**Operations Research Multiple Choice Questions**

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

**Answer:** Scientific basis

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

**Answer:** Scientists, different disciplines

3. Mention two applications of OR.

**Answer:** Industry Planning

4. How can a hospital benefit from the application of OR methods?

**Answer:** To solve waiting for problems

5. OR ___ inter-disciplinary approach.

**Answer:** Imbibes

6. OR increases the effectiveness of ___ ability.

**Answer:** Decision making

7. OR gives a qualitative solution

**Answer:** True

8. One of the OR phases is the Action phase

**Answer:** True

9. Diagram belongs to the physical model

**Answer:** True

10. Allocation problems are represented by the iconic model

**Answer:** False

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

**Answer:** False

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

**Answer:** False

13. OR imbibes ___ team approach.

**Answer:** Inter-disciplinary

14. Linear programming is the tool of ___.

**Answer:** OR

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 ___.

**Answer:** Define the problem

17. ___ represents a real-life system.

**Answer:** Model

18. ___ represents the controlled variables of the system

**Answer:** Parameters

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

**Answer:** Linear

20. LPP requires existence of ___, ___, ___ and ___.

**Answer:** An alternate course of action

21. Solution of decision variables can also be ____.

**Answer:** Fractious

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

**Answer:** True

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

**Answer:** True

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

**Answer:** Feasible

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

**Answer:** Half-plan

26. The feasible region is a convex set

**Answer:** True

27. The optimum value occurs the anywhere infeasible region

**Answer:** False

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

**Answer:** False

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

**Answer:** True

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

**Answer:** True

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

**Answer:** True

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

**Answer:** Yes

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

**Answer:** Yes

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

**Answer:** No

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

**Answer:** Yes

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

**Answer:** Yes

37. Artificial variables enter as basic variables.

**Answer:** Yes

38. Dual LPP always reduces the amount of computation.

**Answer:** No

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

**Answer:** Yes

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

**Answer:** Dual

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

**Answer:** ≥

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

**Answer:** Dual

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

**Answer:** True

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

**Answer:** False

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

**Answer:** True

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

**Answer:** Final

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

**Answer:** Resource, levels

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

**Answer:** Upper, lower, bounce

49. Transportation problems are a special type of ___.

**Answer:** LPP

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

**Answer:** Equal

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

**Answer:** Minimum cost

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

**Answer:** Yes

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

**Answer:** Yes

54. Matrix-minima method gives the optimum solution.

**Answer:** No

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

**Answer:** False

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

**Answer:** True

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

**Answer:** False

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

**Answer:** True

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

**Answer:** zero

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

**Answer:** Not equal to

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.

**Answer:** True

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

**Answer:** True

64. The decision variables can take on any value.

**Answer:** False

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

**Answer:** True

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

**Answer:** True

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

**Answer:** False

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

**Answer:** ≠

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

**Answer:** Maximisation problem

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

**Answer:** Infeasible

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

**Answer:** Only once

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

Salesman

**Answer:** (n-1)

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

**Answer:** True

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

**Answer:** False

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

**Answer:** Simplex method

**Operations Research MCQs**

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

- economical
**scientific**- a and b both
- artistic

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

**mathematical models**- physical models diagrammatic
- diagrammatic models

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

- Suitable manpower
**mathematical techniques, models, and tools**- 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 —-**

- Management processes
**Decision making**- Procedures

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

- Personnel factors.
- Financial factors
**Numeric and quantifiable factors.**

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

- Formulating a problem
- Constructing a model
- Establishing controls
**Controlling the environment**

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

_______________ variables and ____________ variables.

- Positive and negative
**Controllable and uncontrollable**- Strong and weak
- None of the above

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

- Battle field
- Fighting
- The opponent
**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?**

**Morse and Kimball (1946)**- P.M.S. Blackett (1948)
- E.L. Arnoff and M.J. Netzorg
- None of the above

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

- Scientists
- Mathematicians
- Academics
**All of the above**

**MCQ on Operations Research**

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

- Conducting experiments on it
- Mathematical analysis
**Both A and B**- Diversified Techniques

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

- Policies
- Actions
**Both A and B**- None of the above

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

- Scientific Models
- Algorithms
**Mathematical Models**- 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?**

- Quailing Theory
- Waiting Line
- Both A and B
**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?**

- Programme Evaluation
- Review Technique (PERT)
**Both A and B**- Deployment of resources

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

- Man and machine

- money

- material

**all of the above**

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

**ueuing Theory**- Decision Theory
- Both A and B
- None of the above

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

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

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

**Constraints are given by inequalities of any type**- Constraints are given by a set of linear equations
- Constraints are given only by inequalities of >= type
- Constraints are given only by inequalities of <= type

**20 – Feasible solution satisfies __________**

- Only constraints
- only non-negative restriction
**[a] and [b] both**- [a],[b] and Optimum solution

**MCQ on Operations Research**

**21 – In Degenerate solution value of objective function _____________.**

- increases infinitely
- basic variables are nonzero
- decreases infinitely
**One or more basic variables are zero**

**22 – Minimize Z = ______________**

- maximize(Z)
**maximize(-Z)**- maximize(-Z)
- none of the above

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

- 2
- not more than 3
- 3
**none of the above**

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

- Solution
- basic solution
**feasible solution**- optimal

**25 -Graphical optimal value for Z can be obtained from**

**Corner points of feasible region**- Both a and c
- corner points of the solution region
- none of the above

**26 -In LPP the condition to be satisfied is**

- Constraints have to be linear
- Objective function has to be linear
- none of the above
**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.

- A triangle
- A rectangle
- An unbounded region
**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?**

- a) b, and c are independent
- a, b, and d are independent
**a and c are independent**- 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?**

**One variable is basic, three variables are non-basic**- Two variables are basic, two variables are non-basic
- Three variables are basic, one variable is non-basic
- 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.

- d(2,-5,3)
**d(-2,5,-3)**- d(2,5,3)
- d(-2,-5,-3)

**MCQ on Operations Research**

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

**payoff.**- penalty.
- reward.
- end-game strategy.

**32- Operations Research approach is?**

**multi-disciplinary**- scientific
- intuitive
- collect essential data

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

- physical model
**mathematical model**- iconic model
- descriptive model

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

**it helps in converting the verbal description and numerical data into****mathematical expression**- decision makers prefer to work with formal models
- it captures the relevant relationship among decision factors
- 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?**

- 0
- 1
**5**- 6

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

**2**- 6
- finite
- infinite

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

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

**38 – Utilization factor is also known as ___________.**

**Traffic intensity**- Kendals notation
- Row minima method
- Unbalanced assignment problem

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

- adding another constraint
- adding another variable
**removing a constraint**- removing a variable

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

**alternative solution**- bounded solution
- infeasible solution
- unbounded solution

**MCQ on Operations Research**

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

- there are multiple solutions
- there exist no solution
- solution is degenerate
**solution is unbounded**

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

- alternative
- bounded
- no solution
**infeasible**

**43 – For any primal problem and its dual ______________.**

- optimal value of objective function is same
**primal will have an optimal solution iff dual does too**- both primal and dual cannot be infeasible
- dual will have an optimal solution iff primal does too

**44 – Principle of complementary slackness states that ____________.**

**primal slack*dual main=0**- primal main+dual slack=0
- primal main+dual surplus=0
- 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 ____________.**

**finite solution**- infinite solution
- bounded solution
- 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 __________.**

- the solution be optimal
**the rim conditions are satisfied**- the solution not be degenerate
- the few allocations become negative

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

**satisfy rim conditions**- prevent solution from becoming degenerate
- ensure that total cost does not exceed a limit
- 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 ____________.**

**Modified Distribution Method**- Least Cost Method
- Vogels Approximation Method
- 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 ________.**

**rows or coloumns**- rows and coloumns
- rows+columns- 1
- rows-columns

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

- adding each entry in a column from the maximum value in that column
- subtracting each entry in a column from the maximum value in that column
**subtracting each entry in the table from the maximum value in that table**- 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 ___________.**

- n
**n-1**- 2n-1
- n-2

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

- slack
- surplus
**artificial**- dual

**53 – Simplex method was designed by ___________.**

**Dantzig**- A.Charnes
- Lemke
- Hungarian

**54 – Dual Simplex Method was introduced by ____________.**

- Dantzig
- A.Charnes
**Lemke**- Hungarian

**55 – The cell with allocation can be called ___________ .**

- Cell
- Empty cell
**Basic cell**- Non-basic cell

**56 – The cell without allocation is called __________.**

- Basic cell
**Non-basic cell**- Empty cell
- Basic solution

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

- customers behavior
**servers behavior**- customers in the system
- server in the system

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

**suddenly and gradually**- gradually
- suddenly
- neither gradually nor suddenly

**59 – Least Cost Method is also known as __________.**

- North West Corner Method
**Matrix Minima Method**- Row Minima method
- Coloumn Minima method

**MCQ on Operations Research**

**60 – The objective of network analysis is to ___________.**

**minimize total project duration**- minimize total project cost
- minimize production delays, interruption and conflicts
- 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.**

- forward pass
- backward pass
**critical**- non critical

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

- first-mover advantage.
- a Nash equilibrium strategy.
- tit-for-tat.
**a dominant strategy.**

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

**sequential game**.- repeated game.
- zero-sum game.
- nonzero-sum game.

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

- sequential game.
**repeated game**.- zero-sum game.
- nonzero-sum game.

**65 – Sequential games can be solved using**

- tit-for-tat.
- dominated strategies.
**backward induction**- 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**

- a prisoners’ dilemma.
- collusion.
**a credible threat.**- tit-for-tat.

**67 – What is the fundamental purpose of game theory?**

- To analyse decision-making
**To analyse strategic interactions**- To predict decision outcome
- To predict firm behaviour

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

- The number of rows equals columns
- All xij= 0 or 1
- All rim conditions are 1
**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**

- Rows or columns
- Rows & columns
- Rows + columns –1 d.
**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**

**Minimize total cost of assignment**- Reduce the cost of assignment to zero
- Reduce the cost of that particular assignment to zero
- All of the above

**MCQ on Operations Research**

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

- Reduced matrix method
- MODI method
**Hungarian method**- None of the above

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

**Obtain balance between total activities &total resources**- Prevent a solution from becoming degenerate
- Provide a means of representing a dummy problem
- None of the above

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

- Adding each entry in a column from the maximization value in that column
- Subtracting each entry in a column from the maximum value in that column
**Subtracting each entry in the table from the maximum value in that table**- Any one of the above

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

**n! solutions**

- (n-1)! solutions

- (n!)nsolutions

- n solutions

**75 -An assignment problem can be solved by**

- Simplex method
- Transportation method
**Both a & b**- none of above

**76 – The assignment problem**

- 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

- Number of rows equals number of columns
- All rim conditions are 1
- Values of each decision variable is either 0 or 1
**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**

- 2n+1
**2n-1**- m+n-1
- m+n

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

- n
- 2n
**n-1**- 2n-1

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

- A transportation problem
**A travelling salesman problem**- A LP problem
- Both a & b

**MCQ on Operations Research **

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

- 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?**

- 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.**

- Lower right corner of the table.
- Upper right corner of the table.
- Highest costly cell of the table.
**Upper left-hand corner of the table.**

** 84 – The table represents a solution that is:**

- 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?**

- MODI method
- northwest corner method
- stepping-stone method
**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**

**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

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

**Profit**- optimization
- cost
- None of the above

**MCQ on Operations Research**

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

- The minimal cost network flows are special cases of transportation problems
**The transportation problems are special cases of the minimal cost****network flows**- There is no difference
- 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**

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

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

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

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

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

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

- the cost of shipping one unit from each origin to each destination
- the destination points and the demand per period at each
- the origin points and the capacity or supply per period at each
**degeneracy**

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

- northwest-corner
- intuitive lowest-cost
- southeast-corner rule
**stepping-stone**

**96 – The transportation method assumes that**

- there are no economies of scale if large quantities are shipped from one source to one destination
- 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.
- there is only one optimal solution for each problem.
- 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?**

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

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

- 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.
**Only squares containing assigned shipments can be used to trace a path back to an empty square.**- An improvement index that is a net positive means that the initial solution can be improved.
- 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.**

- destinations; sources
**units supplied; units demanded**- columns; rows
- positive cost coefficients; negative cost coefficients

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

- Destinations; sources
- Units supplied; units demanded
**Dummy rows; dummy columns**- 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 __________.**

- change index
- new index
- MODI index
**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 __________.**

- stepping-stone method
**matrix reduction**- MODI method
- northwest reduction

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

- the northwest corner rule
**Vogel’s approximation**- Johanson’s theorem
- 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**- Infinity; infinity
- 0; 0
- 1000; 1000

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

**Degeneracy**- Infeasibility
- Unboundedness
- Unbalance

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

- shipping problems
- logistics problems
- generalized flow problems
**network flow problem**

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

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

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

- very high positive costs
- very high negative costs
- 10
**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**

- The solution be optimal
**The rim conditions are satisfied**- The solution not be degenerate
- All of the above

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

**Satisfy rim conditions**- Prevent solution from becoming degenerate
- Ensure that total cost does not exceed a limit
- None of the above

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

- Total supply equals total demand
**The solution so obtained is not feasible**- The few allocations become negative
- 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:**

- Positive & greater than zero
**Positive with at least one equal to zero**- Negative with at least one equal to zero
- None of the above

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

- It is complicated to use
**It does not take into account cost of transportation**- It leads to a degenerate initial solution
- 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**

- m+n
- m*n
**m+n-1**- m+n+1

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

- Equal to zero
**Most negative number**- Most positive number
- Any value

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

- The closed path indicates a diagonal move
- Two or more occupied cells are on the closed path but neither of them represents a corner of the path.
**Two or more occupied cells on the closed path with minus sign are tied****for lowest circled value**- 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**

**It represents per unit cost reduction**- It represents per unit cost improvement
- It ensure no rim requirement violation
- 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**

- It improve the total cost
- It does not disturb rim conditions
**It ensure feasible solution**- 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**

**Balanced**- Unbalanced
- Degenerate
- None of the above

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

- Least cost method
- Vogel’s approximation method
**Modified distribution method**- All of the above

**123 – The degeneracy in the transportation problem indicates that**

- Dummy allocation(s) needs to be added
- The problem has no feasible solution
**The multiple optimal solution exist**- 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:**

- Unbalanced.
- Infeasible.
- Optimal.
**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.**

**all constraints must be satisfied.**- demand must equal supply.
- we must have a number (equal to the number of rows plus the number of columns minus one) of boxes which contain nonzero quantities.
- 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**

- the solution be optimal
**the rim condition are satisfied**- the solution not be degenerate
- all of the above

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

**satisfy rim condition**- prevent solution from becoming degenerate
- ensure that total cost does not exceed a limit
- all of the above

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

- total supply equals total demand
**the solution so obtained is not feasible**- the few allocations become negative
- 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:**

- positive and greater than zero
**positive with at least one equal to zero**- negative with at least one equal to zero
- all of the above

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

- it is complicated to use
**it does not take into account cost of transportation**- it leads to degenerate initial solution
- all of the above