# Mb0048 Solved Assignment Spring 2013

Spring 2013

Master of Business Administration- MBA Semester 1MB0048

–

Operations Research- 4 Credits(Book ID: B1631) Assignment Set - 1 (60 Marks)

Note: Assignment Set -1 must be written within 6-8 pages. Answer all questions.Q1.

Explain the scope of Operations Research. What are the features of OperationsResearch?

10 marks

Q2.

Six Operators are to be assigned to five jobs with the cost of assignment in Rs. givenin the matrix below. Determine the optimal assignment. Which operator will have noassignment?

Operators

Jobs

1

2

3

4

5

1

6 2 5 2 6

2

2 5 8 7 7

3

7 8 6 9 8

4

6 2 3 4 5

5

9 3 8 9 7

6

4 7 4 6 8

10 marks

Q3.

a. Explain the Monte Carlo Simulation. b. A Company produces 150 cars. But the production rate varies with the distribution.

Production Rate

147 148 149 150 151 152 153

Probability

0.05 0.10 0.15 0.20 0.30 0.15 0.05At present the track will hold 150 cars. Using the following random numbersdetermine the average number of cars waiting for shipment in the company andaverage number of empty space in the truck. Random Numbers 82, 54, 50, 96, 85,34, 30, 02, 64, 47.

5 +5 = 10marks(200 - 250words each)

Q4.

Explain the Characteristics and Constituents of a Queuing System.

10 marks(300 - 350wordseach)

Research?

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**Master of Business Administration – MBA Semester 2**

**MB0048-Operations Research-4 Credits**

**(Book ID: B1631)**

**Assignment (60 Marks)**

**Note: Answer all questions within 300 to 400 words each. Each Question carries 10 marks 6 X 10=60**

**Q1. Describe the framework of Operations Research.**

Ø List the seven stages of Operations Research

Ø Briefly explain seven stages of Operations Research

**Answer. a) **The basic dominant characteristic feature of operations research is that it employs mathematical representations or models to analyze problems. This distinct approach represents an adaptation of the scientific methodology used by the physical sciences. The scientific method translates a real given problem into a mathematical representation which is solved and retransformed into the original

**Q2. a. Explain the graphical method of solving Linear Programming Problem.**

**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.**

Ø Explain the concept of linear programming

Ø Describe the graphical method of solving Linear Programming Problem

Ø Frame/formulate the LPP (Objective function & Constraints)

**Answer. a) Linear programming (LP or linear optimization) **is a mathematical method for determining a way to achieve the best outcome (such as maximum profit or lowest cost) in a given mathematical model for some list of requirements represented as linear relationships. The procedure for

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

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

Ø List and briefly explain some of the important terms of the transportation problem

Ø Describe the procedure of MODI method.

**Answer. a) Degeneracy in transportation problem**

If the basic feasible solution of a transportation problem with m origins and n destinations has fewer than m + n – 1 positive (occupied cells), the problem is said to be a degenerate transportation problem.

**Q4. a. Explain the steps involved in Hungarian method of solving Assignment problems.**

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

J1 | J2 | J3 | J4 | |

M1 | 10 | 9 | 7 | 8 |

M2 | 5 | 8 | 7 | 7 |

M3 | 5 | 4 | 6 | 5 |

M4 | 2 | 3 | 4 | 5 |

Ø List the steps in Hungarian method

Ø Solve/ Compute the solution to the problem

**Answer. a). Hungarian method **algorithm is based on the concept of opportunity cost and is more efficient in solving assignment problems. Adopt the following steps mentioned below to solve an AP using the Hungarian method algorithm:

**Q5. a. Explain Monte Carlo Simulation.**

**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.**

Ø Explain what is Monte Carlo Simulation and list the steps of of Monte Carlo Simulation

Ø Solve/ Compute the solution to the problem

**Answer. a). Monte Carlo simulation **is a computerized mathematical technique that allows people to account for risk in 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.

**Q6. a. State the assumptions of game theory.**

**What are the characteristics of Markov chain?****What are the rules for prioritizing jobs?**

**Answer. a**. In game theory one usually makes the following assumptions:

(1) Each decision maker [“PLAYER”] has available to him two or more well-specified choices or sequences of choices (called “PLAYS”).

(2) Every possible combination of plays available to the players leads to a well-defined end-state (win, loss, or draw) that terminates the game.

**SMU MBA WINTER 2015 -2016**

**Dear Students, **

**SMU MBA WINTER 2015-2016 Assignments are available. For Booking ,Kindly mail us on kvsude@gmail.com OR call us to +91 9995105420 or S M S your “ Email ID ” us in the following Format “ On +91 9995105420 we will reach back you with in 24H ”**

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