## field ## Wednesday, 30 October 2013

### MB0048 - OPERATIONS RESEARCH

Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
help.mbaassignments@gmail.com
or
call us at : 08263069601

ASSIGNMENT

 DRIVE FALL 2013 PROGRAM MBADS / MBAN2 / MBAHCSN3 / PGDBAN2 / MBAFLEX 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.

1. Discuss the methodology of Operations Research. Explain in brief the phases of Operations Research.
Answer : Meaning of Operations Research
Operations research (OR) is an analytical method of problem-solving and decision-making that is useful in the management of organizations. In operations research, problems are broken down into basic components and then solved in defined steps by mathematical analysis.

Methodology of Operations Research :

1. Operational Research Techniques. Some methodological aspects of operational research, and some of the main OR techniques, including: Critical Path Analysis, Production, Scheduling, Markov Chains, Queueing Theory, Replacement, Simulation, Stock Control, Dynamic Programming, Decision Theory, Theory of Games. OR202.
2.  Mathematical Programming. Linear programming: from the most basic introduction to sufficient conditions for optimality; duality; sensitivity of the solution; discovery of the solution to small problems by graphical methods, and proof of optimality by testing the sufficient conditions; solution to larger problems by using a computer package. The transportation programme: properties of solution, connection with graph theory, an

2. a. Explain the graphical method of solving Linear Programming Problem.
1.       Initially we draw the coordinate system correlating to an axis the variable x, and the other axis to variable y, as can see in the figure.

2.       We mark, in these axis, a numerical scale appropriate to the values it can take the variables according to the constraints of the problem. To do this work, for each constraint we must to void all variables except the related to a certain axis, so we establishing the right value for such axis. This process must be done for every axis.

3.       Following, we represent all constraints. We take the first one and we draw the line that is obtained by considering the constraint as an equality. In the figure, this is represented with the A-B edge, and the region that

b. A firm produces three types of products viz., A, B and C, which are processed on three different machines viz., M1, M2 and M3. The time required to process on unit of each of the products and the daily capacities of machines available per day are given in the following table. The profit earned by selling one unit of type A, B and C is Rs.10, Rs.15 and Rs.20 respectively. It is assumed that what all is produced is consumed in the market. Formulate this as Linear Programming Problem to maximize the profit.

 Machines Time per unit (minutes) Machine capacity available (min.) Product A Product B Product C M1 5 3 2 400 M2 4 - 3 500 M3 5 2 1 300

3.Explain the steps involved in finding Initial Basic Feasible solution by the following methods:

a. North West Corner Rule method
Answer : North West Corner Rule:

Step 1: The first assignment is made in the cell occupying the upper left hand (North West) corner of the transportation table. The maximum feasible amount is allocated there, that is X11 = min (a1, b1).

So that either the capacity of origin O1 is used up or the requirement at destination D1 is satisfied or both. This value of X11 is entered in the upper left hand corner (Small Square) of cell (1, 1) in the transportation table.

Step 2: If b1 > a1 the capacity of origin O, is exhausted but the requirement at destination D1 is still not satisfied, so that at least one more other variable in the first column will have to take on a positive value. Move down vertically to the second row and make the second allocation of magnitude X21 = min (a2, b1 – x21) in the cell

b. Vogel’s approximation method

Steps of the Vogel’s Approximation Method to get the initial solution
1) Consider each row of the cost matrix individually and find the difference between two least cost cells in it. Then repeat this for each column. Identify the row or column with the largest difference (select any one in case of a tie).

2) Now consider the cell with minimum cost in that column (or row) and assign the maximal possible units to that cell.

3) Delete the row/column, if it is satisfied.

4) Again start with step 1 and calculate the differences, proceed in the same manner as stated in earlier paragraph and continue until all units have been assigned.

4. Explain Monte Carlo Simulation method. What are the advantages and limitations of Simulation?
Answer : Monte Carlo simulation is a computerized mathematical technique that allows people to account for variability in their process to enhance 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.

The expression "Monte Carlo method" is actually very general. Monte Carlo (MC) methods are stochastic techniques--meaning they are based on the use of random numbers and probability statistics to investigate problems. You can find MC methods used in everything from economics to nuclear physics to regulating the flow of traffic. Of course the way they are applied varies widely from field to field, and there are dozens of subsets of MC even within chemistry. But, strictly speaking, to call something a "Monte Carlo" experiment, all you need to do is use random numbers to examine some problem.

5. Explain the Characteristics and Constituents of a Queuing System.
Answer : Meaning of Queuing Theory:
In general, a queueing system involves customers who enter the system, wait in line (a queue), are served, and leave the system. While many familiar queueing situations involve only people as customers and servers, there are also many applications in which one or both of these entities is inanimate (e.g., an ATM could be the server’ parts on an assembly line could be the ‘customers’). Nevertheless, the terms customer and server are still used. The key features of queueing systems can be classified as characteristics of arrivals, service discipline, and characteristics of service.

Characteristics of a Queuing System
Two important issues relevant to a queue involve the timing and types of arrivals. Usually, the timing of arrivals is described by specifying the average rate of arrivals per unit of time (a), or the average interarrival time (1/a).

There are at least two issues related to the types of arrivals. First, the arrivals may occur one at a time or in batches (such as a carload, for example). Second, the arrivals might well be treated as essentially all the same, or they may

6.a. What do you mean by dominance? State the dominance rules for rows and columns.
Answer : Dominance in ethology is an "individual's preferential access to resources over another". Dominance in the context of biology and anthropology is the state of having high social status relative to one or more other individuals, who react submissively to dominant individuals. This enables the dominant individual to obtain access to resources such as food or potential mates at the expense of the submissive individual, without active aggression. The absence or reduction of aggression means unnecessary energy expenditure and the risk of injury are reduced for both. The opposite of dominance is submissiveness.

Dominance may be a purely dyadic relationship, i.e. individual A is dominant over individual B, but this has no implications for whether either of these is dominant over a third individual C. Alternatively, dominance may be

b. What are the differences between PERT and CPM?