M.C.A-M.C.A 4th Sem BM E2 - 412: (Elective) FOUNDATION OF DECISION PROCESSES(University of Pune, Pune-2013)
M.C.A. (Management Faculty) (Semester - IV)
Examination, 2013
BM E2 - 412: (Elective) FOUNDATION OF DECISION PROCESSES
(2008 Pattern)
Time : 3 Hours Max. Marks : 70
Instructions : i) Question No.1 is compulsory.
ii) Solve any two questions from remaining.
iii) Figures to the right indicate full marks.
iv) Use of electronic calculator is allowed.
1. a) At a bus terminal every bus should leave with driver. At the terminus they
keep 2 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 drivers.
Use the following random numbers : 30, 54, 34, 72, 20, 02, 76, 74, 48, 22.
b) Explain the elementary queuing system in detail.
c) Solve the following game :
Player Y
Y1 Y2 Y3
X1 1 2 7
Player X
X2 6 7 2
X3 6 6 1
2. a) A student tries to be punctual for the classes. If he is late on a day he is 80%
sure to be on time the next day. If he is on time then there is 20% chance that
he will be late on the next day. How often in the long run is he expected to
be late for the class ?
b) Customers arrive at a one window ticket counter according to a Poisson
distribution with a mean of 10 minute and service time per customer is exponential with a mean of 6 minutes.
The space in front of ticket counter can accommodate only three customers including the serviced one. Other
customers have to wait outside this space. Calculate :
1) Probability that customer can come directly to the space in front of the
ticket window.
2) Probability that an arriving customer will have to wait outside the directed
space.
3) How long an arriving customer is expected to wait before getting the service ?
4) Utilization parameter of the entire system.
5) Probability that a customer has to wait for more than 10 minutes in the
system.
3. a) Book-store sales a particular book of a Tax Laws for Rs. 250. It purchases
the book for Rs. 200 per copy. Since some of the tax laws changes every
year become outdated and the book can be disposed at Rs. 130 each.
According to past experience the annual demand for this book is between 18 to 23 copies.
Assuming that the order for this book can be placed only once during a year. The problem
before the stock manager is to decide how many copies of the book should be purchased for the next year.
From the past data, the probability distribution of number of copies sold is as
follows :
No. of copies sold 18 19 20 21 22 23
Probability 0.05 0.10 0.30 0.40 0.10 0.05
Calculate the VPI and find optimal strategy. 10
b) Define Markov Chain. Explain the concept of Markov Chain with suitable
example. 10
4. a) You are given the following estimates concerning a Research and Development
programme : 10
Decision Prob. of Outcome Prob. of Payoff Value
Di Decision Di Number Outcome Xi Outcome Xi
Given Given Di (Rs '000)
Research P(Xi/Di)
P(Di/R)
Develop 0.5 1 0.6 600
2 0.3 -100
3 0.1 0
Do not 0.5 1 0.6 600
develop 2 0.0 -100
3 1.0 0
Construct and evaluate the decision tree diagram for the above data and
identify the most optimal decision. Show your calculations for evaluation.
b) State the axioms of utility. Explain the use of utility theory in Decision Making
with suitable example.
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| Earning: ₹ 7.10/- |
