MB0048 - Operations Research

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Summer 2013

Master of Business Administration- MBA Semester 2

MB0048 - Operations Research- 4 Credits

(Book ID: B1631)

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. The basic characteristic feature of Operations Research is that it employs mathematical representations or models to analyse problems. Discuss the methodology of Operations Research.

(Meaning – 2 marks, Methodology – 8 marks) 10 marks

Answer : Operation research :

Operations research, or operational research , is a discipline that deals with the application of advanced analytical methods to help make better decisions. It is often considered to be a sub-field of mathematics. The terms management science and decision science are sometimes used as synonyms.

Employing techniques from other mathematical sciences, such as mathematical modeling, statistical analysis, and mathematical optimization, operations research arrives at optimal or near-optimal solutions to complex decision-making problems.

Q2. Linear Programming is most widely used technique for large number of applications in business industry as well as in various other fields. Explain in brief the steps involved in linear programming problem formulation with an example.

(Meaning – 3 marks, Steps – 3 marks, Example – 4 marks) 10 marks

Answer :  Linear programming :

A Linear Programming problem (LPP) is a special case of a Mathematical Programming problem. From an analytical perspective, a mathematical program tries to identify an extreme (i.e., minimum or maximum) point of a function f(x₁, x₂, …x_n), which furthermore satisfies a set of constraints, e.g., g(x₁, x₂, …x_n) ≥ b. Linear programming

is the specialization of mathematical programming to the case where both, function f - to be called the objective

function and the problem constraints are linear.

Q3. Explain the steps involved in finding Initial Basic Feasible solution by the following methods:

a. North West Corner Rule method (Steps – 3 marks)

b. Matrix minimum method (Steps – 3 marks)

c. Vogel’s approximation method (Steps – 4 marks)

Answer : a. North West Corner Rule method:

Step 1

• The first assignment is made in the cell occupying the upper left-hand (north-west) corner of the table.

• The maximum possible amount is allocated here i.e. x₁₁= min (a₁, b₁). This value of x₁₁ is then entered in the cell (1,1) of the transportation table.

Q4. A Service store employs one cashier at its counter. 9 customers arrive on an average every 5 min while the cashier can serve 10 customers in 5 min. Assuming Poisson distribution for arrival rate and exponential distribution for service rate. Find

a. Average number of customers in the system

b. Average number of customers in the queue

c. Average time a customer spends in a system

d. Average time a customer waits before being served.

(Formulas – 2 marks, Calculation/Solution/Interpretation – 8 marks) 10 marks

Answer : Formulas used are :

We let  ƛ =mean number of arrivals per time period

µ = mean number of people or items served per time period

The arrival rate and the service rate must be for the same time period

a . The average number of customers or units in the system, L:    L_s =  ƛ/( µ-ƛ)

Q5. a. Explain the Monte Carlo Simulation.

(Explanation – 5 marks)

Answer : Monte Carlo Simulation:

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. Probability distributions are a much more realistic way of describing uncertainty in variables of a risk analysis.  Common probability distributions include:

Q6. a. A Game refers to a situation of conflict and competition in which two or more competitors are involved in decision making in anticipation of certain outcome. Define the following with respect to games:

i. Pay-off matrix

ii. Strategy

iii. Two- person zero-sum game

iv. Saddle point

(Defining each – 4 mark)

Answer : i. Pay-off matrix:

The basic tool of game theory is the payoff matrix. This matrix represents known payoffs to individuals (players) in a strategic situation given choices made by other individuals in that same situation. This tool lists all payoffs with all possible combinations of alternative actions and external conditions.

Dear students get fully solved assignments

Send your semester & Specialization name to our mail id

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