DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH ALIGARH MUSLIM UNIVERSITY ALIGARH

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Appendix B BOS 03.04.2018

DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH ALIGARH MUSLIM UNIVERSITY ALIGARH

M.A. /M.Sc. I Semester (Operations Research) Course Code: ORM1001

Linear Programming and Simulation Techniques

Credit: 4 Max Marks: 30+70 =100

Course objectives: To understand the basic concept and properties of linear programming and simulation with their applications.

Course outcomes: After successful completion of this course, the students will be able to

 Formulate real life problems to linear programming and apply appropriate solving techniques to obtain optimum solution.

 Estimate the measures of performance of a modeled system through simulation.

Syllabus

Unit-I: Convex sets, Convex hull, Convex cone, Convex and Concave functions, Separating and Supporting Hyper-planes and their properties. Linear Programming Problems (LPP). Review of Simplex Methods, Duality in LPP and its properties, Dual Simplex Method, Primal-Dual Relations, Weak duality and Strong Duality.

Unit-II: Complementary Slackness theorem and Conditions, Economic interpretations. Revised Simplex Method, Sensitivity Analysis in Linear Programming, Parametric Linear Programming, Decomposition Principle in LPP.

Unit –III: Simulation and Monte-Carlo Methods: Introduction to Simulation and Monte-Carlo Method; Random Number Generation: Linear congruential generator, Combined linear congruential generator, Statistical tests for pseudo-random numbers. Test for autocorrelation, Gap test.

Unit IV: Random Variate Generation: Inverse transform method and generation of random variates from Exponential, Weibull, Geometric, Empirical continuous and discrete distributions, Generation of nominal variates. Acceptance and rejection method and generation of Poisson and

Gamma variates.

Suggested Readings:

1. Hillier and Lieberman (1991): Introduction Mathematical Programming, McGraw Hill.

2. H.A.Taha (2009): Operations Research: An Introduction, Macmillan.

3. Gass S.I. (1975): Linear Programming Methods and Applications, McGraw Hill Book Co.

4. A.Ravindaran, Don T. Philips and J.J.Soleberg (2007): Operations Research: Principles and Practice, 2nd ed., Wiley.

5. Ignizio and Cavalier (1994): Linear Programming, Prentice Hall.

6. Banks, J., Carsen II, J.S. and Nelson, B.L.(1999): Discrete Event System Simulation, PHI.

7. Rubinstein, R.Y. (1981): Simulation and the Monte-Carlo Method, John Wiley & Sons.

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Appendix B BOS 29.05.2015

DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH ALIGARH MUSLIM UNIVERSITY,ALIGARH

M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002

Linear Algebra and Real Analysis

Credit: 4 Max Marks: 30+70=100

Course objectives: To introduce the concepts of linear algebra and real analysis which is necessary as a prerequisite for optimization problems.

Course outcomes: On successful completion of this course, the students will be able to

 The knowledge of this course will able the students to counter the mathematical complexities in solving the optimization problems.

Syllabus

Unit I: Vectors: Fields, vector spaces, subspaces, linear dependence and independence. Basis and dimensions of a vector space, Finite dimensional vector spaces. Vector spaces with linear product, Gramsshmidt orthogonalization process, Orthonormal basis and orthonormal projection of a vector.

Unit II: Algebra of matrices, Rank of matrix, Echelon matrix, Inverse of a matrix, Product form of inverse, Partitioned matrices, elementary matrices, Kronecker products, simultaneous linear equations. Real quadratic forms, reduction and classification of quadratic forms. Eigen values and Eigen vectors, Caley-Hamilton theorem.

Unit-III: Recap of elements of set theory, Introduction to real numbers. The extended real numbers, Introduction to n-dimensional Euclidean space, open and closed intervals, closed, open and compact sets and their properties, Bolzano-Weirstrass theorem.

Unit IV: Convergent, divergent and bounded sequences and subsequences, limits inferior and limits superior. Cauchy sequence, Monotonic sequence. Infinite series and its convergence. Real valued functions, continuous functions, continuity and compactness, continuity and connectedness, Discontinuities, monotonic functions, uniform continuity, sequences of functions.

1. Rudin Walter (1976): Principles of Mathematical Analysis, McGraw Hill, 3rd Edition.

2. Apostol, T.M.: Mathematical Analysis 2nd Edition.

3. Malik, S.C.: Mathematical Analysis, Wiley Eastern Ltd.

4. Biswas, S. (1984): Topics in Algebra of Matrices, Academic Publications.

5. Hadley G. (1987): Linear Algebra: Narosa Publishing House.

6. Hoffman K. & Kunze, R. (1971): Linear Algebra, 2nd ed., Prentice Hall, Inc.

7. Searle S. R. (1982): Matrix Algebra Useful for Statistics, John Wiley & Sons, Inc.

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Appendix III B B.O.S- 05.05.03

DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH ALIGARH MUSLIM UNIVERSITY,ALIGARH

M.A. /M.Sc. I-Semester (Operations Research) Paper (ORM1003)

Probability-I

Credit: 4 Max Marks: 30+70 =100

Course objectives: To understand the basic elements of probability theory.

 Provide a foundation for understandings of advanced probability courses.

 Apply the theory of probability in applications of statistics.

Syllabus

Unit I : Random experiment, sample space, field, CT-field, sequences of sets, limsup and liminf of sequences of sets, Measure and probability measure, Lebesgue and Lebesgue-Stieltjes measure, Measurable and Borel measurable function, Integration of a measurable function w.r.to a measure, Monotone coveragence theorem, Fatous lema and dominated convergence theorem.

Unit II : Random variable (r.v.) and functions of r.v., Probability density and Probability mass function, Distribution function and its properties, Representation of distribution as a mixture of distributions, Compound, truncated and mixture distributions.

Unit III : Mathematical expectation and moments, Probability generating function (PGF), moment generating function (MGF), and characteristic function (CF) and their interrelationships, Properties of CF. Examples of discrete distributions: Degenerate, Uniform, Bernaulli, Binomial, Poisson, Geometric, Negative Binomial and Hyper geometric distribution, Convergence of distribution function.

Unit IV: MGF and CF for continuous r.v., Inversion theorem, Examples of continuous distributions: Uniform, Normal, Exponential, Gamma, Beta, Weibull, Pareto, Laplace, Lognormal, Logistic and Log-Logistic distribution.

Books Recommended:

1. Ash, Robert (1972): Real Analysis and Probability, Academic Press.

2. Bhat, B. R (1981 ): Modern Probability Theory, Wiley Eastern Ltd., New Delhi.

3. Rohatgi, V. K. (1988): An Introduction to Probability and Mathematical Statistics, Wiley, Eastern Limited.

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Appendix B B.O.S. 03.04.2018

DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH ALIGARH MUSLIM UNIVERSITY, ALIGARH

M.A./ M.Sc.I Semester (Operations Research) Course Code: ORM1011

Statistical Quality Management

Credit: 4 Max Marks: 30+70 =100

Course objectives: To provide knowledge of quality and process control through statistical techniques.

 After completion of course student will be able to apply methodologies of SQM to improve the quality of production.

Syllabus

Unit I: Overview of Quality and Process control, Deming’s and Juran’s critical points related to quality, Costs in quality, control charts for variables and attributes, moving average and moving range, exponentially weighted moving average, Cu-Sum control and construction of the Cu-sum, V-mask and decision interval.

Unit II: Economic Design of X Charts, Quality and Process optimization problems. Six—Sigma concepts, Six Sigma methodologies: DMAIC and DMADV. Capability indices C_p, C_pk, and C_pm, Estimation of the proportion of defectives (rework and scrap).

Unit III: Quality loss functions, Estimation of quality loss, Taguchi loss function, equal and unequal N-type, L-type and S-type loss functions.Acceptance sampling plans, rectification plan,Acceptance sampling plans for attribute inspection; single, double andtheir properties (OC curves, ATI, AOQ, ASN), Multiple, Sequential sampling plans.

Unit IV: Acceptance Sampling procedure for inspection by variables: Single sampling plan for one sided and two sided specification with known and unknown S.D.lot by lot inspection plan. Use of Design of Experiments in SPC: signal and input variables, full factorial experiments, 2^k full factorial experiments, 2² and 2³ construction designs and analysis of data.

1. Montgomery, D. C. (2012): Introduction of Statistical Quality Control; Wiley.

2. Montgomery, D. C. (2009): Design and Analysis of Experiments; Wiley.

3. G. Schilling (1982): Acceptance Sampling in Quality Control; Marcel Dekker.

4. Amitava Mitra (2016): Fundamentalsof Quality Control and Improvements; John Wiley.

5. J.R. Evans. W.M. Lindsay (1996): The Management and Control of Quality; West Publishing Company.

6. Kaoru Ishikawa (1992): Introduction to Quality Control, Chapman and Hall.

7.John S. Oakland (2008): Statistical Process Control; Elsevier.

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Appendix C BOS 30.05.2019 DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH

ALIGARH MUSLIM UNIVERSITY, ALIGARH M.A./ M.Sc. I-Semester (Operations Research)

Course Code-ORM1021 Computing-I

Credit: 4 Max Marks: 30+70 =100

Course objectives: To learn programming with FORTRAN and have knowledge of the optimization software packages TORA and LINGO.

 Student will be able to write programming codes in FORTRAN. Also they will be able to solve optimization problems through software packages.

Syllabus

Unit I: Programming with FORTRAN 90/95 : Arithmetic Statements: Constants and Variable, names and types of constants and variables-Real and integers, arithmetic operators, arithmetic expressions-real and integer, mixed mode expressions, scalar relational operators, scalar logical expressions and assignments, built -in- mathematical functions, Input and output statements Specification statements, Format definition, unit numbers, internal files, formatted input, formatted output, list-directed I/O, carriage control, Edit descriptors, unformatted I/O, direct file and its processing.

Unit II: Control Constructs: Branching, IF Statements and Constructs, the Case Constructs.

Looping: Do While, Do and nested DO Constructs, Cycle and Exit statements. The GOTO statement. Arrays Features, Elementary operations, where and forall statements and constructs.

Functions and Subroutines: Statement Function, Function Subprograms and Subroutines, Calling a subprograms and subroutines.

Unit III: Introduction to Python: Python data structures, data types. indexing and slicing, vectors, arrays, developing programs, functions, modules and packages, data structures for statistics, tools for statistical modeling, data visualization, input and output.

Unit -IV: Software Packages: TORA and LINGO-Solution of simultaneous linear equations, Linear programming Problems, finding feasible and optimal solutions to primal and dual using Simplex and other Methods. Obtaining feasible and optimal solutions to Transportation and assignment models and finding optimal strategies in Zero-sum games

1 Rajaraman V. (2015):Computer Programming in Fortran 90 And 95, PHI Learning Pvt Ltd.

Delhi

2 Metcalf, M. and Reid, J. (2000): FORTRAN 90/95 Explained, Oxford University Press.

3 Chapman, S.J. (1999): Introduction to FORTRAN 90/95, Tata McGraw Hill Publishing Company.

4 Salaria, R.S. (1999): A Modern Approach to Programming in Fortran, Khanna Book Publishing, Delhi

5 Haslwanter, T. (2016):An Introduction to Statistics with Python: With Applications in the Life Sciences, Springer.

6. Sheppard, K. (2018): An Introduction to Python for Econometrics, Statistics and Data Analysis, Oxford University Press.

7 H.A.Taha (2013) An Introduction to Operations Research,9th Edition, Prentice Hall, NJ.

8 LINGO User’s Guide (2013), LINDO systems Inc. U.S.

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M.A./ M.Sc. I Semester (Operations Research) Paper ( ORM1071)

Lab Course-I Based on theory Papers (ORM1001, ORM1002, ORM1003, ORM1011)

Max Marks: 40+60=100

M.A./ M.Sc. I Semester (Operations Research) Paper (ORM1072)

Lab Course-II (ORM1021)

Max Marks: 40+60=100

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Appendix III B BOS 05.05.03

M.A./ M.Sc. I Semester (Operations Research) Course Code-ORM2001

Probability II

Credit: 4 Max Marks: 30+70 =100

Course objectives: To Introduce the advanced concepts of probability theory.

Course outcomes: On successful completion of this course, the students will be able to.

 Describe the advanced techniques of Probability theory including LLN and CLT.

 Apply the results of advanced Probability in statistical theory

Syllabus

Unit I : Derivation of central ;c2, t and F distributions. Ideas of non-central distributions. Multidimensional r.v., its pdf/pmf and cdf. Bivariate distributions.

Joint, Marginal and conditional distributions, conditional moments and their properties, covariance and correlation

between two r. v.

Unit II : Bivariate and multivariate normal, multinomial and multi-hypergeometric distributions, Distributions of functions of r. vs (discrete and continuous).

Unit III : Chebyshev, Markov, Jensen, Liapunov, Holder, Minkowski and Kolmogrov inequality, various models of convergence and their interrelationships Convergence of rational Functions of r.vs. (Cramer).

Unit IV : Continuity theorem (Levy-Cramer Statements only), Kolmogrov's three series criterion, Weak and strong law of large numbers, Central limit theorems in De Moivre-Laplace, Lindberg-Levy and Liapunov's versions. 0-1 law of Borel and Kolmogrov.

1. Ash, Robert (1972): Real Analysis and Probability, Academic press.

2. Bhat, B.R (1981 ): Modern Probability Theory, Wiley Eastern Ltd. New Delhi.

3. Rohatgi, V.K. (1988): An Intoduction to Probability and Mathematical Statistics, Wiley Eastern Limited.

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M.A./ M.Sc. II-Semester (Operations Research) Course Code-ORM2002

Stochas ti c Process e s

Credit: 4 Max Marks: 30+70 =100

Course objectives: To introduce the concepts of stochastic processes.

 Describe the techniques of stochastic processes.

 Apply the concepts and results of stochastic process in the real life scenario, including queuing theory, branching process, MCMC, etc.

Syllabus

Unit I: Markov Chains: Definition, Basic ideas and specification of Stochastic Processes, Markov Chains, Transition probability matrix ( P ), Chapman-Kolrnogorov equation, Evaluation of P" through spectral decomposition, classification of states, stationary distribution.

Unit II: Branching Process: Properties of generating function of branching process; Probability of extinction, Distribution of total progeny, Random walk and gambler's ruin problem.

Unit III: Continuous time Markov Processes; Poisson process, Simple Birth- Process, Simple Death-process, Simple Birth-Death process.

Unit IV: Statistical Inference for Markov Chains and Renewal Process: Estimation of transition probabilities, Tests of hypothesis about tmp, Renewal process, Renewal equation, Renewal theorem.

1. Medhi, J. (1994): Stochastic Processes, Wiley Eastern Ltd. 2¹¹ct Ed.

2. Bailey, Norman T. (1965): The Elements of Stochastic Processes, John Wiley & Sons, Inc., New York.

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Appendix III B BOS 05.05.03

DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH ALIGARH MUSLIM UNIVERSITY ALIGARH

M.A. /M.Sc II Semester (Operations Research) Course Code (ORM 2003)

Sample Surveys

Credit: 4 Max Marks: 30+70 =100

Course objectives: To introduce the concepts of sample surveys and designs.

 Describe the methods of sample surveys.

 Apply the methods in data collections and data analysis.

Syllabus

Unit I : Estimation of population mean, total and proportion in SRS and Stratified sampling.

Estimation of gain due to stratification. Ratio and regression methods of estimation. Unbiased ratio type estimators. Optimality of ratio estimate .Separate and combined ratio and regression estimates in stratified sampling and their comparison.

Unit II : Cluster sampling: Estimation of population mean and their variances based on cluster of equal and unequal sizes. Variances in terms of intra-class correlation coefficient.

Determination of optimum cluster size. Varying probability sampling: Probability proportional to size (pps) sampling with and without replacement and related estimators of finite population mean.

Unit III : Two stage sampling: Estimation of population total and mean with equal and unequal first stage units. Variances and their estimation. Optimum sampling and sub-sampling fractions (for equal fsu's only).Selection of fsu's with varying probabilities and with replacement.

Unit IV: Double Sampling: Need for double sampling. Double sampling for ratio and regression method of estimation. Double sampling for stratification. Sampling on two occasions.

Sources of errors in surveys: Sampling and non-sampling errors. Various types of non -sampling errors and their sources .Estimation of mean and proportion in the presence of non-response.

Optimum sampling fraction among non-respondents. Interpenetrating samples. Randomized response technique.

1. Cockran, W.G., (1977): Sampling Techniques, 3rd edition, John Wiley.

2. Des Raj and Chandak (1998): Sampling theory, Narosa.

3. Murthy, M.N. (1977): Sampling theory and methods. Statistical Publishing Society, Calcutta.

4. Sukhatme et al. (1984): Sampling theory of surveys with applications, Lowa state university press and ISAS.

5. Singh, D. and Chaudary, F.S. (1986): Theory and analysis of sample survey designs.

New age international publishers

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Appendix B BOS 03.04.2018

M.A. /M.Sc. II Semester (Operations Research) Paper (ORM2004)

Advanced Linear Programming

Credit: 4 Max Marks: 30+70 =100

Course objectives: To understand the advance concept and techniques of linear Programming.

 Students will be able to deal with complex nature of linear programming. They will also be able to solve multi-objective linear programming problem in uncertain environment.

Syllabus

Unit I: Linear Programming under uncertainty, Stochastic LPP formulation, Chance constrained LPP, Probabilistic programming, Bounded variable LPP theory and Simplex method procedure.

Unit II: Linear Fractional Programming Problem (FLPP) Formulations, Relationship between LPP and FLPP, Primal Simplex Method, Charnes & Cooper's Transformation, Dinkelbach's Algorithm, Big M Method, The Two-Phase Simplex Method, FLPP properties and theorems, Multi-objective FLPP formulations.

Unit III: Fuzzy sets vs Crisp sets, Properties of fuzzy sets, Cardinality of fuzzy set: Scalar and Relative, Types of Fuzzy Sets, α-cut set, Closed interval α-cut, Convex Fuzzy sets, Membership functions and properties. LPP Formulation under Fuzziness.

Unit IV: Metric Spaces: Fundamental concepts of metric spaces, properties and theorems. Multi- objective Optimization LPP Formulations, Concepts and Definitions. Multi-objective Optimization LPP techniques: Simplex method and Graphical method, Reference Point, Weighted sum method, Goal programming, Preemptive goal programming, Fuzzy goal programming.

1. Rao, S.S. (2010): Optimization Theory and Applications, Wiley Eastern.

2. Hillier and Lieberman (2010): Introduction Mathematical Programming, McGraw Hill.

3. Bazara, Jarvis and Sherali (1990): Linear Programming and Network Flows, John Wiley.

4. Ignizio and Cavalier (1994): Linear Programming, Prentice Hall.

5. Ravindran A., Philips, D.T., and Soleberg, J.J. (2007): Operations Research, Principal and Practice, 2nd Edition John Wiley.

6.Bajaliov E.B. (2003): Linear fractional programming: theory, methods, application and software,Springer.

7. Masatoshi Sakawa (1993): Fuzzy set and interactive multi-objective optimization, Springer.

8. Erwin Kreyszig (2006): Introductory Functional Analysis with Applications, Wiley.

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M.A. /M.Sc. Semester- II (Operations Research) Paper (ORM2011)

Inventory and Warehouse Management

Credit: 4 Max Marks: 30+70 =100

Course objectives: To efficiently handle inventory problems and warehouse management.

Course outcomes: On successful completion of this course, the students will be able to

 Students will be able to formulate and solve inventory models with certain and uncertain demand.

 Student will be able to know the objectives, functions and management of warehouse

Syllabus

UNIT I: Introduction: Meaning and function and objectives of Inventory, Reasons for and against Inventory, Types of Inventory, Factors Involved in Inventory Problem Analysis, Demand for Inventory Items, Replenishment, Lead Time, Safety stock, Planning Period, operating cycle. Inventory Cost Components, Financial Statements and Inventory. Inventory Management System.

UNIT II: Inventory Control Techniques: Selective Inventory Control Techniques (ABC, VED, SDE, HML, FNSD, XYZ, GOLF, SOS). The Analytical Structure of Inventory, Single Item Inventory Control Models, with and without Shortages, with Quantity Discounts, (EOQ, POQ), Multi item Inventory Models with Constraints. Determining of Safety stock and service level. P-System and Q-system.

UNIT III: Probabilistic Inventory Control Models: Single and Multi period Inventory Control Models with Uncertain Demand, Scheduling Period system, Order level system with uniform and instantaneous demand. Economic Production Quantity Model (EPQ), Joint Economic Lot Sizing Model.

UNIT IV: Warehouse Management: Fundamentals, Role, Types, objectives and functions of warehouse. Warehouse Planning & Layout, Profiling, Warehouse practices and performance, Warehouse Systems and Operations, Policy and Emerging Issues in Warehousing, Warehouse corporations, Warehousing Act., Free-Trade Warehousing Zones(FTWZ), APMC Act., Public Private Partnership (PPP), Innovation in warehousing.

1. Naddor, F. (1966): Inventory System, John Wiley & Sons, Inc. New York.

2. Sven Axsater: Inventory Control. International Series in Operations Research &

Management Science. Springer. 2nd Edition. 2006.

3. Zipkin: Foundations of Inventory Management, Mc-Graw Hill Inc., 2000.

4. Sharma, J.K. (2013): Operations Research: Theory and Applications, McMillan India Ltd.

5. Edward Frazelle, World-Class Warehousing and Material Handling, The McGraw Hill Publishing Company Limited. Edition-2004

6. David Mulcahy, Warehouse Distribution and Operations Handbook, McGraw-Hill Publishing Company Limited. ISBN: 0070440026

7. Tompkins, James A. Warehouse Management Handbook, Tompkins Press, ISBN 0965866916

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BOS 23.12.2015 DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH

ALIGARH MUSLIM UNIVERSITY ALIGARH M.A./ M.Sc. II Semester (Operations Research): CBCS

Course Code-ORM2021

Data Analysis with Minitab, LINGO and R

Credit: 2 Max Marks: 30+70 =100

Course objectives: To learn data analysis using software MINITAB, LINGO and R.

 Knowledge of MINITAB, LINGO and R.

 Solution of problems of data analysis and optimization through MINITAB, LINGO and R.

Syllabus

Unit I: Data Analysis-Concept of data types, scales of measurement. Meaning, purpose and method of data analysis. Classification and cross tabulation of data. Determination of sample size.

Basic steps to design a questionnaire. Concept of hypothesis testing, level of confidence and significance and p value, Inferential analysis using t-test and chi-square, One way and two way ANOVA. Correlation and regression analysis. Screening of data. Statistical data analysis software. Issues to consider when choosing statistical software.

Unit II: Minitab – Introduction to Minitab, Accessing Minitab, Minitab Worksheet, Menu and Session Commands, Entering Data, Doing Arithmetic’s, Generating Random numbers, Types of data and levels of measurement, Presenting Data in Tables and Charts, Histogram and normal probability curve, Stem-and-leaf, Box plots, Bar charts, Pie charts and scatter diagrams, Descriptive Measures and Measures of dispersion, Correlation coefficient, Regression Analysis, (simple and multiple), fitted line plots, stepwise regression, forward selection and backward elimination, logistic regression (Binary, Ordinal and Nominal), One Sample and Two Sample Tests of Hypothesis, Analysis of Variance, Chi-Square Test.

Unit III: LINGO- Introduction, Using sets, set looping functions, set based modelling examples, variable domain functions, data, INIT and CALC Functions, Window Commands, Line commands, Operators and Functions, Interfacing with external Files and spreadsheets and developing models.

Unit IV: R - Introduction to R language. Creation of data object, vector, factor and data frame.

Extraction operators in R, data import/export. Summary of data and statistical graphics with R.

The function curve. Linear Programming with R, Optimization with R Common distributions in R.

Common statistical tests. Correlation and regression analysis.

1. MINITAB Handbook – Jonathan D.Cryer, Barbara F.Ryan and Brian L. Joiner -Amazon, 2012

2. Braun W.J.and Murdock D.J. (2007):A First Course in Statistical Programming with R, Cambridge University

3. LINGO User Manual (Vol.I-III), LINDO Systems Inc.2011

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-- - -- - -- -- --- ---

DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH ALIGARH MUSLIM UNIVERSITY ALIGARH

M.A./ M.Sc. II Semester (Operations Research):

Lab course based on (ORM2003, ORM2011)

Credit: 2 Max Marks: 40+60=100

DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH ALIGARH MUSLIM UNIVERSITY ALIGARH

M.A./ M.Sc. II Semester (Operations Research):

Course Code-ORM2072 Lab course based on (ORM2021)

Credit: 2 Max Marks: 40+60=100

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Appendix A BOS 30.07.2016

DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH ALIGARH MUSLIM UNIVERSITY ALIGARH

M.A. /M.Sc. (Operations Research) III Semester

Optimization Theory & Techniques-I

Credit: 4 Max Marks: 30+70 =100

Course objectives: To introduce and understand the concept of non linear optimization problems Course outcomes: On successful completion of this course, the students will be able to

 Students will be able to solve non-linear constrained and unconstrained optimization problems

Syllabus

Unit I: Unconstrained Optimization: Fibonacci Golden section and Quadratic interpolation methods for one dimensional problems. Steepest descent, Conjugate gradient and Variable metric methods for multidimensional problems.

Unit II: Nonlinear Programming: Generalized Convexity, Quasi and Psuedo convex functions and their properties. The general Nonlinear Programming Problem; Difficulties introduced by nonlinearity. The Kuhun-Tucker necessary conditions for optimality; Insufficiency of K-T conditions; Sufficiency conditions for optimality; Solution of simple NLPP using K-T conditions.

Unit III: Quadratic Programming: Beale’s Method; Restricted basis entry method (Wolfe’s method); Proof of termination for the definite case; Resolution of the semi definite case. Duality in Quadratic Programming.

Unit IV: Convex Programming: Methods of feasible directions; Zoutendijk’s method, Rozen’s gradient projection method for linear constraints; Kelly’s cutting plane method to deal with nonlinear constraints.

1. Hadley G. (1970): Nonlinear and Dynamic Programming, Addison Wesley.

2. Bazara and Shetty (1979): Nonlinear Programming, John Wiley.

3. Rao, S.S. (1989): Optimization Theory and Applications, Wiley Eastern.

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Appendix A BOS 30.07.2016

M.A. /M.Sc. (Operations Research) III Semester

Course Code-ORM3002 Marketing & Financial Management

Credit: 4 Max Marks: 30+70 =100

Course objectives: To understand consumer buying behavior and financial management.

 Knowledge of marketing management, consumer-buying behavior and financial management.

 Financial Analysis and planning

Syllabus

Unit 1: Marketing Management: Meaning and definitions of marketing and marketing management, importance of marketing management in Indian economy, functions of marketing.

New Product Search: Screening new products, assessing user reaction to new products, breakeven analysis. Factors affecting Pricing decision, Pricing methods.

Unit II: Consumer Buying behavior: Brand Switching models, Purchase incidence models.

Advertisement: Objective & functions of advertisement models (Single period, Carryover effect and competitive models) Media selection model. Game theory models for Promotional Effort.

Unit III: Pricing: Short term pricing and promotional pricing. Distribution Models: Warehouse location, Vehicle routing. Channels of distribution, Transportation decision, Locating company’s wholesale dealers and warehouses.

Unit IV: Financial Management, Financial Analysis and Planning, Concept and measurement of cost of capital, Capital structure decisions, Dividend Policies.Short term and Long term Financial Planning. Application of Mathematical programming in Capital and Capital Budgeting Problems.

1. Fitzroy, P.T. (1976): Analytic Methods for Marketing Management, McGraw Hill.

2. Khan, M.Y. and Jain, P.K. (1987): Financial Management, McGraw Hill.

3. Comuejols, G. and Tutuncu, R. (2007): Optimization Methods in Finance, Cambridge University Press.

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Appendix A BOS 30.07.2016

M.A. /M.Sc. III Semester(Operations Research) Course Code-ORM3003

Network Flows and Dynamic Programming

Credit: 4 Max Marks: 30+70 =100

Course objectives:To understand basic concept of Network flows and Dynamic Programming with their application.

 Solution of optimization problem through network analysis.

 Applications of dynamic programming in real life programs.

Syllabus

Unit I: Basic concept of network analysis,the maximal flow problem, max flow min cut theorem, max flow labeling algorithm, LP representation of networks, Unimodular property of constraint matrix.

Unit II: The shortest route problem, shortest route algorithm, The minimal cost flow problem, Network Simplex Method, Minimal Spanning Tree Algorithm, The Out of Kilter algorithm for minimal cost network flows problem.

Unit III: Bellman’s principal of Optimality, general recursive relationship of Dynamic programming, forward and backward recursion, computational procedure for solving D.P., solution of stage coach problem by D.P.

Unit IV: The general characteristics of D.P. problems, solution of cargo loading problem (formulated as knapsack problem), the solutions to Inventory, replacement, investment and LP problem by DP.

Books recommended:

1. Bazara, M.S., Jaruis, J.J. (1977): Linear Programming and Network Flow, John Wiley.

2. Hu, T.C. (1970): Integer Programming and Network Flows, Addison Wesley.

3. Ecker, J., and Kapferschmid, M. (1988): Introduction to Operations Research, John Wiley.

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Appendix B BOS 03.04.2018

M.A. /M.Sc. III Semester (Operations Research) Course Code: ORM3004

Decision Theory and Scheduling Management

Credit: 4 Max Marks: 30+70 =100

Course objectives: Introduction of Decision Theory and its application. Concept of project scheduling problems.

 Decision making under certainty and uncertainty

 Decision making with multiple objectives

 Replacement models and failure mechanism of items

 Solution technology for project scheduling problems

Syllabus

Unit I: Decision Theory an Introduction and Its Applications, Decision Making under Certainty (DMUC); Decision making under Uncertainty – Criterion of Optimism, Pessimism, Laplace, Hurwitz and Regret. Decision Analysis under Risk (DMUR) - EMV, EOL, EPPI, EVPI Criterion.

Unit II: Decision Trees Analysis and its Applications, Baye’s Rule Decision Trees Analysis. Basic elements of statistical decision theory, Decision problems as a two-person game, Concept of Loss

& Risk functions, Prior and Posterior Distributions, Bayesian expected loss, Non-randomized decision rule and randomized decision rules, Bayes, Minimax and admissible decision rules.

Unit III: Replacement Model and failure mechanism of items; Replacement of that deteriorates with time, Replacement Policy when money value is taken into consideration, replacement of an item that fails suddenly (completely fail) - Individual and group replacement policies, age and block replacement. Recruitment, Mortality and Promotional Problems, Equipment Renewal Problem.

UNIT IV: Project Scheduling: Determination of critical tasks, critical path method (CPM) for known activity times, Various types of floats, Formulation of CPM as a linear programming problem. Program Evolution and review technique (PERT) for probabilistic activity times.

Updating of PERT charts. Project Crashing. Resource levelling and resource scheduling.

1. Johnson, L.A. and Montgomery, D.C. (1975): Operations Research in production planning, scheduling and inventory control, John Wiley & Sons.

2. Taha, H.A. (2016): Operations Research, Macmillan Pub. Co.

3. Sharma, J.K. (2013): Operations Research, Macmillan Pub. Co.

4. Berger, J.O. (1993): Statistical Decision Theory and Bayesian Analysis, Springer-Verlag.

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Appendix A BOS 30.07.2016

DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH ALIGARH MUSLIM UNIVERSITY, ALIGARH

M.A./M.Sc. (Operations Research) III-Semester

Lab. Course – Based on ORM-3001, 3003, 3004

Credit: 2 Max Marks: 40+60=100

M.A./M.Sc. (Operations Research) III-Semester

Course Code-ORM3072 Lab. Course – Project

Credit: 4 Max Marks: 40+60=100

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Appendix A BOS 30.07.2016

M.A. /M.Sc. (Operations Research) IV Semester

Optimization Theory & Techniques – II

Credit: 4 Max Marks: 30+70 =100

Course objectives:To understand the concept of integer programming and some other advanced optimization techniques.

 Formulation of real life problems as integer programming problems

 Solution of integer programming problem

 Knowledge of separable and geometric programming

Syllabus

Unit I: Applications of Integer Programming - Capital budgeting problem, The Knapsack problem, travelling salesman problem, Fixed-charge problem, Cutting stock problem and the set covering, Plant Location Problem.

Unit II: Cutting Plane methods: Dantzig and Gomery cuts, Gomery’s dual fractional, All Integer and Mixed Integer Methods; Primal all integer method.

Unit II: Branch and Bound method: Branching, bounding and fathoming, Land and Doig’s method;

Dakin’s approach, branching rules and penalties. Solution of Knapsack problems by branch and bound method. Zero-One Integer Programming: Equivalence of 0-1 problems and linear programming, Conversion of zero-one NLIPP to 0-1 LP problem, Bala’s additive algorithm for 0-1 problems.

Unit IV:Separable programming - Piecewise linear Approximation of nonlinear function, Mixed Integer Approximation of Separable NLPP. Geometric Programming: Posynomial, Unconstrained Geometric Programming Problem (GPP) using differential Calculus, Unconstrained GPP using Arithmetic – Geometric Inequality, Constrained GPP. Concept of Genetic Algorithm.

1. Taha, H.A. (1975): Integer Programming, Acad. Press.

2. Salkin, H.M. (1975): Integer Programming, Addison Wesky.

3. Hu, T.C. (1970): Integer Programming & Nelson Flu, Addison Wesky.

4. Greenberg, H. (1971): Integer Programming, Acad. Press.

5. Rao, S.S. (1989): Optimization: Theory and Applications, Wiley Eastern.

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Appendix A BOS 30.07.2016 DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH

ALIGARH MUSLIM UNIVERSITY ALIGARH M.A. /M.Sc. (Statistics/Operations Research)

IV Semester

Course code – STM/ORM4002 Reliability Theory and Survival Analysis

Credit: 4 Max Marks: 30+70 =100

Course objectives: To introduce the elementary and advanced concepts of reliability and survival analysis.

 Describe the basic concepts of reliability and survival analysis in real life scenario.

 Apply these tools in application areas like quality improvement, biostatistics, econometrics, demography. etc.

Syllabus

Unit I: Definition of Reliability function, hazard rate function, pdf in form of Hazard function, Reliability function and mean time to failure distribution (MTTF) with DFR and IFR. Basic characteristics for exponential, normal and lognormal, Weibull and gamma distribution, Loss of memory property of exponential distribution.

Unit II: Reliability and mean life estimation based on failures time from (i) Complete data (ii) Censored data with and without replacement of failed items following exponential distribution [N C r],[N B r], [N B T], [N C(r, T)], [N B(r T)], [N C T]. Accelerated testing: types of acceleration and stress loading. Life stress relationships. Arrhenius – lognormal, Arrhenius-Weibull, Arrhenius- exponential models.

Unit III: Basis of Survival analysis, Parametric methods - parametric models in survival analysis, Exponential, Weibull, Delta method in relation to MLE, Fitting of these models in one sample and two sample problems. Reliability of System connected in Series, Parallel, k-out-of-n.

Unit IV: Regression models in survival analysis. Fitting of Exponential, Weibull, Coxproportional, hazard models. Model checking and data diagnostics - Basic graphical methods, graphical checks for overall adequacy of a model, deviance, cox - snell, martingale, and deviance residuals.

1. Sinha, S.K. (1980): Reliability and life testing, Wiley, Eastern Ltd.

2. Nelson, W. (1989): Accelerated Testing, Wiley.

3. Zacks, S.O.: Introduction to reliability analysis, probability models and statistical, Springer- Verlag.

4. Meeker and Escobar (1998):

5. Klein, J.P. and Moeschberger, M.L. (2003): Survival Analysis, technique for censored and trucated data, Springer.

6.Tableman, M. and Kim, J.S. (2004): Survival Analysis Using S, Chapman & Hall/CRC.

7. Lawless J.F. (2003): Models and Methods for life time data, Second edition, Wiley.

8. Collett (2014): Modeling Survival data in medical Research, Third edition, Chapman &

Hall/CRC.

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Appendix A BOS 30.07.2016

M.A. /M.Sc. IV Semester(Operations Research) Course Code-ORM4003

Total Quality & Supply Chain Management

Credit: 4 Max Marks: 30+70 =100

Course objectives: To Introduce and understand quality and supply chain management systems Course outcomes: On successful completion of this course, the students will be able to

 Quality audit and material requirement planning.

 Global supply chain management.

Syllabus

Unit –I: Total Quality Management (TQM): Introduction, Overview, Principal Objectives, Deming Approach, CII – Quality Excellence Model, Malcolm Baldrige National Quality Award Model, Leadership, Customer satisfaction, Employee Involvement. Continuous Process Improvement – Juran’s Trilogy, PDSA Cycle, 5S, Kaizen. Supplier Partnering, Selection and Evaluation of Suppliers.

Unit–II: Introduction to ISO 9000- quality management systems-guidelines for performance improvements - Series, Evolution & Standards, Application of ISO 9001:2008 Standard, Clauses, Implementation. Quality Audit, Benchmarking, Quality Function Deployment (QFD), Failure Mode and Effect Analysis (FMEA). Introduction of ISO 14000 Quality management system.

Unit–III: Material Requirement Planning (MRP) - inputs, processing, outputs, benefits &

requirements, Capacity requirements planning. Enterprise Resource Planning (ERP). Just in Time – Push system, Kanban and pull system, MRP VS JIT system, JIT Implementation, JIT production process.

Unit–IV: Introduction of Supply Chain Management – Objectives & Principals, trends in supply chain management, Decision phases in supply chain, Global supply chains, Management responsibilities, Procurement, E- Business, Supplier Management.

Book Recommended:

1. Poornima M. Charantimath: Total quality management, Pearson Education.

2. Kaoru Ishikawa: Introduction to Quality Control, Chapman and Hall.

3. Juran J.M. and Gryna F.M. : Juran's Quality Control Handbook, 4th edition, McGraw Hill.

4. Amitava Mitra: Fundamentals of Quality Control and Improvement. 2nd Edition, Prentice-Hall Inc.

5. David Simchi-Levi, Philip Kaminsky, and Edith Simchi-Levi: Designing and Managing the Supply Chain: Concepts, Strategies, and Case Studies, 2nd Edition, McGraw-Hill.

6. Richard, B.C., Ravi, S., F. Robert, J. and Nicholas J.A.: Operations & Supply Management, 12th Edition, McGraw-Hill.

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ALIGARH MUSLIM UNIVERSITY ALIGARH M.A. /M.Sc. (Operations Research)

IV Semester Course Code-ORM4004 Applied Business Statistics

Credit: 4 Max Marks: 30+70 =100

Course objectives: To gain important statistical techniques to tackle business management problems Course outcomes: On successful completion of this course, the students will be able to

 The students will be able to analyze data and make valid conclusions based on appropriate statistical techniques.

Syllabus

Unit I: Time Series Analysis - Time series and its components with illustrations, additive, multiplicative and mixed models. Determination of trend by the Methods of least squares and Moving Average. Growth curves and their fitting- Modified exponential, Gompertz and Logistic curves. Determination of seasonal indices by Ratio to moving average, ratio to trend and link relative methods.

Demand Analysis - Introduction, Demand and supply, price elastics of supply and demand. Nature of the distribution of income and wealth, Pareto law and lognormal distribution of income distribution curves, Gini coefficient and Lorenz Curve.

Unit II: Recap of statistical inference and the properties of good estimators. Statistical intervals for single and two samples, Testing of hypothesis, parametric test (for one and two samples problems) - Z-test, t-test, F-test and Chi-square test for categorical data and goodness of fit. Application of these tests.

Unit III: Non-parametric tests for one & two samples: Sign test, Wilcoxon signed rank test, Kolmogrov-Smirnov test, Test of independence (run test), Wilcoxon-Mann-Whitney test, Median test, Kolmogrov-Smirnov test, Wald Wolfowitz’s runs test. Spearman’s and Kendall’s test.

Kruskal–Wallis test. Ansari-Bradely test, Mood test, Kendall’s Tau test, test of randomness.

Application of these tests.

Unit IV: Correlation analysis, rank, partial and multiple Correlations. Introduction of linear models, Method of least squares, linear and multiple linear regression models and their properties, parameter estimation and hypothesis testing. Inverse Regression Problem (Calibration) and Logistic Regression

1. Gupta, S.C. and Kapoor, V.K. (2008): Fundamentals of Applied Statistics, S. Chand & Sons.

2. Miller, Irwin and Miller, Marylees (2006): John E. Freund's: Mathematical Statistics with Applications, (7th Edn.), Pearson Education, Asia.

3. R. Lyman Ott and Michael Longnecker (2001): An Introduction to Statistical Methods and Data Analysis, Fifth Edition, Thomson Learning, Inc.

4. Gibbons, J.D. : Non-parametric Statistical Inference, McGraw Hill Inc.

5. Montgomery, D.C. and Peck, E. : Introduction to Linear Regression Analysis.

6. Conover, W.J. : Practical Nonparametric Statistics, Wiley series.

7. Bhisham C., Gupta and Irwin Guttman: Statistics and Probability with Applications, Wiley.

9. Milton, J.S. and Jesse, C.A.: Introduction to Probability and Statistics, McGraw Hill Inc.

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Appendix A BOS 30.07.2016

M.A. /M.Sc. IV Semester(Operations Research) Course Code-STM/ORM4005

Queuing Theory & Applied Stochastic Processes

Credit: 4 Max Marks: 30+70 =100

Course objectives: To introduce the elementary and advanced concepts of queuing theory.

 Describe the applied concepts of stochastic process.

 Apply the tools of stochastic process in queuing models and other related areas of applications.

Syllabus

Unit I: Concepts of Death and Birth process in Queuing system, Elements of Queuing System, steady state solution, Measures of effectiveness of (M/M/1):(FIFO/), (M/M/1):(FIFO/N), (M/M/S):(FIFO/), (M/M/S):(FIFO/N),Waiting time distribution of M/M/1 and M/M/S models.

Unit II: Non Markovian Queuing Systems: Concept of embedded Markov chain, Steady state solution, Mean number of arrivals, expected queue length and expected waiting time in equilibrium. (M/E_K /1) Model - Concept of Erlangian service distribution, steady state solution, Measures of effectiveness. Introduction to Queuing Systems Networks.

Unit III: Machine Repair Models - (M/M/1): (GD/M/n), (M/M/c): (GD/M/n). Power Supply Models, Deterministic Models. Application of Stochastic Process on System Reliability:

Availability and maintainability concepts, Markovian models for reliability and availability of repairable two-unit systems, Replacement model, Maintained system, Minimal Repair Replacement Polices.

Unit IV: Stochastic Processes on survival and competing risk theory: Measurement of competing risks, inter-relations of the probabilities, estimation of crude, net & partially crude probabilities, Neyman’s modified Chi-square method, Independent & dependent risks.

1. Mehdi, J. (1994): Stochastic Processes, Wiley Eastern, 2nd Ed.

2. Sheldon, M. Ross (1996): Stochastic Processes, Wiley Eastern, 2nd Ed.

2. Groos, Da Harris, C.M. (1985): Fundamental of Queuing Theory, Wiley.

3. Biswas, S. (1995): Applied Stochastic Processes, Wiley.

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M.A./M.Sc. (Operations Research) IV-Semester

Course Code-ORM-4071

Lab. Course – Based on ORM-4001, 4002, 4004, 4005

Credit: 2 Max Marks:40+60=100

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ALIGARH MUSLIM UNIVERSITY ALIGARH Course Code-STM-4091

Applied Statistics-(Open Elective)

An open elective course to be offered to M.A./M.Sc. Students of Faculty of Science other than M.A./M.Sc. (Statistics) and M.A./M.Sc. (Operations Research)

Credit: 4 Max Marks: 30+70 =100

Course objectives: To introduce the elements of applied statistics

 Describe the concepts of applied statistics in real life scenario.

 Apply the techniques in data science.

Unit I: Measures of central tendency, measures of dispersion, measures of skewness and kurtosis, basic concept of probability theory, introduction to random variables and its probability distributions, standard probability distributions: Bernoulli, binomial, Poisson, geometric, normal, exponential and lognormal.

Unit II: Bivariate data and scatter diagram, simple correlation, partial and multiple correlation, simple and multiple regression analysis, sampling distributions, testing of hypothesis (p-value approach): Z-test, t-test, F-test and Chi-square test.

Unit III: Principles of experimental design, statistical models for experimental design, completely randomized design, randomized block design, Latin square design, analysis of variance for one- way and two-way classifications.

Unit IV: Concept of sample surveys, simple random sampling with replacement and without replacement, stratified random sampling, systematic random sampling.

1. Siegel, A. F. and Morgan, C. J. (1995): Statistics and Data Analysis: An Introduction, 2^nd Edition, John Wiley & Sons, Inc. New York

2. Freund, J. E. and Perles, B. M. (2006): Modern Elementary Statistics, 12^th Edition, Pearson Higher Education.

3. Snedecor, G. W. and Cochran, W. G. (1989): Statistical Methods, 8^th Edition, Wiley.

4. R. Lyman Ott and Michael Longnecker (2001): An Introduction to Statistical Methods and Data Analysis, 5^th Edition, Thomson Learning, Inc.

5. Hogg R.V., Tanis E.A. & Zimmerman, D. (2014): Probability and Statistical Inference, 9^th Edition, Pearson Education.

Last Updated 28.12.2019