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Master of
Business Administration- MBA Semester 2
MB0048-Operations
Research-4 Credits
(Book ID:
B1631)
Assignment (60 Marks)
Note: Answer all questions within 300 to 400 words
each. Each Question carries 10 marks 6 X 10=60
Q1. Discuss the methodology of
Operations Research. Explain in brief the phases of Operations Research.
Answer. a). The basic dominant characteristic
feature of operations research is that it employs mathematical representations
or models to analyze problems. This distinct approach represents an adaptation
of the scientific methodology used by the physical sciences. The scientific
method translates a real given problem into a mathematical representation which
is solved and retransformed into the original context. The OR approach to
Q2. a. Explain the graphical method
of solving Linear Programming Problem.
b. A paper mill produces two grades
of paper viz., X and Y. Because of raw material restrictions, it cannot produce
more than 400 tons of grade X paper and 300 tons of grade Y paper in a week.
There are 160 production hours in a week. It requires 0.20 and 0.40 hours to
produce a ton of grade X and Y papers. The mill earns a profit of Rs. 200 and
Rs. 500 per ton of grade X and Y paper respectively. Formulate this as a Linear
Programming Problem.
Answer. a). Linear programming (LP,
or linear optimization) is a mathematical method for determining a way to achieve the best
outcome (such as maximum profit or lowest cost) in a given mathematical model
for some list of requirements represented as linear relationships. 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 decision variables to be made.
Step 2:
Identify the variables involved and
Q3. a. Explain how to solve the
degeneracy in transportation problems.
b. Explain the procedure of MODI
method of finding solution through optimality test.
Answer. a). Degeneracy in
transportation problem
If the basic
feasible solution of a transportation problem with m origins and n destinations
has fewer than m + n – 1 positive (occupied cells), the problem is said to be a
degenerate transportation problem.
Degeneracy
can occur at two stages:
1. at the
initial solution
2. during
the testing of the optimal solution
To resolve
degeneracy,
Q4. a. Explain the steps involved in
Hungarian method of solving Assignment problems.
b. Find an optimal solution to an
assignment problem with the following cost matrix:
|
|
J1
|
J2
|
J3
|
J4
|
|
M1
|
10
|
9
|
7
|
8
|
|
M2
|
5
|
8
|
7
|
7
|
|
M3
|
5
|
4
|
6
|
5
|
|
M4
|
2
|
3
|
4
|
5
|
Answer. a). Hungarian method algorithm is based on the concept of
opportunity cost and is more efficient in solving assignment problems. Adopt
the following steps mentioned below 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 other elements of the row.
Step 2:
Prepare column reduced matrix by subtracting minimum value of the column from
the other values of that
Q5. a. Explain Monte Carlo
Simulation.
b. A Company produces 150 cars. But
the production rate varies with the distribution.
|
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 track will hold 150
cars. Using the following random numbers determine the average number of cars
waiting for shipment in the company and average number of empty space in the
truck. Random Numbers 82, 54, 50, 96,
85, 34, 30, 02, 64, 47.
Answer. a). Monte Carlo simulation is a computerized mathematical
technique that allows people to account for risk in quantitative analysis and
decision making. The technique is used by professionals in such widely
disparate fields as finance, project management, energy, manufacturing,
engineering, research and development, insurance, oil & gas,
transportation, and the environment.
Monte Carlo
simulation furnishes the decision-maker with a range of possible outcomes and
the probabilities they will occur for any choice of action
Q6. a. Explain the dominance
principle in game theory.
b. Describe the Constituents of a
Queuing System.
c. Differentiate between PERT and CPM.
Answer. a). Dominance principle in
game theory,
At times, a
convex combination of two or more courses of action may dominate another course
of action. Whenever a
course of action
(say A s or B q ) is dominated by others, then that course of action ( A
s or B q ) can be deleted from the pay-off matrix. Such a deletion will not
affect the choice of the solution, but it reduces the order of
Spring-2015
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assignments at nominal price of Rs.120 each.
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