ITM 341
Advanced
Operations Research
(For CNM
Cases)
Assignment - II
Assignment Code: 2016ITM341A2 Last Date
of Submission: 30th April 2016
Maximum
Marks:100
Attempt all the questions.
All the questions are compulsory and carry equal marks.
Section-A
Ques. 1 Write
Short note to explain the following:
a) Use of Sensitivity Analysis in Linear
Programming. Particularly highlight the use
of
“Shadow
Prices” and “Reduced Cost”.
b) Use of Goal Programming. How it differs
from Linear Programming?
Ques. 2 Use Simplex method to solve the
following L.P. problem.
Maximize : Z = 2X1 – X2 + X3
Subject to the
constraint:
3X1 + X2 + X3
≤ 60
X1 -
X2 + 2X3 ≤ 10
X1 +
X2 - X3 ≤ 20
X1,
X2, X3 ≥ 0
Ques. 3 Write
short note on the following:
a) Zero –
Sum Game
b) Pure
and Mixed Strategies in Game theory
c) Using Utility concept to arrive at decisions
d) Assumptions that are made for switching
problems in Markov Chain.
Ques. 4 Explain
the following in a Transportation Problem.
a) How to find that there are multiple solution
b)
What meant is degeneracy. What does it signify about the nature of the
constraints.
c) What
are the methods by which an Initial Feasible solution can be obtained.
Section-B
Case Study
A firm has developed a new storage
device for computers and must now decide what do with the idea. The expected
life of the product is 10 years. One possibilities to immediately least the
products rights to a different company which will market and sell the product.
The form expects to gain Rs. 2.25Cr as fees. Two other possibilities exists.
These are to build a large manufacturing plant now to product the product or
build a small plant now to produce the produce with the option to expand the
plant in 4 years. The expected payoff from producing the product depends on the
market acceptance of the product in the first 4 years and during the last 6
years. If the market acceptance of the product in the first 4 years is low, the
firm will stop production and reduce losses at this point. It is felt that
there is a 70% chance of high market acceptance for the product in the first 4
years. If the market acceptance is high in the first 4 years the probability of
a high market acceptance in the next years is 60%. The following table given
the net payoff’s estimated in crores of Rupees for the product.
|
Market acceptance
|
|
|
|
|
|
First 4 years
|
Next 6 years
|
Large plant
|
Small plant Don’t
expand
|
Small plant Expand
|
|
High
|
High
|
7.5
|
5
|
6
|
|
High
|
Low
|
2
|
3
|
2
|
|
low
|
-
|
(1)
|
1.5
|
-
|
You are required to give your recommendation
to the firm ?
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