# Mb0048 Operations Research Solved Assignments

**SMU MBA WINTER 2015 -2016**

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**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 ”**

**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 ”**

**SMU MBA SPRING 2016-2017**

**Dear Students, **

**SMU MBA SPRING 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 ”**

**DRIVE SPRING 2016**

**PROGRAM MBA**

**SEMESTER II**

**SUBJECT CODE &**

**NAME**

**MB0048 ****OPERATIONS RESEARCH**

**1 Discuss the various stages involved in the methodology of Operations Research. Briefly explain the techniques and tools of Operations Research.**

[Operations Research Methodology-5

Techniques and tools of Operations Research-5]

**Answer**: __Operations Research Methodology__

**Definition: **The first and the most important step in the OR approach of problem solving is to define the problem. One needs to ensure that the problem is identified properly because this problem statement will indicate the following three major aspects:

- Description of the goal or the objective of the study
- Identification of the decision alternative to the system
- Recognition of the limitations, restrictions, and requirements of the system

**Construction: **

**2 a. Explain the steps involved in linear programming problem formulation. Discuss in brief the advantages of linear programming.**

**Alpha Limited produces & sells two different products under the brand names black & white. The profit per unit on these products in Rs. 50 & Rs. 40 respectively. Both the products employ the same manufacturing process which has a fixed total capacity of 50,000 man-hours. As per the estimates of the marketing research department of Alpha Limited, there is a market demand for maximum 8,000 units of Black & 10,000 units of white. Subject to the overall demand, the products can be sold in any possible combination. If it takes 3 hours to produce one unit of black & 2 hours to produce one unit of white, formulate the model of linear programming.**

[Steps involved in LPP-4

Advantages of LPP-3

Formulation of LPP-3]

**Answer**: a) The procedure for mathematical formulation of a linear programming problem consists of the following major steps:

- Study the given situation to find the key decisions to be made
- Identify the variables involved and designate them by symbols xj(j=1,2….)
- State

**a. What is degeneracy in transportation problem? How it can be resolved?****Solve the following transportation problem using Vogel’s approximation method.**

Factories | Distribution Centres | Supply | |||

C1 | C2 | C3 | C4 | ||

F1 | 3 | 2 | 7 | 6 | 50 |

F2 | 7 | 5 | 2 | 3 | 60 |

F3 | 2 | 5 | 4 | 5 | 25 |

Requirements | 60 | 40 | 20 | 15 |

[Degeneracy in transportation problem and resolving it-5

Computation/Solution to the problem-5]

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

A basic solution to an m-origin, n destination transportation problem can have at the most m+n-1 positive basic variables (non-zero), otherwise the basic solution degenerates. It follows that whenever the number

**a. Explain the steps in Hungarian method. Differentiate between Transportation and Assignment problem.****Find the optimal assignment of four jobs and four machines when the cost of assignment is given by the following table:**

J1 | J2 | J3 | J4 | |

M1 | 10 | 9 | 8 | 7 |

M2 | 3 | 4 | 5 | 6 |

M3 | 2 | 1 | 1 | 2 |

M4 | 4 | 3 | 5 | 6 |

[Steps in Hungarian method-3

Differences between Transportation and Assignment problem-3

Computation/Solution to the problem-4]

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

Step 1: Prepare row

**Define Simulation. Explain the Simulation procedure. Discuss the use of Simulation with an example.**

[Meaning of Simulation-2

Simulation procedure-4

Use of simulation with an example-4]

**Answer**: Simulation is the process of defining a model of a real system and conducting experiments with this model for the purpose of understanding the behaviour (within the limits imposed by a criterion or a set of criteria) for the operation of a system

**Simulation **

**Explain the following:****Economic Order Quantity( EOQ)****PERT and CPM****Operating Characteristics of a Queuing System**

[Explanation of Integer programming model-4

Explanation of PERT and CPM-3

Explanation of Operating Characteristics of a Queuing System-3]

**Answer**: a) **Economic Order Quantity( EOQ)**

The Economic Order Quantity (EOQ) is the number of units that a company should add to inventory with each order to minimize the total costs of inventory—such as holding costs, order costs, and shortage costs. The EOQ is used as part of a continuous review inventory system in which the level of inventory

**SMU MBA SPRING 2016-2017**

**Dear Students,**

**SMU MBA SPRING 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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