## Wednesday, June 15, 2022

### BMP/SEM1/PAPER 4/6: OPERATIONS RESEARCH AND STATISTICS

UNIT – I Definition of operations research, models of operations research, scientific methodology of operations research, scope of operations research, importance of operations research in decision making, role of operations management, limitations of OR.

UNIT – II Linear Programming: Introduction – Mathematical formulation of a problem – Graphical solutions, standard forms the simplex method for maximization and minimization problems. Method application to management decisions. Transportation problem – Introduction – Initial basic feasible solution - NWC method – Least cost method – Vogel’s method – MODI – moving towards optimality – solution procedure without degeneracy

UNIT – III Assignment problem – Algorithm – Hungarian method – simple problems.

UNIT – IV Sequencing and replacement model: Sequencing problem – processing through 2 machines, 3 machine – s jobs and k machines and traveling salesman problem. Replacement of items that deteriorate gradually – with time, without time, that fails completely – individual replacement – group replacement.

UNIT – V Network models and simulation. Network models for project analysis CPM; Network construction and time analysis; cost time trade off, PERT – problems.

UNIT-VI -  Game Theory

STATISTICS

Module I (9 hours) Introductory Concepts Unit 1 Introduction to the subject of Statistics, population and sample, variables and attributes.

Unit 2 Types of data – qualitative, quantitative, univariate, multivariate, cross sectional, time series, discrete, continuous, primary, secondary. Scales of measurement – nominal, ordinal, interval, ratio.

Unit 3 Construction of frequency distributions (univariate and bivariate). Organisation and presentation of data through diagrams (bar and pie) and graphs (frequency curve, histogram, cumulative frequency curves), stem and leaf plot.

Module II (15 hours) Univariate Data Analysis Unit 1 Measures of location or central tendency - arithmetic mean, median, mode, geometric mean, harmonic mean – properties, positional averages or quantiles – quartiles, deciles, percentiles and their interpretations. Comparison of the different averages. Unit 2 Measures of dispersion - absolute measures - range, mean deviation, quartile deviation, standard deviation - properties with proof, relative measures. Unit 3 Moments – about origin, about an arbitrary point, central moments, relationship between moments about origin and moments about mean, skewness and kurtosis - concept and measures, box and whisker plot – construction and applications.

Module III (12 hours) Bivariate Data Analysis Unit 1 Linear Correlation - Scatter diagram, product moment correlation coefficient - properties, Spearman;s rank correlation coefficient. Unit 2 Regression - Dependent and independent variables, objectives of regression, derivation of linear regression model by the method of least squares, estimation of regression coefficient and coefficient of determination and their interpretations.

MODULE IV

Chi Square test