7:38 ... -;- .

61 of 157 2

Total No. of Questions : SJ

SEAT No. =I~---~
P-3765 )Total No. of Pages : 4
(6025)-42
M.B.A.
302: GC-12: DECISION SCIENCE
(2019 Pattern) (Semester - III)
lime: 2½ Hours/ /Max. Marks : 50
Instructions to the candidates:
1) Each question carries JO marks.
2) Graph paper will /not be provided.
3) Use of non-scientific calculator is allowed.

QI) Solve any five of the following: IS x 2 = IOI

a) Define optimistic time estimate in PERT.
b) Enlist different queue discipline in queuing theory.
c) What is saddle point in Game theory?
d) Define Markov Chain.
e) Mention assumptions underlying Linear Programming Problem (LPP).
f) Write different methods of initial solution to transportation problem.
g) Write condition for balanced assignment problem.
h) What do you mean by optimal solution in solving transportation problem?

Q2) Solve any two of the following: 12 XS= 101

a) Solve the following LPP by graphical solution
Max Z= 9x1 + 3x2
Subject to
2x 1 + 3x2 !'> 13
2x 1 + x2 !', 5
X
1
+x2 Q

P.T.O.

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7:38

P.T.O.

b) Explain the steps in solving transportation problem.

c) Explain the use of various tools of decision theory in today's business

environment.

QJ) Solve any one of the following: (I x 10 = 10(

a) Three brands of product P, Q and R having market share as 30%, 30%
and 40% respectively. Customers shift their brands. Brand switching
matrix every quarter is given below.
To
From p Q R
p 50% 30% 20%

Q 20% 70% 10%

R 20% 20% 60%

Apply concept of Markov Chain to find market share at the end of First
& Second quarter.

b) Using the following cost matrix determine i) Optimal job assignment

ii) Optimal cost assignment.
Cost ('000 Rs.)
Job
Machinist 2 3 4 5

A 10 3 3 2 8

B 9 7 8 2 7

C 7 5 6 2 4

D 3 5 8 2 4

E 9109 610

(60251-42 2

Q4) Solve any one of the following: (I x 10 = 101

a) XYZ company is considering three options for managing its data
processing operations: continue with own staff, outsourcing or the use
of combination. The annual profit of each option depends on demand as

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7:38 ,11 lllif,,

D 3 5 8 2 4

E 9109 610

I602SI-42 2

Q4J Solve any one of the following: 11 x 10 = 101

a) XYZ company is considering three options for managing its data
processing operations: continue with own staff, outsourcing or the use
of combination. The annual profit of each option depends on demand as
follows:
Profit
Staffing Demand ('000 Rs.)
option High Medium Low
Own staff 650 650 600
Outsourcing 900 600 300
Combination 800 650 500
Determine Optimal strategy for
i) Maxi-min
il) Laplace
iii) Hurwicz (a= 0.6) &
iv) Regret criterion.
b) The machine operator has to perform two operations, turning and threading
on a number ofdifferent jobs. The time required to perform these operation
on these machines is given below.
Determine sequencing of jobs to minimize the total time. Also find idle
time of operations on both machines.
Jobs I 2 3 4 5 6
Turning time 03 12 05 02 09 II
(in min)
Threading time 08 10 10 06 03 01
(in min)

QSJ Solve any one of the following: 11 x 10 = 101

a) Vijay has started new retail outlet in the mid ofthe market. In market there
is business & competition, therefore survival of new outlet is very rare
chance of survival is almost 5%. Vijay has started such 7 new retail outlet.
Find out the probability i) no shop will survive and ii) exactly 5 shops will
survive.

I602SI-42 3

b) The three estimates for activities of a project are given below :

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 7:39
chance of survival is almost 5%. Vijay has started such 7 new retail outlet.
·:nd out the probability i) no shop will survive and ii) exactly 5 shops will
64 of 157rvive.
1602S1-42 3

b) The three estimates for activities ofa project are given below:

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

Pessimistic 7 7 12 15 8 7
duration
Most likely 6 4 6 2 4
duration
Optimistic 5 2 3 2
duration

Draw network diagram. Find out Critical path & Project duration. Estimate
expected Standard deviation of critical path.

0000

1602S1-42 4

Total No. of Questions : 51 SEAT No.: I.___ _ __,

P-3766 (Total No. of Pages : 2
16025)-43

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7:40 ... -;- . ,

16025)-3001 2

Total No. of Questions: SJ

SEAT No. =~I- - - - ~
P3854 )Total No. of Pages : 3
(6025)-3002
S. Y.M.B.A. (Project Management)
302 - GC - 12 : DECISION SCIENCE
(2021 Pattern) (Semester- DI)
lime: 2½ Hours/ /Max. Marks: 50
Instructions to the candidates:
I) Each question ca"ies JO marks.
2) Graph paper will not be provided.
3) Use of non-scientific calculator i.f allowed.
4) All questions are compulsory:

QI) Solve any five. (Sx2=10(

a) Define balanced transportation problem.

b) State linear programming.
c) Define conditional probability.
d) Define saddle point.
e) State what is critical path.
f) Define mean arrival rate.
g) Define probability.

Q2) Solve any two of the following. (2xS=IO(

a) Discuss dependent Event and Independent Event.

b) Describe the role ofquantitative techiniques in decision making.
c) Solve the following problem graphically.
Maximize Z = 3x + 4y
Subject to x + y 6
2x+y~8
x,y 0

P.T.O.

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7:41

P.T.O.

Q3) Solve any on of the following. 1101

a) How should the activities be assigned to the workers so that the job is
completed in minimum time?
Workers
Activities 2 3 4
A 14 12 15 15
B 21 18 18 22
C 14 17 12 14
D 6 5 3 6
OR
b) Find initial solution by using North - West comer method and Least
Cost Method (LCM) IlOJ
DI D2 DJ D4 supply

SI 19 30 50 IO 7

s2 70 30 40 60 9

SJ 40 8 70 20 18
Demand 5 8 7 14 34

Q4) Solve any one of the following. (IOI

a) The following table gives the activities in a construction project and
other relevant information
Activity 1-2 1-3 2-3 2-4 3-4 4-5
Duration 20 25 IO 12 6 10
(Days)
i) Draw the network diagram for the project.
ii) Find critical path.
iii) Determine the expected project completion time.
OR

I6025J-3002 2

b) A departmental store has a single cashier. During the rush hours, customers
arrive at a rate of20 customers per hour. The cashier takes on an average
2.5 minutes per customer for processing.
i) What is the probability the cashier is idle?
ii) What is the average number of customers in the queuing system?
iii) What is average queue length?
1v What is the avera e times ent b a customer in the s stem? 10

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7:41
i) Draw the network diagram for the project.
ii) Find critical path.
iii) Determine the expected project completion time.
OR

I602SI-3002 2

b) A departmental store has a single cashier. During the rush hours, customers
arrive at a rate of20 customers per hour. The cashier takes on an average
2.5 minutes per customer for processing.
O What is the probability the cashier is idle?
ii) What is the average number of customers in the queuing system?
iii) What is average queue length?
iv) What is the average time spent by a customer in the system? IIOI
Q5) Solve any one of the following. 1101
a) From the pay off matrix (Profit). Determine optimal strategy by using.
i) Maximin criterion
ii) Maximax criterion
iii) Minimax Regret criterion
iv) Laplace criterion
States is Nature
Strategies N, N2 NJ
s, 7,00,000 3,00,000 1,50,000
s, 5,00,000 4,50,000 0
s3 3,00,000 3,00,000 3,00,000

OR

b) Solve the following game. IIOI

Player (8)
B, B,
Player A, 3 5
(A) A2 4 I

0 Find the value of game.

ii) Find the optimal strategies of player A and player B.

I602S)-3002 3

Total No. of Questions : SJ

SEAT No. =~I- - - - ~
P3855 (6025)-3003
)Total No. of Pages : 2

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Total No. of Questions :5| SEAT No. : 2s891
PA-3623 [Total No. of Pages :3
|5946]- 302
M.B.A.-II
302 -GC-12 : DECISIONSCIENCE
(2019 Pattern)(Semester - II)
Time : 2% Hours) IMax. Marks : 50
Instructions to the candidates: AY 2022-23
) Each question carries 10marks. SPPU - QUESTION PAPER
2) Graph paper willnot be provided. REGULAR - FEB 2023
3) Use of non-scientific calculator is allowed. gtic-202

Q1) Solve âny five ofthe following. [2x5=10|

a) Define ránsition probability in Markov Chain.
5 Mention condition for balanced transportation problem.
c) Define independentevents in probability.
Y Write condition for saddle point in game theory.
Le)
Define EVPI(Expected value ofperfect Information).
Write format of LPP (Linear Programming Problem).
LgY Define critical pathin network diagram.
h) List elements of queuing'system
[2x5=10)
02) Solve any two of the following static

a) Discuss different decision enviornment in Decision Theory.

Describe role of linear programming problem (LPP) in managerial decision

/02/2023
making.
Determine the initial solution of following transportation problem using
North West Corner Method.
Destinations

Sources DI D2 D3 D4 Supply
SI 19 30 50 10
S2 40 15 18
S3 30 20 20 25 18
Demand 05 08 0714 3
PIO.
 |1x10=10]
03) Solve any One of the following.
a Solvethe following game by using principle of dominance.
Player B
B1 B2 B3 B4
A1 14 12
IMPO
Player A A2 2 12
-6 16
A 5 12 10

Following data is related to frequency of student absenteeism in a class

No. of students Absent 5 10 15 20 25

Frequency 4 22 16 4210 06
Simulate the students absenteeism forhext 1O weeks. Also find out average
absenteeism. Use the following random númbers.
87, 05, 30, 53,89, 61, 19, 55,23, 58
04) Solve any one of following. [1x10=10]
A computer centre has got four expert programmes The centre needs
four application programmes to be develop. The head of computer centre
after studying carefully programmes to be developed estimes computer
s$

time (in hrs) required by the respective MMPO1603

experts to develop
1
the application
13:30:50

programmes as follow.
Programmes
21/02/2023
A B C D

Programmers 1 120 100 80 90

2 80 90 100 70
202
3 120 140 120 100
4 90 90 80 90
Assign programmers to the programmes
4294.in8such
, a way that total computer
time is minimize.

[5946|-302 2
 b) The profit of organizedretail outlet is
with mean Rs, 4400 &
standard
apprOximately normally distributed
devíation Rs, 620
Find associated probability
3:30 of :profit
50

i) More than 3300

i) less than 5400
IMMÂ
im) between3500 &4400
Giver PIoZ<1.77] =0,4616
5s0
tatic-202
Pf0 <Z<1.61]
44.202 =0.4463
P[0 <Z< 1.45] = 0.4263

|1×10=10|
05) Solve any One of following.
the following list of activities
Aproject has been defined to contain
along with their required time of completion.
F G H I
A B D
Activity
6 2 7 9 atic-202
Time in Dasy 1 4

D GH
Immediate A À BC E,F
predecessor
Path.
Draw network diagram, Jdentify Critical PO16034
every 15 minutes one customer arrives for3cashing
b) In abank on an average 3:
minútes for
only paymnent counter takes 10
the cheque. The staff at the 1

serving acustomer on an average.

02/2023

Find

i) average queue length.

2 0 2counter.
i) Increase in arrival rate for justifying asecond

49,248.1

3
[5946|-302
Total No. of Questions : 5] SEAT No. :
PA-4364 [Total No. of Pages : 3

[5946]-3002 OCT 2022 - 2019 Pattern

M.B.A.
(GC-12)-302: DECISION SCIENCE
(2021 Pattern) (Semester - III)
Time : 2½ Hours] [Max. Marks : 50
Instructions to the candidates :
1) All questions are compulsory.
2) Each question carries 10 marks.
3) Each question has an internal option.
4) Use of simple calculator is allowed.

Q1) Solve any Five out of eight questions : [10]

a) Define dependent event.

b) Define critical path.
c) State mined strategy.
d) State unbalanced transportation problem.
e) Define saddle point.
f) Memorize mean service rate.
g) State full form of CPM.
h) Define Monte Carlo simulation.

Q2) Solve any two out of three questions : [10]

a) Explain the applications of Markov chain.

b) Compare CPM and PERT.

c) Describe the importance of decision science in decision making.

P.T.O.
Q3) a) Use the graphical method to solve the following LPP. [10]
Maximize Z = 100x + 100y
Subject to constraints
6x + 4y  24
4x + 2y  16
3.5x + 3y  21
x, y  0
OR
b) Obtain the initial feasible solution of the following transportation problem
using i) NWCM and ii) LCM. [10]
D1 D2 D3 D4 Supply
S1 19 30 50 10 7
S2 70 30 40 60 9
S3 40 8 70 20 18
Demand 5 8 7 14 34

Q4) a) A bakery keeps a stock of popular brand of cake. Daily demand based
on past experience is given below. [10]
Daily Demand 0 10 20 30 40 50
Probability 0.01 0.15 0.20 0.50 0.12 0.02
Using the following random numbers simulate the demand for next 10
days and also calculate the average demand for the cake basis of simulated
data.
Random numbers : 45, 72, 56, 51, 79, 9, 61, 43, 31 and 81
OR
b) Draw network diagram from the following activities and find critical path
and total slack of activities. [10]
Job A B C D E F G H I J K
Job time 13 8 10 9 11 10 8 6 7 14 18
days
Immediate - A B C B E D,F E H G,I J
predecessor.

[5946]-3002 2
Q5) a) Given the following pay off matrix use i) Laplace criterion ii) Minimax
Regret criterion iii) Hurwicz criterion ( = 0.6) to find optimal strategy.[10]
Action
A1 A2 A3 A4
S1 10 5 8 6
States of Nature S2 3 9 15 2
S3 –3 4 6 10

OR
b) Solve the following assignment problem for minimization. [10]
1 2 3 4 5
A 8 8 8 11 12
B 4 5 6 3 4
C 12 11 10 9 8
D 18 21 18 17 15
E 10 11 10 8 12



[5946]-3002 3
Total No. of Questions : 5] SEAT No. :
P8034 [Total No. of Pages : 3
[5860]-302
M.B.A. - II
302-GC-12 : DECISION SCIENCE April 2022 - 2019 Pattern

(2019 Pattern) (Semester - III)

Time : 2½ Hours] [Max. Marks : 50

Instructions to the candidates:
1) Each question carries 10 marks.
2) Graph paper will not be provided.
3) Use of non-scientific calculator is allowed.

Q1) Solve any five: [5×2=10]

a) Define Probability.

b) List techniques of initial solution for Transportation problem.

c) Enlist various methods of decision making under uncertainity.

d) What is 2×2 zero sum game?

e) Enumerate any two quantitative techniques for optimal decision in business.

f) List the drawbacks of graphical solution in LPP.

g) Define total float in Network diagram.

h) Define (M/M/I, Infinite, FIFO) in Queuing theory.

Q2) Solve any two of the following: [2×5=10]

a) Discuss the use of CPM & PERT in Project Management.

b) Explain the role of quantitative techniques in decision making.

c) Describe the steps in Solving Assignment Problem.

P.T.O.
Q3) Solve any one of the following: [1×10=10]
a) A small bank is allocating maximum 0%. Rs. 21,00,000/- for personal &
car loans. The interest rates per annum are 11% for car loan & 13% for
personal loans. The loans are repaid at the end of one year period. The
amount of personal car cannot exceed 40% of the car loans. Past
experience has shown that bad debts to 1.2% of all personal loans.
Formulate & solve the above problem to find the optimum loan
allocations.
b) Following is the distribution of defective pieces in a manufacturing process
of a MNC in Pune.
No. of defective items 0 10 20 30 40 50
Probability 0.01 0.20 0.15 0.50 0.12 0.02
Consider the following sequence of random numbers.
38, 58, 19, 51, 66, 15, 24, 78, 42, 08
Using this sequence, simulate the number of defective items for next
10 days.

Q4) Solve any one of the following: [1×10=10]

a) In a group of 1000 customers, there are 650 who uses Jio connection,
400 uses Airtel connection and 150 uses both connections, Jio & Airtel.
If a customer is selected at random, what is the probability that he uses :
i) Jio only
ii) Airtel only
iii) Only one of the two connection and
iv) At least one of the two connections.
b) A repairman is to be hired to repair machines which breakdown at an
average rate of 6 per hour. The breakdown follow poisson distribution.
The productive time of a machine is considered to cost Rs. 20 per hour.
Two repairman Mr. X & Mr. Y have been interviewed for this purpose
Mr. X charged Rs. 100 per hour. and he services breakdown machines
at rate of 8 per hour. Mr. Y demand Rs. 140 per hour and he services at
an average rate of 12 per hour. Which repairmen should be hired?
(Assumes 8 hours shift per day).

[5860]-302 2
Q5) Solve any one of the following: [1×10=10]

a) Given the following:

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

Duration 3 4 4 5 4 2 2 3 2
(in days)

Construct the project network. Calculate project duration & determine

critical path.

b) Determine the optimal strategies for A & B in the following game. Obtain
value of game.

B’s Strategy

B1 B2 B3

A1 9 8 –7

A’s A2 3 –6 4

Strategy A3 6 7 7



[5860]-302 3
Total No. of Questions : 5] SEAT No. :
P2187 [5465]-2004
[Total No. of Pages : 4

M.B.A.
OCTOBER 2018
204 : DECISION SCIENCE
(2016 Pattern) ( Semester - II)
Time : 2 ¼ Hours] [Max. Marks : 50
Instructions to the candidates:
1) Each question has an internal option.
2) Each question carries 10 marks.
3) Graph paper will not be provided.
4) Use of non-scientific calculator is allowed.

Q1) Marketing manager has 5 salesmen & 5 sales districts considering the
capabilities of the salesman & the nature of the district, the marketing manager
estimates that sales & per month (in hundred Rs) for each salesman in each
district would be as follows. [10]
Sales district
Salesman A B C D E
1 32 38 40 28 40
2 40 24 28 21 36
3 41 27 33 30 37
4 22 38 41 36 36
5 29 33 40 35 39
What is a maximun sale that may be expected in an optimum assignment?
OR
A construction company moves material form three plants to three projects.
Project X requires 50 truck loads, project Y requires 75 and project Z require
50 truck loads. Plant A can supply 45 truck load per week plant B can supply
60 & plant C can supply 60. Using cost information given below determine
optimal transportation schedules for the company. [10]
Transportation cost per truck load in (Rs)
To/From X Y Z
A 40 80 30
B 60 70 90
C 80 20 50
Find initial solution by using VAM.
OR
P.T.O.
Q2) Use the graphical method to solve the following LPP [10]
Maximize Z = 100x + 100y.
Subject to the constraints.

6 x  4 y  24
4 x  2 y  16
3.5 x  3 y  21
x, y  0

OR
A bakery keeps stock of popular brand of cake. Daily demand based on past
experience is given below: [10]
Daily Demand 0 10 20 30 40 50
Probability 0.01 0.15 0.20 0.50 0.12 0.02
Using the following random numbers simulate the demand for next 10 days.
i) Find stock situation (unsold cake) if the owner of the bakery decides to
make 30 cakes every day.
ii) Also find average demand for the cakes on basis of simulated data.
Random Number : 45, 72, 56, 51, 79, 09, 61, 43, 31, and 81.

Q3) A manufacturing company faced with the problem of choosing from four
products to manufacture. The potential demand of each product may turn out
to be good, satisfactory or poor. The probabilities of each type of demand
are 0.6, 0.2 and 0.2 respectively. [10]
Profit in Rs.
Product Good Satisfactroy Poor
A 40,000 10,000 1,100
B 40,000 20,000 7,000
C 50,000 15,000 8,000
D 40,000 18,000 15,000
Advise the company about type of product to be manufacture using EMV
criterion. Determine expected value of perfect information. Ignore probability
and suggest optimum strategy using Hurwicz criteria (  = 0.7).
OR

[5465]-2004 2
 a) Following is the pay-off matrix in terms of increase in votes to
X (loss to Y) using three different starategies available to each player for
advertising. Find the optimum strategies adopted by X for the campaign.[5]

Candidate Y
Strategies I II III
I 300 200 100
Candidate
X

II 600 500 400

III 600 400 600
b) Explain the characteristics of queuing system. [5]

Q4) The following are the time estimates and the precedence relationships of the
activities in a project network. [10]
Activity A B C D E F G H I J K
Immediate - - - A B B C E D F,G H,1
Predecessor
Activity
Duration in
Weeks 4 7 3 6 4 7 6 10 3 4 2

Draw the project network diagram. Determine the critical path and the project
completion time.
OR
7 jobs are processed in three machines are given below. [10]
Jobs J1 J2 J3 J4 J5 J6 J7
Machines
M1 3 8 7 4 9 8 7
M2 4 3 2 5 1 4 3
M3 6 7 5 11 5 6 12
Determine optimal sequence of jobs and idle time of all three machines.

[5465]-2004 3
Q5) a) Tickets numbered from 1 to 20 are mixed up and a ticket is drawn at
random. What is the probability that the ticket drawn has a number which
is a multiple of 3 or 7? [5]
b) A card is drawn at random from a well shuffled pack. Find the probability
that card is [5]
i) An ace ii) Not diamond
OR
The Indian IT employees spent on an average 77 hours logged on to the
Internet while at work. Assume the times are normally distributed and that of
standard deviation is 20 hours. [10]
a) What is the probability a randomly selected employee spent fewer than
50 hours logged on to the Internet?
b) What precentage of employees spent more than 100 hours logged on to
the Internet?
c) What precentage of employee logged on to the internet between 50 to
100 hours?
Given that
Z 1.15 1.35
Area 0 to Z 0.3749 0.4115



[5465]-2004 4
Total No. of Questions : 5] SEAT No. :
P1430 [Total No. of Pages : 4
[5365]-2004
M.B.A.
204: DECISION SCIENCE APRIL 2018

(2016 Pattern) (Semester-II)

Time : 2¼Hours] [Max. Marks : 50
Instructions to the candidates:
1) Each question carry equal marks.
2) Each question has an internal option.
3) Graph paper will not be provided.
4) Non-Scientific calculator is allowed.
Q1) a) A computer center has four expert programmers. The center needs. four
application programs to be developed. The head of computer center
after carefully studying, estimates . The time required (in minutes) by the
expert to develop the application programm. Find the assignment schedule
so that time will be minimized. [10]
A B C D
Programes
1 120 100 80 90
Expert

2 80 90 110 70
3 110 140 120 100
4 90 90 80 90
OR
a) Discuss the role of quantitative techniques in decision making. Give an
example. [5]
b) Find the initial feasible solution using North-West corner method for the
given matrix. [5]
Store
A B C D Supply
I 10 20 5 7 10
Warehouse

II 13 9 12 8 20
III 4 15 7 9 30
IV 14 7 1 0 40
V 3 12 5 19 50
Demand 60 60 20 10 150
150
[5365]-2004 1 P.T.O.
Q2) Solve the following LPP graphically to maximize Z =3x+4y, subject to,
x + y ≤ 6, and 2x + y ≤ 8, where x ≥ 0, y ≥ 0. [10]
OR
The rainfall distribution of monsoon season is as follows.
Rainfall(in cm) 0 1 2 3 4 5
Frequency 50 25 15 5 3 2
Using the following random number-67,63,39,55,29,78,70,6,78, and 76,
simulate the rainfall for next 10 days and find the average rainfall. [10]

Q3) A businessman has three alternative actions that he can take. Each of the
action can be followed by any of the four posible events. The conditional
payoff for each action-event combination are as under. [10]
Nature
N1 N2 N3 N4
S1 4 0 -5 3
action

S2 -2 6 9 1
S3 7 3 2 4
Find the optimal strategy using:
a) Maxmini criteria
b) Laplace criteria and
c) Hurwicz criteria (α = 0.6)
OR
In a service department manned by one server, on an average one customer
arrives every 10 minutes. It has been found that each customer requires 6
minutes to be served find out. [10]
a) Probability that the server is idle.
b) Average queue length.
c) Average time spent by each. Customer in the system.
d) Probability that there would be 2 customers in the queue.

[5365]-2004 2
Q4) Following information is gathered for a project. [10]
Activity Preceding activity Duration(weeks)
A - 1
B A 3
C A 4
D A 3
E D 2
F B,C,E 4
G D 9
H D 5
I H 2
J F,G,I 2
a) Draw network diagram.
b) Determine critical path and its duration.
OR

We have seven jobs, each of which has to go through two machines A&B in
the order AB. The processing time for the jobs on the two machines (in hrs)
are given as,
Job 1 2 3 4 5 6 7
Machine A 3 12 15 6 10 11 9
Machine B 8 10 10 6 12 1 3
Determine the sequence of these jobs to minimized total elapsed time.T. [10]

Q5) A card is drawn froma pack of cards. What is the chance of drawing a red
queen given that the card drawn was a face card. [10]

OR

[5365]-2004 3
 In a sample of 1000 scores, the mean of a certain test is 14 and the standard
deviation is 2.5. Assuming the distribution to be normal, find. [10]

a) How many students have scored between 12 and 15 ?

b) How many scored above 18?

(Given Z at 0.8 = 0.2881

Z at 0.4 = 0.1554

Z at 1.6 = 0.4452)



[5365]-2004 4
Total No. of Questions : 5] SEAT No. :
P3865 [Total No. of Pages : 3
[5265] - 2006
M.B.A.
OCTOBER 2017
204 : DECISION SCIENCE
(2016 Pattern) (Semester - II)
Time : 2¼ Hours] [Max. Marks :50
Instructions to the candidates:
1) Each question has an internal option.
2) Each question carries 10 marks.
3) Graph paper will not be provided.
4) Non Scientific calculator is allowed.
Q1) A project manager has 4 subordinates and 4 task. His estimate of the time that
each would take to perform each task is given in the matrix below. How
should be the task allocated, so that the total man hours are minimized. [10]
I II III IV
1 8 26 17 11
2 13 28 4 26
3 38 19 18 15
4 19 26 24 10
OR
Find the initial feasible solution for a given transportation matrix to reduce the
cost using VAM method. [10]
D1 D2 D3 D4 Supply
01 5 3 6 2 19
02 4 7 9 1 37
03 3 4 7 5 34
90
Demand 16 18 31 25 90

Q2) Solve the given LPP using graphical method to maximize Z = 100x + 150y,
Subject to, 2x + y ≤ 30,
x + 3y ≤ 45
Where, x ≥ 0, y ≥ 0. [10]
OR

P.T.O.
 A bakery keeps stock of branded cake. Daily demand based on the past
experience and its probability is given below.
Demand 0 15 25 35 45 50
Probability 0.01 0.15 0.20 0.50 0.12 0.02
Consider the following sequence of random number - and
48, 78, 9, 51, 56, 77, 15, 14, 68 and 09.
a) Simulate the demand for next 10 days.
b) Find the Average demand of Cake.
c) Find the stock situation of cake at the end of each day, if the owner of
bakery decides to make 35 cakes every day. [10]

Q3) For the given profit matrix, find the optimal strategy using, [10]
a) Max Mini criteria.
b) Laplace criteria.
c) Hurwicz criteria (α = 0.7).
N1 N2 N3 N4
S1 30 10 10 8
S2 40 –15 5 7
S3 50 20 –6 10
OR
Solve the following game using dominance rule. [10]
Player B
Strategy 1 2 3 4 5
I 1 3 2 7 4
Player A

II 3 4 1 5 6
III 6 5 7 6 5
IV 2 0 6 3 1

Q4) We have 5 jobs each of which must go through the machines A, B & C. in the
order ABC. Processing time in (hrs.) is as follows : [10]
Job 1 2 3 4 5
Machine A 5 8 6 9 5
Machine B 2 1 4 5 3
Machine C 3 7 5 6 7
Determine the sequence of the jobs that will minimize the total elapsed time.
Also find the idle time for all machines as well.
OR
[5265] - 2006 2
 Write short notes on (any Two) : [10]
a) Concept of PERT and CPM.
b) Concept of Network diagram with example.
c) Dummy activities and events with example.
d) Floats and its types with example.

Q5) A box contains 6 white and 8 red balls. The Second box contain 9 white and
10 red balls. One ball is drawn at random from the first box and put in the
second box without noticing its colour. A ball is drawn at random from Second
box. What is a probability that it is red? [10]
OR
In an intelligence test administered to 1000 students, the average score was 42
and the standard deviation 24. [10]
Find -
a) The number of students lying between 30 and 54 marks.
b) The value of score exceeded by top 100 students.
(Given Z at 0.5 = 0.1915, Z at 1.28 = 0.4).

llll

[5265] - 2006 3
Total No. of Questions : 10] SEAT No. :

P3929 [Total No. of Pages : 4

[4970] - 2004
M.B.A. (Semester - II)
204 : DECISION SCIENCE APRIL 2016

(2013 Pattern)
Time : 2½Hours] [Max. Marks : 50
Instructions to the candidates :-
1) Attempt 5(five) questions.
2) Each questions has an internal option.
3) Each question carry equal marks.(10)
4) Figures to the right indicate mark for questions.
5) Graph will not be provided, Draw a diagram on answer sheet.
6) Non Scientific calculator is allowed.

Q1) Solve the following problem for maximizing the Production output. The
data refers to the production of an article for the given operators and
machines. [10]
Machines
Operators A B C D
1 10 5 7 8
2 11 4 9 10
3 8 4 9 7
4 7 5 6 4
5 8 9 7 5
OR
Q2) Solve the following L.P.P. using graphical method [10]
Minimize Z = 6X1 + 14X2
Subject to 5X1 + 4X2 > 60
3X1 + 7X2 < 84
X1 + 2X2 > 18
X1, X2 > 0

P.T.O.
Q3) In a bank on an average every 15 min a customer arrives for cashing the
cheque. The staff at the payment counter takes 10 min for serving a customer
on an average. [10]
Calculate :
a) Probability that system is busy.
b) Average Queue Length.
c) Average no of customers in the bank.
d) Average waiting time of customer in queue before sevice.
OR
Q4) At a bus depo every bus should leave with driver. At the terminus they
should keep two drivers as reserved if anyone on scheduled duty is sick and
could not come following is the Probability distribution that driver become
sick. [10]
No of Sick drivers 0 1 2 3 4 5
Probability 0.30 0.20 0.15 0.10 0.13 0.12
Simulate for 10 days and find utilization of reserved drivers. Also find how
many days and how many buses cannot run because of non Availability of
the drivers.
Use following random numbers 30,54,34,72,20,02,76,74,48,22.

Q5) Solve the following game using Principle of Dominance. [10]

Player B
Player A I II III IV V VI
1 4 2 0 2 1 1
2 4 3 1 3 2 2
3 4 3 7 –5 1 2
4 4 3 4 –1 2 2
5 4 3 3 –2 2 2
OR

[4970]-2004 2
Q6) A farmer wants to decide which of the 3 crops he should plant. The farmer
has categorized the amount of rainfall as High, Medium and Low, Extimated
profit is given below. [10]
Rainfall Estimated Profit (in Rs.)
Crop A Crop B Crop C
High 8000 3500 5000
Medium 4500 4500 4900
Low 2000 5000 4000
Farmer wishes to Plant one crop. Decide the best crop using.
a) Hurwicz Alpha Criterion (Coefficient of Optimism a = 0.6)
b) Laplace Criterion
c) Minimax Regret Criterion

Q7) The following information is gather for a project : [10]

Activity Preceding Activity Duration
A - 1
B A 3
C A 4
D A 3
E D 2
F B,C,E 4
G D 9
H D 5
I H 2
J F,G,I 2
a) Draw the Network Diagram.
b) Determine the Critical Path and Project Duration.

OR

Q8) Write short Notes on.

a) Concept of Network diagram with example. [5]
b) Dummy Activities and events with example. [5]

[4970]-2004 3
Q9) a) What is the probability that a leap year selected at random will have 53
Mondays? [5]
b) The daily production (in number of units) for a week in a factory is
56,59,62,57,53,60,66 units. If it is checked at random on a day, what
is the probability that it will be less than the average? [5]
OR

Q10)a) There are three stock items, each of which can be substituted for the
other. Each has stock out probability of 0.03 and is independent of
others. The material manager wants to know the probability that [5]
i) All item are in stock
ii) No item in stock.
b) A card is drawn at random from a well shuffled Pack. Find the
Probability that [5]
i) It is not a spade
ii) It is a face card.

eee

[4970]-2004 4
Total No. of Questions : 10] SEAT No. :
P3793 [4870]-2004
[Total No. of Pages : 4

M.B.A.
OCTOBER 2015
204 : DECISION SCIENCE
(2013 Pattern) (Semester - II)

Time : 2½ Hours] [Max. Marks : 50

Instructions to the candidates:
1) Attempt Five questions.
2) Each question has an internal option.
3) Each question carries 10 marks.
4) Figures to the right indicate marks for question.
5) Graph will not be provided, draw neat diagrams on answer sheet only, if required.
6) Non scientific calculator is permitted.

Q1) A company wants to give advertisements in two local news papers, one Hindi
and one English. Expected coverage through the Ads, is 1000 and 1500 people
per ads. respectively. Each Ads in a Hindi costs Rs. 3000/- and for an English
is Rs. 5000/-. Company decided not to place more than 10 ads, in the Hindi
and at least 6 ads. in the English daily. The Total advertisement budget is
Rs, 50,000/-. Formulate the problem as L.P. Model. [10]
OR

Q2) Four different machines have four different jobs. The following matrix gives
the costs in rupees of job on machine. The set up and take down time costs
are assumed to be prohibitively high for changovers. How should the jobs be
assigned to the various machines so that the total costs is minimised. [10]
Machines
M1 M2 M3 M4
J1 5 7 11 6
Jobs J2 8 5 9 6
J3 4 7 10 7
J4 10 4 8 3

P.T.O.
Q3) A person wants to hire for repairing machines which breakdown at on average
rate per hour, which following Poisson Distribution. A and B two repairmen
interviewed. ‘A’ charges Rs. 100/- per hour and services breakdown machines
at the rate of 6 per hour. B demands Rs. 125/- per hour and services at an
average of 8 machines per hour. Downtime of a machine costs Rs. 25/- per
hour, which repairman should be hired? [10]

OR

Q4) Three brands of product P, Q and R are having market share as 30%, 30%
and 40% respectively. Customers shifts their brands. Brand switching matrix
every quarter is given below: [10]

From To

A B C
A 50% 30% 20%

B 20% 70% 10%

C 20% 20% 60%

Find market share at the end of quarter.

Q5) A production unit is not knowing the product acceptance probability and the
data are given below: [10]
Anticipated 1st year profit Rs. ‘000
Accpetance
Product Full Partial Minimal
Good 8 70 50
Fair 50 45 40
Poor –25 –10 0
Determine the optimal decision under each of the following criteria :
a) Maximax
b) Maximin
c) Minimax Regret
OR

[4870]-2004 2
Q6) Player A and B are playing with the following Matrix. [10]
Player B
Player A 1 2 3 4 5
I 1 3 2 7 4
II 3 4 1 5 6
III 6 5 7 6 5
IV 2 0 6 3 1

Solve the following game by using Dominance Rule.

Q7) Write short notes on (any two): [5 + 5 = 10]

a) Concept of PERT and CPM.
b) Concept of Network diagram with example.
c) Dummy Activities and events with example.
d) Floats and its types with example.
OR
Q8) Draw the network diagram for the following list of activities: [10]
Activity Immediate Activity Immediate
Predecessor Predecessor
A - L K
B A M K
C B N K
D C O D
E D P O
F E Q B
G E R N
H C S L, M
I C, F T S
J G, H, I U P, Q
K J V U

[4870]-2004 3
Q9) a) A card is drawn from ordinary pack and a gambler bets that it is a spade
or an ace. What are the odds against his winning this bet?
b) What is the chance that a leap year, selected at random will contain 53
sundays?
[5 + 5 = 10]

OR
Q10)Find the probability distribution of the number of sixes in three tosses of a
dice. [10]

E E E

[4870]-2004 4