Download - MB0048 Answer Keys
SIKKIM MANIPAL UNIVERSITY - DDE
Master of Business Administration – MBA Semester II
MB0048 - OPERATIONS RESEARCH – 4 Credit
(Book ID 1631)
Model Question Paper – Answers
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 customer’s 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 player’s strategy is to adopt a specific course of action, irrespective of the opponent’s
strategy, the player’s 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) Refer Unit 13
b. Degeneracy in Transportation problems (3 Marks) Refer Unit 6
c. Operating Characteristics and constituents of a Queuing system (4 Marks) Refer Unit 9
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
Machine Operators Cost (Rs)
A 5 200
B 3 130
C 2 110
D 1 50
E 4 80
Total Rs. 570
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 = 10Marks
(To compute the expected project length, the earliest and latest time of each event is
determined. The expected project length is 17 weeks. The critical path is 1-3-5-6 and
activities 1-3, 3-5 and 5-6 are the critical activities (as events 1,3.5 and 6 have zero slack).
The variance of the project length is : 9 weeks.) Refer Unit 14
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 = 10Marks
(The expected project duration is 17 weeks. The probability of completing the project within
4 weeks earlier than expected is nothing but the probability of completing the project within
13 weeks (i.e 17-4) . For Z= -1.33, from normal table, area = 0.0918. The probability of
completing the project 4 weeks earlier than expected is 0.0918 or 9.18%.)
(The probability of completing the project not more than 4 weeks later than expected is
nothing but probability of completing the project within 21 (i.e. 17+4) weeks. For Z = 1.33
from normal table area = 0.9082. The probability of completing the project not more than 4
weeks later than expected is 0.9082 or 90.82%)
(The due date of project is 19 weeks. For Z=0.66, from normal table; area = 0.7514. The
probability of completing the project within 19 weeks is 0.7514 of 75.14%)