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PROGRAM - MBA -
SEMESTER II
SUBJECT CODE & NAME - MB0048 - OPERATIONS RESEARCH
1. Discuss the
various stages involved
in the methodology
of Operations Research.
Briefly explain the techniques and tools of Operations Research.
Operations Research Methodology
1. Definition: The first and the most important step in the OR
approach of problem solving is to define the problem. One needs to ensure that the problem is identified
properly because this
problem statement will
indicate the following
three major aspects:
·
Description of the goal or the objective of the
study
2. a. Explain the steps involved
in linear programming problem formulation.
Discuss in brief the advantages of linear programming.
The procedure
for mathematical formulation
of a linear
programming problem consists of the following major steps:
Step: 1 : - Study the
given situation to find the key decisions to be made
Step: 2 : - Indentify
the variables involved and designate them by symbols Xj (j = 1,2)
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2. b. Alpha Limited produces & sells two different products under the
brand names black & white. The profit per unit on these products in Rs. 50
& Rs. 40 respectively. Both the products
employ the same manufacturing process which has a fixed total capacity
of 50,000 man-hours. As per the
estimates of the
marketing research department
of Alpha Limited, there is a market demand for maximum 8,000 units of
Black & 10,000 units of white. Subject to the overall demand, the products can be sold in any
possible combination. If it takes 3 hours to produce one unit of black & 2
hours to produce one unit of white, formulate the model of linear programming.
Answer:
Let X1 and X2
be the quantity of two product x and y produced
So they can produce X1
+ X2 <= 8000+10,000 due to restrictions of demand,
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3. a. What is degeneracy in
transportation problem? How it can be resolved?
Degeneracy in transportation problem: A basic
solution to an
m-origin, n destination
transportation problem can have at the most m+n-1 positive basic
variables (non-zero), otherwise the basic
solution degenerates. It
follows that whenever
the number of
basic cells is less than m + n – 1, the transportation problem is a
degenerate one.
3. b. Solve the following transportation problem using Vogel’s
approximation method.
|
Factories
|
Distribution Centres
|
Supply
|
|||
|
C1
|
C2
|
C3
|
C4
|
|
|
|
F1
|
3
|
2
|
7
|
6
|
50
|
|
F2
|
7
|
5
|
2
|
3
|
60
|
|
F3
|
2
|
5
|
4
|
5
|
25
|
|
Requirements
|
60
|
40
|
20
|
15
|
|
Answer:
|
Factories
|
Distribution Centres
|
Supply
|
Row difference
|
|||||||||||
|
C1
|
C2
|
C3
|
C4
|
|
Round - 1
|
Round - 2
|
Round - 3
|
Round - 4
|
||||||
|
F1
|
3 (10)
|
2 (40)
|
7
|
6
|
50
|
1
|
3-2
|
3
|
6-3
|
x
|
X
|
x
|
x
|
|
|
F2
|
7 (25)
|
5
|
2 (20)
|
3 (15)
|
60
|
1
|
3-2
|
1
|
3-2
|
1
|
3-2
|
1
|
3-2
|
|
Service charges as Rs. 150 per assignment.
4. a. Explain the steps in Hungarian method. Differentiate between Transportation and
Assignment problem.
Hungarian method
algorithm is based
on the concept
of opportunity cost and
is more efficient
in solving assignment
problems. The following
steps are adopted to solve an AP using the Hungarian method algorithm.
Step 1: Prepare row ruled matrix by selecting the minimum values
for each row and subtract it from the other elements of the row.
4. b. Find the
optimal assignment of
four jobs and
four machines when
the cost of assignment is given by the following
table:
|
J1
|
J2
|
J3
|
J4
|
|
|
M1
|
10
|
9
|
8
|
7
|
|
M2
|
3
|
4
|
5
|
6
|
|
M3
|
2
|
1
|
1
|
2
|
|
M4
|
4
|
3
|
5
|
6
|
Answer:
The same as each row &
column’s minimum value is zero.
Row
Reduced Matrix:
|
|
J1
|
J2
|
J3
|
J4
|
|
M1
|
3
|
2
|
1
|
[0]
|
|
M2
|
[0]
|
1
|
2
|
3
|
Service charges as Rs. 150 per assignment.
5. Define Simulation. Explain the
Simulation procedure. Discuss
the use of Simulation with an
example.
Meaning of Simulation: Simulation is also called experimentation in
the management laboratory.
While dealing with
business problems,
simulation is often
referred to as
‘Monte Carlo Analysis’.
Two American mathematicians, Von
Neumann and Ulan,
in the late
1940s, found a problem
in the field
of nuclear physics
too complex for
analytical solution and too
dangerous for actual
6 Explain the following:
a. Integer programming model
b. PERT and CPM
c. Operating Characteristics of a Queuing System
a. Explanation of Integer programming model
The IPP
is a special
case of Linear Programming
Problem (LPP), where
all or some
variables are
constrained to
assume non-negative integer
values. In LPP,
the decision variables as well as
slack or surplus variables were allowed to take any real or fractional value.
However, there are certain real life
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