccupied cell, move either vertically or horizontally.
(ii) Turning is allowed only on an occupied cell.
83. What does ‘MODI’ stand for in MODI Method?
The full form of MODI is Modified Distribution.
84. How do we balance an unbalanced transportation model problem?
A dummy row (or column) is used to balance an unbalanced transportation problem.
85. How do we convert a maximisation transportation problem into a minimisation problem?
In order to convert a maximisation transportation problem into a minimisation one,
we take the maximum profit element and subtract all other profit elements from it
and replace the original values with the difference.
86. How do we deal with prohibited and preferred routes in transportation?
The cost of a prohibited route is replaced with Big ‘M’ and the cost of preferred routs
is replaced with zero before solving the transportation problem.
87. What is a transhipment problem?
A transhipment problem is a special case of transportation problem where each
demand/supply point can act as a potential intermediate supply/demand point.
88. Give one additional application of transportation model.
Transportation model finds its application in the area of production scheduling.
UNIT 3
Assignment Model
89. Which OR model has been modified to form the assignment model?
The transportation model has been modified to form the assignment model.

Page 7 of 10
90. Name the two methods used for solving an assignment problem.
The two methods for solving an assignment problem are:
(i) The Hungarian method
(ii) The Branch and Bound method.
91. How do we balance an unbalanced assignment problem?
A dummy row (or column) is used to balance an unbalanced assignment problem.
92. How do we convert a maximisation assignment problem into a minimisation problem?
In order to convert a maximisation assignment problem into a minimisation one, we
take the maximum profit element and subtract all other profit elements from it and
replace the original values with the difference.
93. Give one application of the assignment model.
Assignment model is used to assign jobs to workers/machines.
Game Theory
94. Give any two underlying assumptions of a game.
Any two of the following:
(i) The number of participants is finite.
(ii) Each participant has a finite number of strategies available.
(iii) Each player knows the strategies available to the adversary, but he does not
know which strategy will the adversary adopt.
(iv) All possible outcomes are calculable.
(v) All players are rational. They play to win.
95. What is a zero-sum game?
A game where the sum of the winnings and losses of all the players is equal to zero,
is known as a zero-sum game.
96. What is a non-zero-sum game?
A game where the sum of the winnings and losses of all the players is not equal to
zero, is known as a zero-sum game.
97. What is a two-player game?
A game played between exactly two opponents is called a two-player game.
98. What is an n-player game?
A game involving more than two players is known as an n-player game.
99. What is a two-player, zero-sum game?
A game involving exactly two players, where the sum of the gain and loss of the
players is equal to zero, is known as a two-player, zero sum game.
100. What is a payoff element?
The element of a game that denotes the numerical outcome for the competing players
when they each adopt a particular strategy, is called the payoff element.
101. What is a payoff matrix?
The matrix consisting of all the possible payoff elements for all the combinations of
strategies that can be adopted by the two players, is known as the payoff matrix.
102. What does a positive payoff element signify?
A positive payoff element signifies a profit for row player and an equivalent loss for
the column player.

Page 8 of 10
103. What does a negative payoff element signify?
A negative payoff element signifies a loss for row player and an equivalent profit for
the column player.
104. What does a payoff element with value ‘zero’ signify?
If the value of a payoff element is zero, it signifies no profit and no loss situation for
both players.
105. Explain maximin strategy.
The maximin strategy is assumed to be adopted by the row player where he chooses
the maximum of the minimum payoff elements from each row.
106. Explain minimax strategy.
The minimax strategy is assumed to be adopted by the column player where he
chooses the minimum of the maximum payoff elements from each column.
107. What is saddle point?
If a payoff element is simultaneously the minimax as well as the maximin element, it
is known as the saddle point. The saddle point gives V, the value of the game.
108. What is a pure strategy game?
A pure strategy game is a game where saddle point exists.
109. What is a mixed strategy game?
A mixed strategy game is a game where the saddle point does not exist.
110. State the principle of dominance.
(i) If all the elements in the ith row are less than or equal to the corresponding
elements of the jth row, then the ith strategy is said to be dominated by the jth
strategy.
(ii) If all the elements in the rth column are greater than or equal to the
corresponding elements of the sth column, then the rth strategy is said to be
dominated by the sth strategy.
111. Name the methods for solving 2×2 mixed strategy games.
The methods for solving 2×2 mixed strategy games are:
(i) The algebraic method
(ii) The odds method.
112. Which method is used for solving 2×n or m×2 games, where m, n > 2?
The graphical method is used for solving 2×n or m×2 games, where m, n > 2.
113. Which method is used for solving m×n, where m, n > 2?
The LP approach is used for solving m×n, where m, n > 2.
114. Give one application of game theory.
Game theory is used for determining the possible outcomes of a competitive
situation.
Unit 4
Sequencing Problem
115. Name the algorithm used for solving a sequencing model problem.
The Johnson’s algorithm is used for solving a sequencing model problem.

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116. Which condition(s) must be satisfied while solving n-job, m-machine sequencing problems, where
m>2?
For the Johnson’s algorithm to be applicable on a “more than two-machine
sequencing problem,” at least one of the following two conditions must be fulfilled:
(i) Minimum time value on the first machine should be greater than or equal to the
maximum time value on all the intermediate machines, combined, or
(ii) Minimum time value on the last machine should be greater than or equal to the
maximum time value on all the intermediate machines, combined.
117. Give one application of sequencing model.
The sequencing model is used for finding the optimum sequence for performing jobs
(and the corresponding optimum time required), when several jobs have to be
performed on a few machines.
Queuing Theory
118. List the characteristics of M/M/I/∞/FIFO queuing model.
The characteristics of M/M/I/∞/FIFO queuing model are as follows:
(i) The arrival pattern follows the Poisson distribution.
(ii) The service rate follows the exponential distribution.
(iii) Number of servers is one.
(iv) The capacity of the system is infinite.
(v) The queue discipline is FIFO (first-in, first-out).
119. What does λ denote in queuing theory?
λ denotes the arrival rate.
120. What does μ denote in queuing theory?
μ denotes the service rate.
121. What is traffic density?
In queuing theory, traffic density is given by λ/μ.
Unit 5
Project Management
122. Give one characteristic of a project.
Any one of the following:
(i) Unique.
(ii) Non-repetitive.
(iii) Requires huge resources.
(iv) Requires large capital.
(v) Requires large manpower.
(vi) Requires great effort.
(vii) Requires long time.
(viii) Requires detailed planning.
123. Define activity.
The operations or tasks into which a project is divided are known as activities. An
activity is represented by an arrow or arc in a network diagram.
124. Define event.
An event is a specific accomplishment in a project. It takes place at a particular instant
of time and does not consume any time or resource. An event is represented by a
node in a network diagram.

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125. What is a predecessor activity?
An activity that must be completed immediately prior to the start of another activity
is known as its predecessor activity.
126. What is a successor activity?
An activity that cannot be started until one or more of the other activities are
completed is known as the successor activity.
127. What are concurrent activities?
Activities that can be accomplished simultaneously are known as concurrent activities.
128. What is a merge event?
An event at which more than one activities end is known as a merge event.
129. What is a burst event?
An event from which more than one activities start is known as a burst event.
130. What is a merge and burst event?
An event at which more than one activities end, and from which more than one
activities start, is known as a merge and burst event.
131. What is a dummy activity?
A dummy activity is a fictitious activity used to fulfil some specific purpose in a
network. It does not consume any time or resource.
132. Explain Fulkerson’s rule.
The Fulkerson’s rule, used for node numbering in a network diagram, is as follows:
(i) Identify all nodes that have no incoming activities and number them in any
order.
(ii) Erase all the outgoing activities from all the numbered nodes.
(iii) Repeat the above two steps till all the nodes are numbered.
133. What is dangling error?
In a network diagram, a dangling error is said to have occurred when more than one
node does not have any outgoing activity.
134. What is looping error?
A looping error is encountered if, during the flow of activities, we cross the same part
of the network diagram more than once.
135. What is redundancy error?
If an activity (mostly a dummy) is used unnecessarily in a network, it indicates
redundancy error.
136. What is the full form of PERT?
The full form of PERT is Programme Evaluation and Review Technique.
137. What is the full form of CPM?
The full form of CPM is Critical Path Method.
138. Define critical path.
The critical path of a project involves those activities, which, if delayed, will result in
the entire project getting delayed.

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2019 question bank (with answers) for viva