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Transcript
Get fully solved assignment, plz drop a mail with your sub code
[email protected]
Charges rs 125/subject and rs 700/semester only.
if urgent then call us on 08791490301, 08273413412
our website is www.smuassignment.in
DRIVE- Fall 2014
PROGRAM-MBADS / MBAN2 / MBAHCSN3 / PGDBAN2 / MBAFLEX
SEMESTER- II
SUBJECT CODE & NAME- MB0048 OPERATIONS RESEARCH
Q1 Explain the types of Operations Research Models. Briefly explain the phases of Operations
Research. (Meaning of Operations Research, Types of Operations Research Models, Phases of
Operations Research) 2,4,4
Answer:
Definitions of operations research
Churchman, Aackoff, and Aruoff defined operations research as “the application of scientific methods,
techniques and tools to the operation of a system with optimum solutions to the problems” where
'optimum' refers to the best possible alternative.
The objective of OR is to provide a scientific basis to the decision-makers for solving problems involving
interaction with various components of the organisation. This can be achieved by employing a team of
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.
Graphical Methods to Solve LPP
While obtaining the optimal solution to an LPP by the graphical method, the
statement of the following theorems of linear programming is used:
 The collection of all feasible solutions to an LPP constitutes a convex set whose extreme points
correspond to the basic feasible solutions.
 There are a finite number of basic feasible regions within the feasible solution space.
 If the convex set of the feasible solutions of the system of simultaneous equation is a convex
polyhedron, then at least one of the extreme points gives an optimal solution.
 If the optimal solution occurs at more than one extreme point, the value of the objective function
will be the same for all convex combination of these extreme points.
Q3. a. Explain how to solve the degeneracy in transportation problems.
b. Explain the procedure of MODI method of finding solution through optimality test.
(a. Degeneracy in transportation problem, b. Procedure of MODI method ) 5, 5
Answer:
a. 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. The degeneracy can
develop in two ways:
Case 1 - The degeneracy develops while determining an initial assignment via any one of the initial
Q4.
a. Explain the steps involved in Hungarian method of solving Assignment problems.
b. What do you mean by unbalanced assignment problem? How do you overcome it?
Answer.
a.)
Hungarian Method Algorithm
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.
Step 2: Prepare column-reduced matrix by subtracting minimum value of the column from the other
values of that column.
Q5. A) Explain Monte Carlo Simulations.
Answer: Monte Carlo simulations, a statistical technique used to model probabilistic (or “stochastic”)
systems and establish the odds for a variety of outcomes. The concept was first popularized right after
World War II, to study nuclear fission; mathematician Stanislaw Ulam coined the term in reference to an
uncle who loved playing the odds at the Monte Carlo casino (then a world symbol of gambling, like Las
Vegas today). Today there are multiple types of Monte Carlo simulations, used in fields from particle
physics to engineering, finance and more.
B) A Company produces 150 cars. But the production rate varies with the distribution.
Production 147
148
149
150
151
152
153
rate
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.
Production rate and probability
Q6.
a. Explain the dominance principle in game theory.
b. Describe the Constituents of a Queuing System.
c. Differentiate between PERT and CPM
a.
Dominance
In a rectangular game, the pay-off matrix of player A is pay-off in one specific row ( r row ) th exceeding
the corresponding pay-off in another specific row( s row ) th . This means that whatever course of action is
adopted by player B, for A, the course of action Ar yields greater gains than the course of action As .
Therefore, Ar is a better strategy than As irrespective of B’s strategy. Hence, you can say that Ar
dominates As . Alternatively, if each pay-off in a specific column ( p column ) th is less than the
Get fully solved assignment, plz drop a mail with your sub code
[email protected]
Charges rs 125/subject and rs 700/semester only.
if urgent then call us on 08791490301, 08273413412
our website is www.smuassignment.in