MB0048 - OPERATIONS RESEARCH

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ASSIGNMENT

DRIVE	FALL 2015
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.

Q1 Describe the framework of Operations Research.

Answer: Operations Research (OR) is an approach used to improve service delivery or to strengthen other aspects of programs. Although OR can include diagnostic or evaluative studies, the most common use of OR is the intervention study, consisting of five steps:

1.       Identifying problems related to service delivery;

2.       Identifying possible strategies to address these problems;

3.       Testing these strategies under quasi-experimental conditions;

4.       Disseminating the findings to program managers and policymakers; and

5.       Using the information to improve service delivery programs (Fisher et al., 1991).

This approach is particularly useful in testing new and potentially controversial strategies to service delivery. The implementing organization can experiment with the new approach on a limited scale, without having to adopt it throughout the organization.

Q2 a. 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

Qb. A paper mill produces two grades of paper viz., X and Y. Because of raw materialrestrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Ypaper in a week. There are 160 production hours in a week. It requires 0.20 and 0.40 hours toproduce 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.

Q3 a. Explain some of the important terms of the transportation problem.

Answer: The transshipment problem is similar to the transportation problem except that in the transshipment problem it is possible to both ship into and out of the same node (point). For the transportation problem, you can ship only from supply points to demand points. For the transshipment problem, you can ship from one supply point to another or from one demand point to another. Actually, designating nodes as supply

b. Explain the steps of MODI (Modified Distribution) method.

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

Q4 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 depending on the agent-task

b. Find an optimal solution to an assignment problem with the following cost matrix:

Answer: The solution is as follows.

First, the minimum element in each row is subtracted from all the elements in that row.

This gives the following reduced-cost matrix.

Q5 a. Explain 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 infeasible to apply a deterministic algorithm. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration and generation

b. Hindustan Bakery is popular for its delicious fruit cakes. The table below shows the daily demand for the bakery’s cakes.

Daily Demand	0	15	25	35	45	50
Probability	0.01	0.15	0.2	0.5	0.12	0.02

Simulate the demand for cakes for 10 days using the following sequence of random numbers:

22, 26, 48, 53, 93, 89, 42, 91, 25, 20

If 35 cakes are baked every day in Hindustan Bakery, determine the inventory stock. In addition, estimate the daily average demand for cakes on the basis of simulated data.

Answer:

Q6 a. State the assumptions of game theory.

Answer: Game theory is the study of the ways in which interacting choices of economic agents produce outcomes with respect to the preferences (or utilities) of those agents, where the outcomes in question might have been intended by none of the agents. The meaning of this statement will not be clear to the non-expert until each of the italicized words and phrases has been explained and featured in some examples.

c. What are the rules for prioritising jobs?

Answer: Prioritizing daily tasks is key to successful time management. When you prioritize, you make sure you accomplish the most important tasks first. Make time management a habit — your stress level (and your boss's!) will thank you. Follow this process:

1.       Start with a master list.

Write down every single task, both mundane and critical,

Dear students get fully solved  SMU MBA assignments

Send your semester & Specialization name to our mail id :

“ help.mbaassignments@gmail.com ”

or

Call us at : 08263069601

(Prefer mailing. Call in emergency )