SIKKIM MANIPAL UNIVERSITY - DDE

Master of Business Administration MBA Semester II

MB0048 - OPERATIONS RESEARCH 4 Credit

(Book ID 1631)

Model Question Paper

Duration: 2 hours Total marks: 140

__________________________________________________________________________

Section-A

1Mark x 50 = 50 Marks

Answer the following

1. Which of the following is an example of a mathematical model?

a. Iconic model

b. Replacement model

c. Analogue model

d. General model

2. Which phase in Operations Research involves making recommendations for the decision

process?

a. Judgement Phase

b. Research Phase

c. Action Phase

d. Recommendation Phase

3. A production manager of a manufacturing organisation is asked to manage and optimise

the utilisation of the resources. He/she has to deal with all the aspects of buying like when to

buy, how much to buy, etc. Which of the following tool or technique of Operations Research

should be used?

a. Linear programming

b. Inventory control methods

c. Transportation model

d. Goal programming

4. Models in which the input and output variables follow a defined probability distribution

are

a. Deterministic

b. Probabilistic

c. Symbolic

d. Sequencing

5. ______________________ has several objective functions, each having a target value.

a. Queuing model

b. Linear programming

c. Goal programming

d. Inventory control method

6. In linear programming we need to ensure that both the objective function and the

constraints can be expressed as linear expressions of _________________.

a. Basic variables

b. Decision variables

c. Constraints

d. Objective function

7. Optimisation refers to the maximisation or minimisation of the __________________ .

a. Objective functions

b. Constraints

c. Co-efficients of decision variables

d. Constants

8. When a linear programming problem is represented in the canonical form, the

minimisation of a function is mathematically equivalent to the ______________ of this

function.

a. Maximisation of the negative expression

b. Minimisation of the negative expression

c. Minimisation of the positive expression

d. Maximisation of the positive expression

9. Which of the following defines the measure of effectiveness of the system as a

mathematical function of its decision variables?

a. Objective function

b. Optimum strategy

c. Constraints

d. Queuing theory

10. In Linear Programming Problems, both objective function and constraints can be

expressed as ____________________.

a. Linear equalities

b. Non-linear equalities

c. Linear inequalities

d. Non-linear inequalities

11. Any inequality in one direction ( or ) may be changed to an inequality in the opposite

direction ( or ) by multiplying both sides of the inequality by _____________.

a. 0

b. -1

c. 1

d. 10

12. According to which of the basic assumptions of linear programming problem, all co-

efficients of decision variables in the objective and constraints expressions are known and

finite?

a. Linearity

b. Deterministic

c. Additivity

d. Divisibility

13. Linear programming is a powerful tool for ____________________________.

a. Maximising a nonlinear objective function

b. Optimising costs

c. Solving a system of equalities and inequalities

d. Selecting alternatives in a decision problem

14. In graphical analysis, the __________________ equation is replaced to form a linear

equation.

a. Linear Programming constraint

b. Inequality constraint

c. Binding constraint

d. Redundant Constraint

15. in which of the following case, only one optimum solution will be obtained in a graphical

solution method?

a. A unique optimal solution

b. Multiple optimal solution

c. An unbounded solution

d. Infeasible problem

16. Which of the following is a characteristic of simplex method?

a. All constraints are equations

b. Convexity

c. Boundaries of feasible region are planes

d. Objective function can be represented by a line

17. Slack and surplus variables can be incorporated in the objective function with

______________ coefficients.

a. One

b. Zero

c. Three

d. Four

18. When the primal problem is unbounded, the dual is_______________.

a. Multiple optimal solutions

b. Infeasible

c. Degenerate

d. Unbounded or infeasible

19. The objective of formulation of __________________ is to develop an integral

transportation schedule that meets all demands from the inventory at a minimum total

transportation cost.

a. Assignment problem

b. Transportation problem

c. Game theory

d. Simulation

20. A basic solution to an m-origin, n destination transportation problem can have at the most

__________________ positive basic variables (non-zero), otherwise the basic solution

degenerates.

a. m - n - 1

b. m - n + 1

c. m + n + 1

d. m + n 1

21. The number of rows is not equal to the number of columns and vice versa in

___________________________.

a. Linear programming problem

b. Balanced assignment problem

c. Unbalanced assignment problem

d. Quadratic programming problem

22. ________________________ is applied when some variables have upper or lower

bounds.

a. Branch and bound technique

b. Integer programming technique

c. Non-integer programming technique

d. Linear programming techniques

23. In which of the following integer programming problems all decision variables are

restricted to integer values?

a. Pure integer programming problems

b. Mixed integer programming problems

c. Zero integer programming problems

d. One integer programming problems

24. Queuing theory is a collection of mathematical models of various queuing systems based

on _____________ concepts.

a. Probability

b. Deterministic

c. Game

d. Sequencing

25. Impatient customers who would not wait beyond a certain time and leave the queue are

said to _________________.

a. Balking

b. Jockeying

c. Reneging

d. Collusion

26. ___________ queuing disciplines are based on the individual customers status.

a. Dynamic

b. Server

c. Service

d. Static

27. ____________ is a rule wherein an important customer is allowed to enter into the service

immediately after entering into the system.

a. FIFO

b. LIFO

c. Priority service

d. Pre-emptive priority

28. When the customer arrivals are completely random, the ____________ is followed.

a. Deterministic model

b. Statistical model

c. Poisson distribution

d. Probability concept

29. _________ represents number of customers waiting in the queue.

a. Service facility

b. Queue length

c. Waiting time

d. Arrival pattern

30. Queuing theory is a collection of _______________________ of various queuing

systems.

a. Mathematical models

b. Game models

c. Simulation models

d. Assignment models

31. In this type of a model, a customer enters the first station and gets a portion of service and

then moves on to the next station, gets some service and finally leaves the system having

received the complete service.

a. Single server- Single queue

b. Single server- Several queues

c. Several servers- Single queues

d. Service facilities in a series

32. Which queuing discipline is based on the stack method?

a. First Come- First Served

b. Priority

c. Random

d. Last Come- First Served

33. _______________ is the process of defining a model of a real system.

a. Simulation

b. Prototyping

c. CPM

d. PERT

34. The technique of ____________ involves the selection of random observations within the

simulation model.

a. Monte Carlo

b. Experimentation

c. Rapid Prototyping

d. PERT

35. Simulation should not be applied in all the cases because it:

a. Requires considerable talent for model building and extensive computer programming

efforts.

b. Consumes much computer time

c. Provides at best approximate solution to problem

d. All of the above

36. ___________________may be defined as a collection of interrelated activities (or tasks)

which must be completed in a specified time according to a specified sequence and require

resources, such as personnel, money, materials, facilities, etc.

a. Projects

b. PERT

c. CPM

d. Simulation

37. ______________ refers to comparing the actual progress against the estimated schedule.

a. Project planning

b. Project scheduling

c. Project controlling

d. CPM

38. For the critical activities, the float is

a. One

b. Two

c. Zero

d. Negative

39. The _________ float for activity is the difference between the maximum time available to

perform the activity and its duration.

a. Total

b. Free

c. Independent

d. Zero

40. What is the abbreviation of PERT?

a. Program Evaluation and Review Technique

b. Probable Evaluation and Review Technique

c. Path Evaluation and Reasoning Technique

d. Predetermined Evaluation and Review Technique

41. If a players strategy is to adopt a specific course of action, irrespective of the opponents

strategy, the players strategy is called _____________ strategy.

a. Pure

b. Chaste

c. Tainted

d. Mixed

42. The critical path of a network is the

a. longest path through the network.

b. path with the most activities.

c. path with the fewest activities.

d. shortest path through the network

43. Which of the following is used to come up with a solution to the assignment problem?

a. MODI method

b. northwest corner method

c. stepping-stone method

d. Hungarian method

44. To find an initial basic feasible solution by Matrix Minima Method, we first choose the

cell with

a. zero cost

b. highest cost

c. lowest cost

d. none of these

45.

Activity 1-2 1-6 2-3 2-4 3-5 4-5 6-7 5-8 7-8

Duration(weeks) 7 6 14 5 11 7 11 4 18

For the network diagram, the critical path is:

a. 1-2-3-5-8

b. 2-4-5-6-7

c. 1-2-3-4-5

d. 1-2-4-7-8

46. The objective function for a LP model is 3X1 + 2X2. If X1 = 20 and X2 = 30, what is the

value of the objective function?

a. 0

b.50

c. 60

d.120

47. A road transport company has one reservation clerk on duty at a time. He handles

information of bus schedules and make reservations. Customers arrive at a rate of 8 per hour

and the clerk can serve 12 customers on an average per hour. The average number of

customers waiting for the service in the system are:

a. 2

b. 5

c. 8

d. 10

48. The number of customers in queue and also those being served in the queue relates to the

____________ efficiency and ______________.

a. Facility, Queue length

b. Service, Capacity

c. Server, Capacity

d. Facility, Capacity

49. If there are 'n' number of workers and 'n' number of tasks to be performed, but some of

the tasks cannot be performed by the workers then it is a form of

____________________________.

a. Infeasible assignment problem

b. Feasible assignment problem

c. Unbalanced assignment problem

d. Balanced assignment problem

50. Network scheduling is a technique for ____________ and __________________ of large

projects.

a. Scheduling, Integrating

b. Planning, Scheduling

c. Integrating, Implementing

d. Planning, Integrating

Section-B

2Marks x 25= 50 Marks

Answer the following

51. i. OR techniques are used to find the best possible solution.

ii. OR methods in industry can be applied in the fields of production, inventory controls and

marketing, purchasing, transportation, and competitive strategies.

State True or False:

a. i -True, ii -False

b. i -True, ii -True

c. i -False, ii -False

d. i -False, ii -True

52. i. ___________________ include all forms of diagrams, graphs, and charts.

ii. ________________ include a set of mathematical symbols to represent the decision

variable of the system.

a. Physical models, Probabilistic models

b. General models, Mathematical models

c. Physical models, Mathematical models

d. General models, Specific models

53. i. ________________ phase deals with formulation of the problems relative to the

objectives.

ii. _________________ phase deals with formulation of hypothesis and model.

a. Judgement, Research

b. Research, Judgement

c. Judgement, Action

d. Research, Action

54. Linear programming is a mathematical technique designed to help managers in their

______________ and ________________.

a. Organising, allocation

b. Planning, organising

c. Planning, decision making

d. Allocation, implementation

55. Which of the following options indicate the advantages of linear programming?

i. It indicates how decision makers can employ productive factors most effectively by

choosing and allocating resources.

ii. It is used to determine the proper mix of media to use in an advertising campaign.

iii. It takes into consideration the effect of time and uncertainty.

iv. Parameters appearing in the model are assumed to be variables.

a. Options i & iv

b. Options i & ii

c. Options i & iii

d. Options ii & iii

56. Identify which among the following are the reasons why sensitivity analysis is important.

i. Values of linear programming parameters might change.

ii. The labour of computation can be considerably reduced.

iii. Useful in planning future decisions.

iv. Linear programming parameters have an uncertainty factor attached to them.

a. Options i & iv

b. Options i & ii

c. Options i & iii

d. Options ii & iv

57. Write the dual of Max Z = 5x1 + 6x2

Subject to

4x1 + 2x2 16

x1 + 2x2 10

5x1 + 2x2 20

x1, x2 0

a. Min W = 16y1 + 10y2 + 20y3

Subject to

4y1 + y2 + 5y3 5

2y1 + 2y2 + 2y3 6

y1, y2, y3 0

b. Min W = 16y1 + 10y2 + 20y3

Subject to

4y1 + y2 + 5y3 5

2y1 + 2y2 + 2y3 6

y1, y2, y3 0

c. Min W = 16y1 + 10y2 + 20y3

Subject to

4y1 + y2 + 5y3 5

2y1 + 2y2 + 2y3 6

y1, y2, y3 0

d. Min W = 16y1 + 10y2 + 20y3

Subject to

4y1 + y2 + 5y3 5

2y1 + 2y2 + 2y3 6

y1, y2, y3 0

58. Consider the below mentioned statements:

i. Hungarian method can be applied to maximisation problem.

ii. All assignment problems are maximisation problems.

State True or False:

a. i-True, ii-True

b. i-False, ii-False

c. i-False, ii-True

d. i-True, ii-False

59. Match the following sets:

Part A

1. Service facility

2. Queuing system

3. Multiple service channels

4. Static queuing discipline

Part B

A. Arrival pattern, service facility and queue

discipline

B. Availability of service, number of service

centres and duration of service

C. Based on Individual Customer status in

the queue

D. Series or parallel arrangement

a. 1D, 2A, 3B, 4C

b. 1A, 2D, 3B, 4C

c. 1B, 2A, 3D, 4C

d. 1B, 2C, 3A, 4D

60. Which of the below aspects form a part of a service system?

i. Configuration of service system

ii. Speed of the service

iii. Cost of the service system

iv. Size of the service system

a. Options i & ii

b. Options i & iv

c. Options i & iii

d. Options ii & iii

61. Consider the following statements:

i. Single server - Single queue model involves one queue one service station facility called

single server models where customer waits till the service point is ready to take him for

servicing.

ii. Different cash counters in an electricity office where the customers can make payment in

respect of their electricity bills provide an example of several servers -several queues model.

State true or false

a. i -False, ii -False

b. i -True, ii -True

c. i -False, ii -True

d. i -True, ii -False

62. A factory produces 150 scooters. But the production rate varies with the distribution

depicted in table below.

Production rate 147 148 149 150 151 152 153

Probability 0.05 0.10 0.15 0.20 0.30 0.15 0.05

At present the truck will hold 150 scooters. Random Numbers 82, 54, 50, 96, 85, 34, 30, 02,

64, 47.

Using the random numbers , the average number of scooters waiting for shipment in the

factory is

a. 0.4/day

b. 0.5/day

c. 0.6/day

d. 0.7/day

63. The Monte Carlo technique is restricted for application involving random numbers to

solve ______________ and _____________ problems.

a. Deterministic, Speculative

b. Probabilistic, Speculative

c. Indeterministic, Stochastic

d. Deterministic, Stochastic

64. Match the following sets:

Part A

1. PERT

2. CPM

3. Events

4. Activities

Part B

A. Used for projects involving activities of

repetitive nature

B. Used for projects involving activities of

non repetitive in nature in which time

estimates are uncertain

C. Represent point in time that signifies the

completion of some activities and the

beginning of new ones

D. Represented by arrows and consume time

and resources.

a. 1A, 2B, 3C, 4D

b. 1A, 2D, 3B, 4C

c. 1D, 2A, 3B, 4C

d. 1B, 2A, 3C, 4D

65. Match the following sets related to the applications of linear programming problems:

Part A

1. Finance

2. Production and operations

management

3. Distribution

4. Marketing

Part B

A. The problem is to determine the quantities of each

product that should be produced.

B. The problem of the investor could be a portfolio-mix

selection problem.

C. The problem is to determine how many

advertisements to place in each medium.

D. The problem is to determine the shipping pattern.

a. 1D, 2A, 3B, 4C

b. 1A, 2D, 3B, 4C

c. 1B, 2A, 3D, 4C

d. 1B, 2C, 3A, 4D

66. Match the following sets:

Part A

1. Saddle point

2. Competitive situations

3. Two person zero sum game

4. Theory of Games and economic

behaviour

Part B

A. Position where Maximin - minimax

coincide

B. Arise when two or more parties with

Conflicting interests operate

C. Rectangular game

D. Developed by John Von Neuman and

Morgenstern

a. 1A, 2B, 3C, 4D

b. 1A, 2D, 3B, 4C

c. 1D, 2A, 3B, 4C

d. 1B, 2C, 3A, 4D

67. In a two person zero sum game, the pay-off matrix of A is:

Player A

Player B

B1 B2 B3

A1 4 7 0

A2 -1 3 6

The pay-off matrix of B is:

a.

Player A

Player B

B1 B2 B3

A1 4 7 0

A2 -1 3 6

b.

Player A

Player B

B1 B2 B3

A1 -4 -7 0

A2 1 -3 -6

c.

Player B

Player A

A1 A2

B1 -4 1

B2 -7 -3

B3 0 -6

d.

Player B

Player A

A1 A2

B1 4 1

B2 7 3

B3 0 6

68. Arrival at a telephone booth are considered to be Poisson with an average time of 10

minutes between one arrival and the next. The length of the phone call is assumed to be

distributed exponentially with mean 3 minutes. The probability that a person arriving at the

booth will have to wait is

a. 0.3

b. 0.6

c. 0.9

d. 1

69. Consider the following assignment problem

P1 P2 P3 P4

T1 20 - 32 27

T2 15 20 17 18

T3 16 18 - 20

T4 - 20 18 24

Optimum assignment schedule is

a. T1 to P1, T2 to P4, T3 to P2, and T4 to P3

b. T1 to P3, T2 to P4, T3 to P2, and T4 to P1

c. T1 to P3, T2 to P2, T3 to P4, and T4 to P1

d. T1 to P3, T2 to P2, T3 to P4, and T4 to P1

70. An activity has an optimistic time of 15 days, a most likely time of 18 days, and a pessimistic time

of 27 days. What is its expected time?

a. 20 days

b. 60 days

c. 18 days

d. 19 days

71.

W1 W2 W3 W4

F1 19 30 50 10 7

F2 70 30 40 60 9

F3 40 8 70 20 18

5 8 7 14

For the above Transportation problem, the total cost using Vogel approximation Method is:

a. 779/-

b. 660/-

c. 550/-

d. 440/-

72. A branch of city bank has one cashier at its counter. On an average nine customers arrive

for every five minutes and the cashier can serve 10 customers in five minutes. Assuming

Poisson distribution for arrival rate and exponential distribution for service rate, find

i. Average number of customer in the system:

a. 1

b. 5

c. 0

d. 9

ii. Average time a customer spends in the system:

i. 1 mins

b. 15 mins

c. 5 mins

d. 20 mins

73.

B1 B2 B3 B4 B5

A1 9 3 1 8 0

A2 6 5 4 6 7

A3 2 4 4 3 8

A4 5 6 2 2 1

i. The saddle point for the game is

a. (2,3)

b. (1,5)

c. (5,6)

d. (4,5)

ii. The value of the game is

a. 8

b. 1

c. 0

d. 4

74. Match the following sets:

Part A

1. Balking

2. Collusion

3. Reneging

Part B

A. Customers Keep on switching over from

one queue to another in a multiple service

centres.

4. Jokeying B. Impatient customers who would not wait

beyond a certain time and leave the queue.

C. Only one person would join the queue, but

demand service on behalf of several

customers.

D. Customers do not join a queue because of

their reluctance to wait.

a. 1D, 2C, 3B, 4A

b. 1D, 2C, 3A, 4B

c. 1C, 2D, 3B, 4A

d. 1C, 2D, 3A, 4B

75. The ABC manufacturing company can make two products P1 and P2. Each of the

products requires time on a cutting machine and a finishing machine. Relevant data are:

Product

P1 P2

Cutting hrs (per unit) 2 1

Finishing hrs (per unit) 3 3

Profit (per unit) Rs.6 Rs.4

Maximum Sales (Unit per

week)

200

The number of cutting hours available per week is 390 and number of finishing hours

available per week is 810.

a. The company should produce

i. 120 units of P1

ii. 150 units of P1

iii. 160 units of P1

iv. 180 units of P1

b. The company should produce

i. 150 units of P2

ii. 180 units of P2

iii. 190 units of P2

iv. 200 units of P2

Section-C 40 Marks

Answer the following questions. 10Marks x 2 = 20Marks

76. Explain the following (10 Marks)

a. Monte Carlo simulation Method (3 Marks)

b. Degeneracy in Transportation problems (3 Marks)

c. Operating Characteristics and constituents of a Queuing system (4 Marks)

77. The assignment cost of assigning any one operator to any machine is given in the

following table. Solve the following assignment problems. (10 Marks)

Machine Operators

I II III IV V

A 160 130 175 190 200

B 135 120 130 160 175

C 140 110 155 170 185

D 50 50 80 80 110

E 55 35 70 80 105

Case Study (20 Marks)

A project is composed of seven activities whose time estimates are listed.

Activity Estimated duration

Optimistic Most likely Pessimistic

1-2 1 1 7

1-3 1 4 7

2-4 2 2 8

2-5 1 1 1

3-5 2 5 14

4-6 2 5 8

5-6 3 6 15

78. (a) Draw the network

(b) Compute the expected project length and variance of the project length

5 Marks x 2 = 10 Marks

79. (c) Compute the probability that the project will be completed-

i. 4 weeks earlier than expected

ii. Not more than 4 weeks later than expected

(d) If the project due is 19 weeks, what is the probability of meeting the due date.

5 Marks x 2 = 10 Marks