Optimization Techniques MCQ Part-1

1. Operations Research approach is _______.

[A] multi-disciplinary

[B] scientific

[C] intuitive

[D] collect essential data

2. A feasible solution to a linear programming problem _____.

[A] must satisfy all the constraints of the problem simultaneously

[B] need not satisfy all of the constraints, only some of them

[C] must be a corner point of the feasible region.

[D] must optimize the value of the objective function

3. If an artificial variable is present in the basic variable column of

optimal simplex table, then the solution is___________.

[A] alternative

[B] bounded

[C] no solution

[D] infeasible

4. In the optimal simplex table, Zj-Cj=0 value indicates

_____________.

[A] alternative solution

[B] bounded solution

[C] infeasible solution

[D] unbounded solution

5. Principle of complementary slackness states that____________.

[A] primal slack * dual main =0.

[B] primal main + dual slack=0

[C] primal main + dual surplus=0

[D] dual slack * primal main not equal to zero

6. The initial solution of a transportation problem can be obtained

by applying any known method. How-ever, the only condition is
that__________

[A] the solution be optimal

[B] the rim conditions are satisfied

[C] the solution not be degenerate

[D] the few allocations become negative

7. The calculations of opportunity cost in the MODI method is

analogous to a_____.

[A] Zj-Cj value for non-basic variable column in the simplex

method.

[B] value of a variable in XB-column of the simplex method.

[C] variable in the B-column in the simplex method.

[D] Zj-Cj value for basic variable column in the simplex method.
8. For a salesman who has to visit n cities, following are the ways of
his tour plan___.

[A] n!

[B] n

[C] (n+a)!

[D] (n-a)!

9. Simplex method was designed by ___________.

[A] Dantzig

[B] A.Charnes

[C] Lemke

[D] Hungarian

10. Dual Simplex Method was introduced by _______.

[A] Dantzig

[B] A.Charnes

[C] Lemke

[D] Hungarian

11. The cell with allocation can be called____

[A] Cell

[B] Empty cell

[C] Basic cell

[D] Non-basic cell

12. The cell without allocation is called_________.

[A] Basic cell

[B] Non-basic cell

[C] Empty cell

[D] Basic solution

13. The problem of replacement is felt when job performing units

fail_____.

[A] suddenly and gradually

[B] gradually

[C] suddenly

[D] neither gradually nor suddenly

14. Least Cost Method is also known as__________.

[A] North West Corner Method

[B] Matrix Minima Method

[C] Row Minima method

[D] Coloumn Minima method

15. A activity in a network diagram is said to be __________ if the

delay in its start will further delay the project completion time.

[A] forward pass

[B] backward pass

[C] critical

[D] non critical

16. The activity which can be delayed without affecting the
execution of the immediate succeeding activity is determined
by_________.

[A] total float

[B] free float

[C] independent float

[D] variance of each float

17. In a transportation problem the number of origins must be

_______the number of destinations.

[A] less than or equal to

[B] greater than or equal to

[C] equal to

[D] less than

18. The calling population is considered to be infinite when

________.

[A] all customers arrive at once

[B] capacity of the system is infinite

[C] service rate is faster than arrival rate

[D] arrivals are independent of each other

19. The minimum number of lines covering all zeros in a reduced
cost matrix of order n can be _____.

[A] at the most n

[B] at the least n

[C] n-1

[D] n+1

20. The Hungarian method was designed by __________.

[A] Dantzig

[B] A.Charnes

[C] Lemke

[D] Khun and Flood

21. A________can have more than one critical path.

[A] network

[B] customer

[C] server

[D] assignment problem

22. Game theory was first coined by ______.

[A] A.Charnes

[B] Khun and Flood

[C] Hungarian

[D] Von Neuman

23. _____________is used to reduce the game.

[A] Transportation Problem

[B] Assignment Problem

[C] Dual simplex method

[D] Graphical Method

24. _____is a mathematical technique used to solve the problem of

allocating limited resource among the competing activities

[A] Linear Programming problem

[B] Assignment Problem

[C] Replacement Problem

[D] Non linear Programming Problem

25. Traveling salesman problem will have a total of _____different

sequences.

[A] n!

[B] n-1

[C] (n-a)!.

[D] n

26. If there exists a saddle point for a given problem it, implies that
the players are using ______strategies.

[A] Pure

[B] Mixed

[C] Optimal

[D] Pure and Mixed

27. FCFS refers to _______in queueing theory.

[A] First Come First Serve

[B] Last In First Out

[C] Service In Random Order

[D] Fastest Server Rule

28. SIRO refers to _______in queueing theory.

[A] First In First Out

[B] Last In First Out

[C] Service In Random Order

[D] Fastest Server Rule

29. If a customers decides not to enter the queue since it is too

long is called_________.

[A] balking

[B] reneging

[C] jockeying

[D] queue

30. When there are two or more parallel queues and customer
move from one queue to another queue it is called___________

[A] balking

[B] reneging

[C] jockeying

[D] system capacity

31. If the operating characteristic vary within time is called_____.

[A] balking

[B] reneging

[C] transient state

[D] steady state

32. The __________ time for an activity can be reduced by using

increased resources.

[A] normal

[B] optimistic

[C] pessimistic

[D] most likely

33. Graphical method of linear programming is useful when the

number of decision variable are _______

[A] 2

[B] 3

[C] 4

[D] 1

34. The activity cost corresponding to the crash time is called the
_____.

[A] critical time

[B] normal time

[C] cost slope

[D] crash cost

35. In the network, only one activity may connect any _______
nodes

[A] 1

[B] 2

[C] 3

[D] 4

36. If the constraint of an LPP has an in equation of less than or

equal to type, the variables to be added are __________.

[A] slack

[B] surplus

[C] artificial

[D] decision

37. A feasible solution of an LPP that optimizes then the objective

function is called _________

[A] basic feasible solution

[B] optimum solution

[C] feasible solution

[D] solution

38. The cost of a slack variable is _________.

[A] 0

[B] 1

[C] 2

[D] -1
39. The cost of a surplus variable is _________

[A] 0

[B] 1

[C] 2

[D] -1

40. In an LPP functions to be maximized or minimized are called

___________.

[A] constraints

[B] objective function

[C] basic solution

[D] feasible solution

41. LPP that can be solved by graphical method has______.

[A] linear constraints

[B] quadratic constraints

[C] non linear constraints

[D] bi-quadratic constraints

42. If the primal problem has n constraints and m variables then

the number of constraints in the dual problem is __________.

[A] mn

[B] m+n

[C] m-n

[D] m/n
43. The area bounded by all the given constraints is called
_____________.

[A] feasible region

[B] basic solution

[C] non feasible region

[D] optimum basic feasible solution

44. The non basic variables are called ___________.

[A] shadow cost

[B] opportunity cost

[C] slack variable

[D] surplus variable

45. If the given Linear Programming Problem is in its standard form

then primal-dual pair is _______

[A] symmetric

[B] unsymmetric

[C] slack

[D] square

46. The dual of the dual is ____________.

[A] dual-primal

[B] primal-dual

[C] dual

[D] primal
47. All the basis for a transportation problem is ____________.

[A] square

[B] rectangle

[C] triangle

[D] polygon

48. Solution of a Linear Programming Problem when permitted to

be infinitely large is called _______

[A] unbounded

[B] bounded

[C] optimum solution

[D] no solution

49. When the total demand is not equal to supply then it is said to
be __________.

[A] balanced

[B] unbalanced

[C] maximization

[D] minimization

50. In the transportation table, empty cells will be called

___________.

[A] occupied

[B] unoccupied

[C] basic

[D] non-basic
51. Closed loops may be ____________ in shape

[A] square

[B] square

[C] triangle

[D] diagonal

52. For finding an optimum solution in transportation problem

____________ method is used.

[A] MODI

[B] Hungarian

[C] Graphical

[D] simplex

53. The assignment algorithm was developed by ____________.

[A] MODI

[B] HUNGARIAN

[C] HUHN

[D] VOGELS

54. An assignment problem is a particular case of ____________.

[A] linear programming problem

[B] transportation problem

[C] replacement problem

[D] network problme

55. The coefficient of slack\surplus variables in the objective
function are always assumed to be ______.

[A] 0

[B] 1

[C] M

[D] -M

56. If there is no non-negative replacement ratio in a sllution which

is sought to be improved, then the solution is ________.

[A] bounded

[B] unbounded

[C] basic solution

[D] non-basic solution

57. The process that performs the services to the customer is

known as ___________.

[A] queue

[B] service channel

[C] customers

[D] server

59. If the kth constraint of the primal problem is equality, then the
corresponding dual variable yk is _______.

(a) unrestricted in sign

(b) restricted in sign

(c) nothing can be said

(d) none of the above.

60. The method used to solve LPP without artificial variables is
called the _ ____ method.

(a) Simplex method

(b) Dual Simplex method

(c) artificial variable method.

(d) none of the above

61. An assignment problem represents a transportation problem

with all demands and supplies equal to _________.

(a) 1

(b)greater than 1

(c) some values greater than 1

(d)all of the above.

62. Degeneracy in a m X n transportation problem occurs when the

number of occupied cells is less than ______.

(a) m+n

(b) m+n+1

(c) m+n-1

(d) m—n+1
63.The formula for free float is ________.

(a) Total float – slack of tail event

(b) Total float – LFT of head event

(c) Total float – EFT of head event

(d) Total float – Slack of head event.

64. If all paths of a network are critical paths then the project
duration cannot be reduced further.

(a) true

(b) false

(c) nothing can be said

(d) none of the above

65. In pure integer programming problems, the optimum values

are ______

(a) all values are integers

(b) All values are either zero or one

(c) Some are non integer values

(d) all are not integers.

66. In mixed integer programming problems, the optimum values
are ______

(a) all values are integers

(b) All values are either zero or one

(c) Some are non integer values

(d) all are not integers.

67. Geometrically the branching process in branch and bound

technique

(a) eliminates that portion of the non-feasible region.

(b) does not eliminate that portion of the feasible region that
contains no feasible Integer solution.

(c) eliminate that portion of the feasible region that contains no

feasible integer solution.

(d) none of the above

68. Economic order quantity results in

(a) Reduced stock outs

(b) equalization of carrying cost and procurement cost

(c) favourable procurement price

(d) none of the above.

69. Minimum inventory equals

(a) EOQ

(b) Reorder level

(c) Safety stock

(d)Excess stock

70. (M/M/1) model is known as

(a) Poisson model

(b) Birth death model

(c) Exponential model

(d) multiserver model.

71. The time interval between consecutive arrivals generally

follows ___ distribution.

(a) Normal distribution

(b) Poisson distribution

(c) Exponential Distribution

(d)Rectangular distribution

72. The non basic variables are called ___________.

A. shadow cost

B. opportunity cost

C. slack variable

D. surplus variable
73. The method used to solve Linear Programming Problem
without use of the artificial variable is called __________.

A. Simplex Method

B. Big-M Method

C. Dual Simplex Method

D. Graphical Mehtod

74. All the basis for a transportation problem is ____________.

A. square

B. rectangle

C. triangle

D. polygon

75. The solution to a transportation problem with m-sources and n-

destinations is feasible if the numbers of allocations are
___________.

A. m+n

B. mn

C. m-n

D. m+n-1
 Optimization Techniques MCQ Questions Part-2

(Linear Programming)
1.In an Linear programming problem, the restrictions or limitations under which the
objective

function is to be optimised are called

1. Constraints

2. Objective function

3. More than one of the above.

4. None of the above

2.Which of the following methods is commonly used to solve assignment problems?

1. Stepping stone method

2. Hungarian method

3. North - west corner method

4. Vogel's approximation method

3.In a transportation problem with 4 supply points and 5 demand points, how many
number

of constraints are required in its formulation?

1. 20

2. 1

3. 0

4. 9
4.Important Points to remember:-

Number of constraints = m + n

Number of variables = m × n

Number of equations = m + n – 1

5.If the ith constraint of a primal (maximisation) is equality, then the dual
(minimisation)

variable ‘yi’ is:

1. ≥ 0

2. ≤ 0

3. Unrestricted in sign

4. None of the above

6.Vogel’s approximation method is connected with

1. Assignment problem

2. Inventory problem

3 Transportation problem

4. PERT
7.In the Simplex method if in pivot column all the entries are negative or zero when
choosing

leaving variable then

1. Solution is Degenerate

2. Solution is infeasible

3. Alternative optima

4. Unbounded

8: Region represented by x ≥ 0, y ≥ 0 is:

A. first quadrant

B. second quadrant

C. third quadrant

D. fourth quadrant

9: The objective function of a linear programming problem is:

A. a constraint

B. function to be optimised

C. A relation between the variables

D. None of these
10: The linear inequalities or equations or restrictions on the variables of a linear
programming problem are called:

A. a constraint

B. Decision variables

C. Objective function

D. None of the above

11: A set of values of decision variables that satisfies the linear constraints and non-
negativity conditions of an L.P.P. is called its:

A. Unbounded solution

B. Optimum solution

C. Feasible solution

D. None of these

12: The maximum value of Z = 3x + 4y subjected to constraints x + y ≤ 4, x ≥ 0 and y ≥

0 is:

A. 12

B. 14

C. 16

D. None of the above

13: The optimal value of the objective function is attained at the points:

A. on X-axis

B. on Y-axis

C. corner points of the feasible region

D. none of these

14: Which of the following is a type of Linear programming problem?

A. Manufacturing problem

B. Diet problem

C. Transportation problems

D. All of the above

15. Objective function of an LP problem is

(a) a constant
(b) a function to be optimized
(c) an inequality
(d) a quadratic equation

16. The optimal value of the objective function is attained at the points
(a) given by intersection of lines representing inequations with axes only
(b) given by intersection of lines representing inequations with X-axis only
(c) given by corner points of the feasible region
(d) at the origin
17. Which of the following statements is correct ?
(a) Every LP problem has at least one optimal solution.
(b) Every LP problem has a unique solution.
(c) If an LP problem has two optimal solutions, then it has infinitely many solutions.
(d) If a feasible region is unbounded then LP problem has no solution

18 For the LP problem Minimize z = 2x + 3y the coordinates of the

corner points of the bounded feasible region are
A(3, 3), B(20,3), C(20, 10), D(18, 12) and E(12, 12). The minimum value of z is
(a) 49
(b) 15
(c) 10
(d) 05

19 For the LP problem maximize z = 2x + 3y The coordinates of the

corner points of the bounded feasible region are
A(3, 3), B(20,3), C(20, 10), D(18, 12) and E(12, 12). The minimum value of z is
(a) 72
(b) 80
(c) 82
(d) 70

20 The corners points of the feasible region determined by the system of

linear constraints are (0, 10), (5, 5) (15, 15), (0, 20). Let z= px + qy,
where p, q > 0.Condition on p and q so that the maximum of z occurs at
both the points (15, 15) and (0, 20) is _____
(a) p = q
(b) p =2q
(c) q = 2p
(d) q = 3p
21. Solution of following LP problem Minimize z =-3x + 2y subject
to 0 ≤ x ≤ 4, 1 ≤ x ≤ 6, x + y ≤ 5 is
(a) -10
(b) 0
(c) 2
(d) 10

22. The corner points of the feasible region determined by the system of
linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Suppose z = px + 3y,
where p > 0. If the maximum of z occurs at both the points (15, 15) and (0, 20), then p = _____ .
(a) 4
(b) 5
(c) 1
(d) 2

23. The position of points O (0, 0) and P (2, -3) in the region of graph of
inequation 2x - 3y < 5 will be _____ .
(a) O inside and P outside
(b) O and P both inside
(c) O and P both outside
(d) O outside and P inside

24.The mathematical model of an LP problem is important because

(a) it helps in converting the verbal description and numerical data into mathematical expression
(b) decision-makers prefer to work with formal models
(c) it captures the relevant relationship among decision factors
(d) it enables the use of algebraic technique
25.Linear programming is a

(a) constrained optimization technique

(b) technique for economic allocation of limited resources
(c) mathematical technique
(d) all of these

26.A constraint in an LP model restricts

(a)value of the objective function

(b)value of a decision variable
(c)use of the available resource
(d)all of these

27.The distinguishing feature of an LP mode is

(a) relationship among all variables is linear

(b) it has single objective function and constraints
(c) value of decision variables is non-negative
(d) all of the above

28.Every mathematical model

(a) must be deterministic

(b) represents data in numerical form
(c) all of these
(d) requires computer aid for its solution
29.A physical model is example of

(a) an iconic model

(b) an analogue model
(c) a verbal model
(d) a mathematical model

30.An optimization model

(a) provides the best decision

(b) provides a decision within its limited context
(c) helps in evaluating various alternatives
(d) all of these

31.The quantitative approach to decision analysis is a

(a) logical approach

(b) rational approach
(c) scientific approach
(d) all of these

32.Operations research practitioners do not

(a) take responsibility for the solution implementation

(b) collect essential data
(c) predict future actions/operations
(d) build more than one model
33.OR approach is typically based on the use of

(a) Physical model

(b) Mathematical model
(c) Iconic model
(d) Descriptive model

34.The mathematical model of an LP problem is important because

(a) it helps in converting the verbal description and numerical data into a mathematical expression
(b) decision-makers prefer to work with formal models
(c) it captures the relevant relationship among decision factors
(d) it enables the use of algebraic technique

35.Operations Research is the outcome of

(a) National emergency Combined efforts of talents of all fields Economics and Engineering
(b) Political problems
(c) Combined efforts of talents of all fields
(d) Economics and Engineering

36.The name of the subject Operations Research is due to the fact that

(a) Problems can be solved by the war approach

(b) The researchers do the operations
(c) The war problems are generally known as operations and inventing
a new way of solving such problems
(d) Mathematical operations are used in solving the problems
37.The person who coined the name Operations Research is:

(a) Bellman
(b) Newman
(c) McClosky and Trefrhen
(d) None of these

38.The objective of Operations Research is:

(a) To find new methods of solving Problems

(b) To derive formulas
(c) Optimal utilization of existing resources
(d) To utilize the services of scientists.

39.The first step in solving Operations Research problem is

(a) Model building

(b) Obtain alternate solutions
(c) Obtain basic feasible solutions,
(d) Formulation of the problem.

40.The model, which gives physical or visual representation of the problem,

is

(a) Analogue model,

(b) Static model,
(c) Iconic model,
(d) Symbolic model
41.A wide class of allocation models can be solved by a mathematical technique known as:

(a) Classical model,

(b) Mathematical Model,
(c) Descriptive model,
(d) Linear Programming model.

42.One of the properties of Linear Programming Model is

(a)It will not have constraints,

(b)It should be easy to solve,
(c)It must be able to adapt to solve any type of problem,
(d)The relationship between problem variables and constraints must be linear.

43.One of the properties of the Linear Programming Model is

(a) It will not have constraints,

(b) It should be easy to solve,
(c) It must be able to adapt to solve any type of problem,
(d) The relationship between problem variables and constraints must be linear.

44.The slack variables indicate

(a) Excess resource available

(b) Shortage of resource available
(c) Nil resources
(d) Idle resource.
45.In the graphical solution of solving Linear Programming problem to
convert inequalities into equations, we

(a) Use Slack variables

(b) Use Surplus variables,
(c) Use Artificial surplus variables
(d) Simply assume them to be equations

46.To transfer the key row in simplex table we have to

(a) Add the elements of the key row to the key number
(b) Subtract the elements of a key row from topmost no key row
(c) Divide the elements of the key row by the key number
(d) None of these

47.When all the elements of replacement ratio column are equal, the
situation is known as

(a) Tie,
(b) Degeneracy
(c) Break
(d) None of these
 Optimization Techniques MCQs

(Queuing Theory)
1.Customer behavior in which the customer moves from one the queue to
another in a multiple channel situation is

(a) balking
(b) reneging
(c) jockeying
(d) alternating

2.Which of the following characteristics apply to the queuing system

(a) customer population

(b) arrival process
(c) both (a) & (b)
(d) neither (a) nor (b)

3.Which of the following is not a key operating characteristic for a queuing

system

(a) utilization factor

(b) percent idle time
(c) average time spent waiting in the system and queue
(d) none of the above

4.Priority queue discipline may be classified as

(a) finite or infinite

(b) limited and unlimited
(c) pre-emptive or non-pre-emptive
(d) all of the above
5.Which symbol describes the interarrival time distribution

(a) D
(b) M
(c) G
(d) all of the above

6.The calling population is assumed to be infinite when

(a) arrivals are independent of each other

(b) the capacity of the system is infinite
(c) sen/ice rate is faster than the arrival rate
(d) all of the above

7.Which of the cost estimates and performance measures are not used for
economic analysis of a queuing system

(a) cost per server per unit of time

(b) cost per unit of time for a customer waiting in the system
(c) the average number of customers in the system
(d) average waiting time of customers in the system

8.The cost of providing service in a queuing system decreases with

(a) decreased average waiting time in the queue

(b) decreased arrival rate
(c) increased arrival rate
(d) none of the above
9.Service mechanism in a queuing system is characterized by

(a) server’s behavior

(b) customer’s behavior
(c) customers in the system
(d) all of the above

10. Which of the following relationships is not true

(a) 𝑤𝑠 = 𝑤𝑞 + 1
𝜇

(b) 𝐿𝑠 = 𝜆𝑤𝑠
(c) 𝐿𝑠 = 𝐿𝑞 + 1
𝜆
(d) 𝐿𝑞 = 𝜆𝑤𝑠

11. The expected length of the non-empty queue is given by

(a) 𝐿 = 𝜇/(𝜇 − 𝜆)
(b) 𝐿 = 𝑠𝜇/(𝑠𝜇 − 𝜆)
(c) 𝐿 = 𝜆/(𝜇 − 𝜆)
(d) 𝜆/(𝜇 − 𝜆) + (1 )
𝜇

12. The potential loss of customers is given by

(a) 𝑃 = 1 𝜆
𝑠 [ ] 𝑃0
𝑠! 𝑠𝜇

(b) 𝑃 = 1 [ 𝜆 ] 𝑃
𝑠 𝑛! 𝜇 0

(c) 𝑃 = 1 [ 𝜆 ]𝑠 𝑃
𝑠 𝑠! 𝜇 0

(d) none of the above

13. Expected waiting time of a customer in the system is

(a) 𝑊𝑞 = 𝐿𝑞 /𝜆𝑒𝑓𝑓
(b) 𝑊𝑞 = 𝐿𝑠 /𝜆𝑒𝑓𝑓
(c) 𝑊 = 𝐿 − ( 1 )
𝑞 𝑠 𝜇

(d) 𝑊𝑞 = 𝐿𝑞 + (𝜆𝑒𝑓𝑓 /𝜇)

14. As per queue discipline, the following is not a negative behavior of a

customer:

(a) Balking
(b) Reneging
(c) Boarding
(d) Collusion.

15. The expediting or follow up function in production control is an example

of

(a) LIFO
(b) FIFO
(c) SIRO
(d) Preemptive
16. In M/M/S: N/FIFO the following does not apply

(a) Poisson arrival

(b) Limited service
(c) Exponential service
(d) Single server

17. The dead bodies coming to a burial ground is an example of

(a) Pure Birth Process

(b) Pure death Process
(c) Birth and Death Process
(d) Constant rate of arrival

18. The system of loading and unloading of goods usually follows:

(a) LIFO
(b) FIFO
(c) SIRO
(d) SBP

19. A steady-state exist in a queue if:

(a) 𝜆 > 𝜇
(b) 𝜆 < 𝜇
(c) 𝜆 ≥ 𝜇
(d) 𝜆 ≤ 𝜇
20. If the operating characteristics of a queue are dependent on time, then
is said to be:

(a) Transient state

(b) Busy state
(c) Steady-state
(d) Explosive state

21. A person who leaves the queue by losing his patience to wait is said to
be

(a) Reneging
(b) Balking
(c) Jockeying
(d) Collusion.

22. The characteristics of a queuing model are independent of

(a) Number of service stations

(b) Limit of the length of the queue
(c) Service Pattern
(d) Queue discipline
23. The unit of traffic intensity is:

(a) Poisson
(b) Markow
(c) Erlang
(d) Kendall

24. The queue discipline in stack of plates is:

(a) LIFO
(b) SIRO
(c) Non-Pre-Emptive
(d) FIFO

25. Office filing system follows:

(a) LIFO
(b) FIFO
(c) SIRO
(d) SBP

26. SIRO discipline is generally found in:

(a) Loading and unloading

(b) Office filing
(c) Lottery draw
(d) Train arrivals at a platform
27. The designation of Poisson arrival, Exponential service, single server, and
limited queue selected randomly is represented by:

(a) (𝑀/𝐸/𝑆): (∞/𝑆𝐼𝑅𝑂)

(b) (𝑀/𝑀/1): (∞/𝑆𝐼𝑅𝑂)
(c) (𝑀/𝑀/𝑆): (𝑁/𝑆𝐼𝑅𝑂)
(d) (𝑀/𝑀/1): (𝑁/𝑆𝐼𝑅𝑂)

𝜆
28. For a simple queue (𝑀/𝑀/1), 𝜌 = is known as
𝜇

(a) Poisson busy period

(b) Random factor
(c) Traffic intensity
(d) Exponential service factor

29. When a doctor attends to an emergency case leaving his regular service
is called:

(a) Reneging
(b) Balking
(c) Pre-emptive queue discipline
(d) Non-Pre-Emptive queue discipline
30. A service system, where the customer is stationary and server is moving
is found with:

(a) Buffet Meals

(b) Outpatient at a clinic
(c) A person attending the breakdowns of heavy machines
(d) Vehicle at Petrol bunk.
Optimization Techniques MCQ Part-4

1. SIRO discipline is generally found in:

(a) Loading and unloading

(b) Office filing
(c) Lottery draw
(d) Train arrivals at a platform

2. The designation of Poisson arrival, Exponential service, single

server, and limited queue selected randomly is represented by:

(a) (𝑀/𝐸/𝑆): (∞/𝑆𝐼𝑅𝑂)

(b) (𝑀/𝑀/1): (∞/𝑆𝐼𝑅𝑂)
(c) (𝑀/𝑀/𝑆): (𝑁/𝑆𝐼𝑅𝑂)
(d) (𝑀/𝑀/1): (𝑁/𝑆𝐼𝑅𝑂)

𝜆
3. For a simple queue (𝑀/𝑀/1), 𝜌 = 𝜇 is known as

(a) Poisson busy period

(b) Random factor
(c) Traffic intensity
(d) Exponential service factor
4. When a doctor attends to an emergency case leaving his
regular service is called:

(a) Reneging
(b) Balking
(c) Pre-emptive queue discipline
(d) Non-Pre-Emptive queue discipline

5. A service system, where the customer is stationary and server is

moving is found with:

(a) Buffet Meals

(b) Outpatient at a clinic
(c) A person attending the breakdowns of heavy machines
(d) Vehicle at Petrol bunk.

6.This department is responsible for the development of queuing

theory:

(a) Railway station

(b) Municipal office
(c) Telephone department
(d) Health department
7.If the number of arrivals during a given time period is independent of the
number of arrivals that has already occurred prior to the beginning of the
time interval, then the new arrivals follow the -----------distribution.

(a) Erlang
(b) Poisson
(c) Exponential
(d) Normal

8.Arrival →Service →Service →Service →Out → The given

sequence represents:

(a) Single Channel Single Phase system

(b) Multi-channel single-phase system
(c) Single-channel multi-phase system
(d) Multi-channel multi-phase system.

9.When the operating characteristics of the queue system

dependent on time, then it is said to be:

(a) Steady-state
(b) Explosive state
(c) Transient state
(d) Anyone of the above
10.The distribution of arrivals in a queuing system can be
considered as a:

(a) Death Process

(b) Pure Birth Process
(c) Pure live process
(d) Sick process

11.Queuing models measure the effect of:

(a) Random arrivals

(b) Random service
(c) Effect of uncertainty on the behavior of the queuing system
(d) Length of queue

12.Traffic intensity is given by

(a) Mean arrival rate/Mean service rate

(b) 𝜆 × 𝜇
(c) 𝜇
𝜆
(d) Number present in the queue / Number served
13.The variance of queue length is:

(a) 𝜌 = 𝜆
𝜇

(b) 𝜌2
1−𝜌

(c) 𝜆
𝜇−𝜆
𝜌
(d)
(1−𝜌)2

14.In queue designation A/B/S : (d/f), what does S represents:

(a)Arrival Pattern
(b)Service Pattern
(c)Number of service channels
(d)The capacity of the system

15.In a simple queuing model the waiting time in the system is given by:

(a) (𝐿 − 𝜆) + ( 1 )
𝑞 𝜇

(b) 1
𝜇−𝜆
𝜇
(c)
𝜇−𝜆

(d) 𝑊𝑞 + 𝜇
 16. With respect to simple queuing model which on of the given below is wrong

(a) 𝐿𝑞 = 𝜆 𝑊𝑞
(b) 𝜆 = 𝜇 𝜌
(c) 𝑊𝑠 = 𝑊𝑞 + 𝜇
(d) 𝐿𝑠 = 𝐿𝑞 + 𝜌

17. In (M /M /1) : (∞/ FCFS) model, the length of the system Ls is given by:

(a) 𝜌2 /1/𝜌
(b) 𝜌/(1 − 𝜌)
(c) 𝜆2 /(𝜇 − 𝜆)
(d) 𝜆2 /𝜇(𝜇 − 𝜆)

18.Which of the following best describes queuing theory?

a. The study of arrival rates.

b .The study of service times.

c. The study of waiting lines.

d. The evaluation of service time costs.

19.Which of the following is a reason to employ queuing theory?

a. To reduce customer wait time in line.

b. To reduce service times.

c. To generate more arrivals to the system.

d . To reduce worker idle time in line.

20.If the service rate decreases as the arrival rate remains constant, then,
in general

a. customer waiting time increases.

b. customer waiting time decreases.

c. service costs increase.

d. customer dissatisfaction decreases.

21. Which type of queuing system are you likely to encounter at an ATM?

a. Single waiting line, single service station.

b. Multiple waiting lines, single service station.

c. Single waiting line, multiple service stations.

d. Multiple waiting lines, multiple service stations.

22. Which type of queuing system are you likely to encounter at a grocery
store?

a. Single waiting line, single service station.

b. Multiple waiting lines, single service station.

c. Single waiting line, multiple service stations.

d. Multiple waiting lines, multiple service stations.

23.If the arrival process is modeled as a Poisson random variable with

arrival rateλ, then the average time between arrivals is

a. 1/μ

b. 1/λ

c. 1/λ2

d. σ

24.For a Poisson random variable, λ represents the ____ number of

arrivals per time period

a. maximum

b. minimum

c. average

d. standard deviation of
25.A Poisson distribution shape can be described as

a. slightly skewed to the left.

b. symmetric around the parameter.

c. skewed to the right.

d. discrete so it lacks any definable shape.

26.If the number of arrivals in a time period follow a Poisson distribution

with mean λ then the inter-arrival times follow a(n) ____ distribution with
mean________.

a. normal;μ

b. constant;λ

c. exponential;λ

d. exponential; 1/λ

27. Times between two successive requests arriving, called the

a. Inter arrival time

b. Arrival time

c. Poisson distribution

d. Average residual service time

28. One of most widely used exponential distributions is called a

a. Passion distribution

b. Possible distribution

c. Poisson distribution

d. Poisson association

29. Customer behavior in which he moves from one queue to another in a

multiple channel situation is

a. Balking

b. Reneging

c. Jockeying

d. Alternating

30. Which of the following characteristics apply to queuing system

a. Customer population

b. Arrival process

c. Both a and b

d. Neither a nor b

31. Priority queue discipline may be classified as

a. Finite or infinite

b. Limited and Unlimited

c. Pre-emptive or non-pre-emptive

d. All of the above

32. The calling population is assumed to be infinite when

a. Arrivals are independent of each other

b. Capacity of the system is infinite

c. Both

d. None
 Optimization Techniques MCQ Part-5
(Replacement Theory)
1. Replacement decision is very much common in this stage

(a) Infant stage

(b) Old age
(c) Youth
(d) In all the above

2. The replacement policy that is imposed on an item irrespective of its failure is

(a) Group replacement

(b) Individual replacement
(c) Repair spare replacement
(d) Successive replacement

3. The total number of allocations in a basic feasible solution to the

transportation problem of m×n size is equal to

(a) m×n
(b) mn-1
(c) m+n+1
(d) m+n-1

4. Contractual maintenance or agreement maintenance with the manufacturer

is suitable for equipment, which is

(a) In its infant state

(b) When a machine is an old one
(c) Scrapped
(d) None of these
5. Which of the following maintenance policy is not used in the old age stage of a machine

(a) Operate up to failure and do corrective maintenance

(b) Reconditioning
(c) Replacement
(d) Scheduled preventive maintenance

6. The following replacement model is said to be a probabilistic model

(a) When money value does not change with time and time is a continuous variable
(b) When money value changes with time
(c) When money value does not change with time and time is a discrete variable
(d) Preventive maintenance policy

7. A machine is replaced with an average running cost

(a) Is not equal to the current running cost

(b) till the current period is greater than that of next period
(c) of the current period is greater than that of the next period,
(d) of the current period is less than that of next period

8. Decreasing failure rate is usually observed in ………………. stage of the machine

(a) infant
(b) youth
(c) old age
(d) any time in its life
9. The type of failure that usually occurs in old age of the machine is

(a) Random failure

(b) Early failure
(c) Chance failure
(d) Wear - out failure

10. The production manager will not recommend group replacement policy in case of

(a) When large number of identical items is to be replaced

(b) Low cost items are to be replaced, where record keeping is a problem
(c) For items that fail completely
(d) Repairable items

11. Which of the following replacement policies is considered to be dynamic in nature?

(a) Time is a continuous variable and the money value does not change with time
(b) When money value does not change with time and time is a discrete variable
(c) When money value changes with time
(d) When money value remains constant for some time and then goes on changing with time

12. When the probability of failure reduces gradually, the failure mode is said to be

(a) Regressive
(b) Retrogressive
(c) Progressive
(d) Recursive
13. ............................... is concerned with the determination of the most economic replacement policy.

(a) Probabilistic programming

(b) Linear programming
(c) Search theory
(d) Replacement theory

14. Which cost of the following is irrelevant to replacement analysis?

(a) Purchase cost of the machine

(b) Operating cost of the machine
(c) Maintenance cost of the machine
(d) Machine hour rate of the machine

15. Group replacement policy is most suitable for

(a) Trucks
(b) Infant machines
(c) Street light bulbs
(d) New cars

16. Replacement of an item will become necessary when

(a) an old item becomes too expensive to operate or maintain

(b) when your operator desires to work on a new machine
(c) when your opponent changes his machine in his unit
(d) when the company has surplus funds to spend
17. The following is not discussed in group replacement policy

(a) Failure Probability

(b) Cost of individual replacement
(c) Loss due to failure
(d) Present worth factor series

18. It is assumed that maintenance cost mostly depends on

(a) calendar age

(b) manufacturing date
(c) running age
(d) user’s age

19. In replacement analysis the maintenance cost is a function of

(a) time
(b) resale value
(c) initial investment
(d) none of these

20. Which of the following is the correct assumption for replacement policy when money value does not chang

(a) No Capital cost

(b) No scrap value
(c) Constant scrap value
(d) Zero maintenance cost
21. Which one of the following does not match the group?

(a) Present Worth Factor (PWF)

(b) Discounted rate (DR)
(c) Depreciation value (DV)
(d) Mortality Tables (MT)

22. Group replacement policy applies to

(a) Irreparable items

(b) Repairable items
(c) Items that fail partially
(d) Items that fail completely & suddenly

23. If a machine becomes old, then the failure rate expected will be

(a) Constant
(b) Increasing
(c) decreasing
(d) we cannot say

24. Replacement is said to be necessary if

(a) Failure rate is increasing

(b) Failure cost is increasing
(c) Failure probability is increasing
(d) Any of these
25. In this stage, the machine operates at highest efficiency and its production rate will be high

(a) Infant stage

(b) Youth stage
(c) Old age
(d) None of these

26. In retrogressive failures, the failure probability ......................... with time

(a) increases
(b) remains constant
(c) decreases
(d) none of these
 Optimization Theory MCQ-6
(Inventory Theory)
1. If small orders are placed frequently (rather than placing large orders infrequently),
then the total inventory cost

(a) increases
(b) reduces
(c) either increases or reduces
(d) is minimized

2. If orders are placed with size determined by the EOQ, then the
reorder costs component is

(a) equal to the holding cost component

(b) greater than the holding cost component
(c) less than the holding cost component
(d) either greater than or less than the holding cost component

3. If EOQ is calculated, but an order is then placed which is smaller than this,
will the variable cost:

(a) increase
(b) decrease
(c) either increase or decrease
(d) no change

4. Which costs can vary with order quantity

(a) unit cost only

(b) reorder cost only
(c) holding cost only
(d) all of these
5. If we find a minimum on a total cost cun/e, with discounted unit cost,
then the optimal order size is

(a) at this valid minimum

(b) at or to the left of this minimum
(c) at or to the right of this minimum
(d) anywhere

6. If we find a valid minimum on a total cost curve with increasing

reorder cost, then the optimal order size is

(a) at this valid minimum

(b) at or to the left of this minimum
(c) at or to the right of this minimum
(d) anywhere

7. When compared to instantaneous replenishment, does a finite

replenishment rate lead to

(a) the same size batches

(b) larger batches
(c) smaller batches
(d) either larger or smaller batches

8. If the total investment in stock is limited, then the best order

quantity for each item will be

(a) equal to the economic order quantity

(b) greater than the EOQ
(c) less than the EOQ
(d) either greater or less than the EOQ
9. If the unit cost rises, then optimal order quantity

(a) increases
(b) decreases
(c) either increase or decrease
(d) none of these

10. The basic information required for an efficient control of inventory is to do with

(a) What items should be stocked?

(b) When should an order be placed to replenish inventory?
(c) How much should be ordered in each replenishment?
(d) all of these

11. One of the important basic objective of Inventory management is

(a) to calculate EOQ for all materials in the organization.

(b) to go in person to the market and purchase the materials
(c) to employ the available capital efficiently so as to yield maximum results
(d) once materials are issued to the departments, personally check how they are used

12. The stock of materials kept in the stores in anticipation of future demand is known as

(a) storage of materials

(b) stock of materials
(c) inventory
(d) raw materials
13. Materials management bring about increased productivity of capital by

(a) very strict control overuse of materials

(b) increasing the efficiency of workers,
(c) preventing large amounts of capital locked up for long periods
in the form of inventory
(d) to apply the principles of capital management

14. We can reduce the materials cost by

(a) using systematic inventory control techniques

(b) ordering the material as and when the need arises
(c) by ordering in bulk quantities
(d) ordering the material at fixed interval irrespective of need

15. The basis for ABC analysis is

(a) interests of Materials manager

(b) interests of the top management
(c) Pareto’s 80-20 rule
(d) None of these

16. ABC analysis depends on the

(a) Quality of materials

(b) Cost of materials
(c) Quantity of materials used
(d) Annual consumption value of materials
17. ‘A’ class materials consumes

(a) 10 % of the total annual inventory cost

(b) 30% of the total annual inventory cost
(c) 70 to 75% of the total inventory cost,
(d) 90% of the total annual inventory cost

18. ‘B’ class of materials consumes ---------% of annual inventory cost

(a) 60 to 70%
(b) 20 to 25%
(c) 90 to 95%
(d) 5 to 8%

19. ‘C’ class materials consume _________ % of annual inventory cost.

(a) 5 to 10 %
(b) 20 to 30%
(c) 40 to 50%
(d) 70 to 80%

20. The rent for the stores where materials are stored falls under

(a) inventory carrying cost

(b) ordering cost
(c) procurement cost
(d) stocking cost
21. Insurance charges of materials cost fall under

(a) ordering cost

(b) inventory carrying cost
(c) stockout cost
(d) procurement cost

22. As the volume of inventory increases, the following cost will increase

(a) Stockout cost

(b) Ordering cost
(c) Procuring cost
(d) Inventory carrying cost

23. As the order quantity increases, which cost will reduce?

(a) Ordering cost

(b) Insurance cost
(c) Inventory carrying cost
(d) Stock out cost

24. Procurement cost may be clubbed with

(a) Inventory carrying charges

(b) Stock out cost
(c) Loss due to deterioration
(d) Ordering cost
25. The penalty for not having materials when needed is

(a) Loss of materials cost

(b) Loss of order cost
(c) Shortage cost
(d) General losses

26. Losses due to deterioration, theft and pilferage comes under

(a) Inventory Carrying charges

(b) Losses due to theft
(c) Does not come under any cost
(d) Consumption cost

27. At EOQ

(a) Annual purchase cost = Annual ordering cost

(b) Annual ordering cost = Annual carrying cost
(c) Annual carrying cost = annual shortage cost
(d) Annual shortage cost = Annual purchase cost

28. If the shortage cost is infinity,

(a) No shortages are allowed

(b) No inventory carrying cost is allowed
(c) Ordering cost is zero
(d) Purchase cost = Carrying cost
29. The inventory maintained to meet unknown demand changes is known as

(a) Pipeline inventory

(b) Anticipatory inventory
(c) De coupling inventory
(d) Fluctuatory inventory

30. Which of the following inventory is maintained to meet

expected demand fluctuations?

(a) Fluctuatory Inventory

(b) Buffer stock
(c) De-coupling inventory
(d) Anticipatory inventory

31. Which of the following increases with the quantity ordered per order?

(a) Carrying cost

(b) Ordering cost
(c) Purchase cost,
(d) Demand

32. The ordering cost per order and average unit carrying cost
are constant, and demand suddenly falls by 75 % then EOQ will:

(a) Decreases by 50%

(b) Does not change
(c) Increases by 50 %
(d) Decreases by 40%