MB0048- OPERATIONS RESEARCH

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ASSIGNMENT

DRIVE	WINTER  2014
PROGRAM	MBADS/ MBAFLEX/ MBAHCSN3/ MBAN2/ PGDBAN2
SUBJECT CODE & NAME	MB0048- OPERATIONS RESEARCH
SEMESTER	2
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. Explain the types of Operations Research Models. Briefly explain the phases of Operations Research.

Answer: Types of Operations Research Models

A model is an idealized representation or abstraction of a real-life system. The objective of a model is to identify significant factors that affect the real-life system and their interrelationships. A model aids the decision-making process as it provides a simplified description of complexities and uncertainties of a problem in a logical structure. The most significant advantage of a model is that it does not interfere with the real-life system.

Classification of OR models

You can broadly classify OR models into the following types.

a. Physical Models include all form of diagrams,

2a. Explain the graphical method of solving Linear Programming Problem.

Answer: Linear programming (LP or linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (mathematical optimization).

More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints. It’s feasible region is a convex polyhedron, which is a set defined as the intersection of finitely many half spaces, each of which is defined by a linear inequality.

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 awake. 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 : Objective function is to maximize the profit

Thus Max. Z=200X₁+500X₂

Constraints 1.Raw materials

         2. Production hour.

LPP is

3 a. Explain how to solve the degeneracy in transportation problems.

Answer: There is a type of linear programming problem that may be solved using a simplified version of the simplex technique called transportation method. Because of its major application in solving problems involving several product sources and several destinations of products, this type of problem is frequently called the transportation problem. It gets its name from its application to

b. Explain the procedure of MODI method of finding solution through optimality test.                                                                                                       

Answer: Transportation Algorithm for Minimization Problem (MODI Method)

After evaluating an initial basic feasible solution to a transportation problem, the next question is how to get the optimum solution. The basic techniques are illustrated as follows:

1. Determine the net evaluations for the non–basic variables (empty cells)

2. Determine the entering variable

3. Determine the leaving variable

4. Compute a better basic feasible solution

4 a. Explain the steps involved in Hungarian method of solving Assignment problems.

Answer: The assignment problem is one of the fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics. It consists of finding a maximum weight matching in a weighted bipartite graph.

In its most general form, the problem is as follows:

There are a number of agents and a number of tasks. Any agent can be assigned to perform any task, incurring some cost that may vary

b. What do you mean by unbalanced assignment problem? How do you overcome it?

Answer: Unbalanced assignment problem: This is the case of assignment problem where the number of persons is not equal to the number of jobs. A dummy variable, either for a person or job  ( as it required) is  introduced with zero cost or time to make it a balanced one.

If number of jobs is not equal to the number of operators then the assignment problem is known as unbalanced assignment problem. In other words in a pay off matrix of assignment problem if number of rows and number of columns are not equal then it is unbalanced assignment problem.

To solve unbalanced assignment prob

Q5.a. Explain the Monte Carlo Simulation.

Answer: Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results; typically one runs simulations many times over in order to obtain the distribution of an unknown probabilistic entity. The name comes from the resemblance of the technique to the act of playing and recording your results in a real gambling casino. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to obtain a closed-form expression, or

b. A Company produces 150 cars. But the production rate varies with the distribution.

Production Rate	Probability
147	0.05
148	0.10
149	0.15
150	0.20
151	0.30
152	0.15
153	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.  5 +5 = 10 marks(200 - 250 words each)

Answer: 

Production Rate	Probability	Cum. Probability	Random Numbers
147	0.05	0.05	00-04
148	0.10	0.15	05-14

6 a. Explain the dominance principle in game theory.

Answer: Game theory is a study of strategic decision making. Specifically, it is "the study of mathematical models of conflict and cooperation between intelligent rational decision-makers".[1] An alternative term suggested "as a more descriptive name for the discipline" is interactive decision theory.[2] Game theory is mainly used in economics, political science, and psychology, as well as logic and biology. The subject first addressed zero-sum games, such that one person's gains exactly equal net losses of the other participant or participants. Today, however, game theory applies to a wide range of behavioral relations, and has developed into an umbrella term for the logical side of decision science, including both humans and non-humans (e.g. computers).

b. Describe the Constituents of a Queuing System.

Answer: Characteristics of a queuing system that impact its performance, for example, queuing requirements of a restaurant will depend upon factors like:

·         How do customers arrive in the restaurant? Are customer arrivals more during lunch and dinnertime (a regular restaurant)? Or is the customer traffic more uniformly distributed (a cafe)?

·         How much time do customers spend in the restaurant? Do customers typically leave the restaurant in a fixed amount of time? Does the customer service time vary with the type of customer?

c. Differentiate between PERT and CPM

Answer: Project management is an important part of every business enterprise. Whenever a new product or service is launched; when embarking on a marketing campaign; or when organizing any new projects; project management is needed to make everything organized and successful.

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