The document is an assignment guide for MBA students, detailing topics in operations research for the summer 2015 program. It provides questions regarding features of operations research, linear programming, Vogel’s approximation method, integer programming, Monte Carlo simulation, and game theory. Students are instructed to send their semester and specialization to a specified email for fully solved assignments.

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ASSIGNMENT
DRIVE SUMMER 2015
PROGRAM MBA/ MBADS/ MBAFLEX/ MBAHCSN3/ PGDBAN2
SEMESTER II
SUBJECT CODE & NAME MB0048 - OPERATIONS RESEARCH
BK ID B1631
CREDITS 4
MARKS 60
Note: Answer all questions. Kindly note that answers for 10 marks questions should be
approximately of 400 words. Each question is followed by evaluation scheme.
Q. 1. What are the features of operations research? What are the limitations of operations
research?
Answer:Operations research OR means to apply scientific and mathematical methods for decision
making and problem solving.
OR doesnotprovide decisionselse itprovidesquantitative datato the managers. The managers use
this data for making decisions.
OR tries to find better solutions to different problems. Hence, it is used to solve complex
management problems.
Q. 2. a. Explain the graphical method of solving Linear Programming Problem.
Answer:Linear programming (LP; also called linear optimization) is a method to achieve the best
outcome (suchas maximumprofitorlowestcost) ina mathematical modelwhose requirements are
represented by linear relationships. Linear programming is a special case of mathematical
programming (mathematical optimization).
More formally,linearprogrammingisatechnique forthe optimizationof alinearobjective function,
subject to linear equality and linear inequality

2. b. A furniture manufacturing company plans to make two products: chairs and tables- from its
available resources, which consists of 400 board feet of mahogany timber and 450 man-hours of
labour. It knows that to make a chair requires 5 board feet and 10 man-hours and yields a profit of
Rs.45 while each table uses 20 board feet and 15 man-hours and has a profit of Rs.80.
Formulate the LPP to maximise the profit.
Answer: Linear programming models consist of an objective function and the constraints on that
function. A linear programming model takes the following form:
Objective function:
Z = a1X1 + a2X2 + a3X3 + . . . + anXn
Q. 3. a. List the steps of the Vogel’s Approximation Method(VAM) to find the initial feasible
solution.
Answer:The Vogel approximation method (Unit cost penalty method) is an iterative procedure for
computinga basicfeasible solution of a transportation problem. This method is preferred over the
twomethodsdiscussedinthe previoussections,becausethe initial basic feasible solution obtained
by this method is either optimal or very close to the optimal solution.
Steps in Vogel Approximation Method (VAM)
The standard instructions are paraphrased below:
b. The XYZ manufacturing company has a current transportation schedule which is being
questioned by the top management as to whether or not it is optimal. The firm has 3 factories and
5 warehouses. The unit transportation costs (in Rs.), factory capacities, and ware house
requirements are given below. Find the initial feasible solution using Vogel’s Approximation
Method (VAM).
Answer:The taskis to use VAMto allocate contractorsto tasks. Itscalesto large problems,soideally
keep sorts out of the iterative cycle. It works as follows:
 Step 1: Balance the given transportation problem if either (total supply>total demand) or
(total supply<total demand)
 Step 2: Determine the penalty cost for each row and column by subtracting the lowest cell
cost in the row or column from the next
Q. 4. a. What is Integer Programming Problem (IPP) ?

3. Answer: Anintegerprogrammingproblem is a mathematical optimization or feasibility program in
whichsome or all of the variables are restricted to be integers. In many settings the term refers to
integerlinearprogramming(ILP),inwhichthe objectivefunctionandthe constraints(other than the
integer constraints) are linear. Integer programming is NP-hard. A special case, 0-1 integer linear
programming, in which unknowns are binary, and
b. Explain Gomory’s all integer algorithm of an IPP.
Answer:A Gomory's Cut is a linear constraint with the property that it is strictly stronger than its
Parent,butit doesnotexclude anyfeasible integersolutionof the LP problem under consideration.
It isused, in conjunction with the Simplex Method, to generate optimal solutions to linear integer
programmingproblems(LIP).Formallythe LP and LIP problems under consideration are as follows:
LP: opt ctx subject to Ax = b, x >= 0
LIP: opt ctx subject to Ax = b, x >= 0 and integer
Q. 5. a. Explain Monte Carlo Simulation.
Answer: Monte Carlo simulation is a computerized mathematical technique that allows people to
account forrisk inquantitative analysisanddecisionmaking.The techniqueis used by professionals
insuch widelydisparate fieldsasfinance,project management,energy,manufacturing,engineering,
research and development, insurance, oil & gas, transportation, and the environment.
Monte Carlo simulation
b. A Company produces 150 cars. But the production rate varies with the distribution.
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 Probability Cumulative probability RN Range
147 0.05 0.05 00 –04
148 0.10 0.15 05 – 14
149 0.15 0.30 15-29
150 0.20 0.50 30 – 49
151 0.30 0.80 50 – 79
152 0.15 0.95 80 – 94
153 0.05 1.00 95 – 99
Simulation for 10 days using the given random numbers

4. Q. 6. a. Explain the dominance principle in game theory
Answer: Ingame theory,strategicdominance (commonlycalledsimplydominance) occurswhenone
strategyisbetterthan anotherstrategyfor one player, no matter how that player's opponents may
play. Many simple games can be solved using dominance. The opposite, intransitivity, occurs in
gameswhere one strategymaybe betteror worse than another strategy for one player, depending
on how the player's opponents may play.
c. Differentiate between PERT and CPM
Answer:CPM and PERT (Program Evaluation and Review Technique) are most commonly used
methods for project management. There are some similarities and differences between PERT and
CPM. PERT can be appliedtoanyfield requiring planned, controlled and integrated work efforts to
accomplish defined objectives.CPM/
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
help.mbaassignments@gmail.com
or
call us at : 08263069601