Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations...
Transcript of Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations...
![Page 1: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/1.jpg)
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.
![Page 2: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/2.jpg)
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.
Suggested Readings:
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.
![Page 3: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/3.jpg)
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.
Course outcomes: On successful completion of this course, the students will be able to
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.
![Page 4: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/4.jpg)
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.
Course outcomes: On successful completion of this course, the students will be able to
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 Cp, Cpk, and Cpm,
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, 2k full
factorial experiments, 22 and 2
3 construction designs and analysis of data.
Suggested Readings:
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.
![Page 5: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/5.jpg)
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.
Course outcomes: On successful completion of this course, the students will be able to
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
Suggested Readings:
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.
![Page 6: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/6.jpg)
DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
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
DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
M.A./ M.Sc. I Semester (Operations Research)
Paper (ORM1072)
Lab Course-II (ORM1021)
Max Marks: 40+60=100
![Page 7: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/7.jpg)
Appendix III B
BOS 05.05.03
DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
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.
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 Intoduction to Probability and Mathematical Statistics,
Wiley Eastern Limited.
![Page 8: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/8.jpg)
DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
M.A./ M.Sc. II-Semester (Operations Research)
Course Code-ORM2002
Stochastic Processes
Credit: 4 Max Marks: 30+70 =100
Course objectives: To introduce the concepts of stochastic processes.
Course outcomes: On successful completion of this course, the students will be able to
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.
Books Recommended:
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.
![Page 9: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/9.jpg)
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.
Course outcomes: On successful completion of this course, the students will be able to
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.
Books Recommended:
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
![Page 10: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/10.jpg)
Appendix B
BOS 03.04.2018
DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
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.
Course outcomes: On successful completion of this course, the students will be able to
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.
Suggested Readings:
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.
![Page 11: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/11.jpg)
DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
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.
Books Recommended:
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
![Page 12: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/12.jpg)
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.
Course outcomes: On successful completion of this course, the students will be able to
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.
Books Recommended:
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
![Page 13: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/13.jpg)
-- - -- - -- -- -------- ------
DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
M.A./ M.Sc. II Semester (Operations Research):
Course Code-ORM2071
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
![Page 14: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/14.jpg)
Appendix A
BOS 30.07.2016
DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
M.A. /M.Sc. (Operations Research)
III Semester
Course Code-ORM3001
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.
Books Recommended:
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.
![Page 15: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/15.jpg)
Appendix A
BOS 30.07.2016
DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
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.
Course outcomes: On successful completion of this course, the students will be able to
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.
Books Recommended:
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.
![Page 16: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/16.jpg)
Appendix A
BOS 30.07.2016
DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
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.
Course outcomes: On successful completion of this course, the students will be able to
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.
![Page 17: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/17.jpg)
Appendix B
BOS 03.04.2018
DEPARTMENT OF STATISTICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
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.
Course outcomes: On successful completion of this course, the students will be able to
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.
Books recommended:
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.
![Page 18: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/18.jpg)
Appendix A
BOS 30.07.2016
DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY, ALIGARH
M.A./M.Sc. (Operations Research)
III-Semester
Course Code-ORM3071
Lab. Course – Based on ORM-3001, 3003, 3004
Credit: 2 Max Marks: 40+60=100
DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY, ALIGARH
M.A./M.Sc. (Operations Research)
III-Semester
Course Code-ORM3072
Lab. Course – Project
Credit: 4 Max Marks: 40+60=100
![Page 19: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/19.jpg)
Appendix A
BOS 30.07.2016
DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
M.A. /M.Sc. (Operations Research)
IV Semester
Course Code-ORM4001
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.
Course outcomes: On successful completion of this course, the students will be able to
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.
Books recommended:
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.
![Page 20: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/20.jpg)
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.
Course outcomes: On successful completion of this course, the students will be able to
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.
Books recommended:
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.
![Page 21: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/21.jpg)
Appendix A
BOS 30.07.2016
DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
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.
![Page 22: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/22.jpg)
Appendix A
BOS 30.07.2016
DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH
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
Books recommended:
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.
![Page 23: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/23.jpg)
Appendix A
BOS 30.07.2016
DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY ALIGARH
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.
Course outcomes: On successful completion of this course, the students will be able to
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): )/( NFIFO ,
(M/M/S): )/( FIFO , (M/M/S): )/( NFIFO ,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. )1//( KEM 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.
Books Recommended:
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.
![Page 24: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/24.jpg)
DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH
ALIGARH MUSLIM UNIVERSITY, ALIGARH
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
![Page 25: Appendix B BOS 03.04.2018 DEPARTMENT OF STATISTICS ... · M.A. /M.Sc. I-Semester (Operations Research) Course Code-ORM1002 Linear Algebra and Real Analysis Credit: 4 Max Marks: 30+70=100](https://reader034.fdocuments.in/reader034/viewer/2022042209/5eacb1cbc3b05b605a4480e0/html5/thumbnails/25.jpg)
Appendix A
BOS 30.07.2016
DEPARTMENT OF STATISITICS & OPERATIONS RESEARCH
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
Course outcomes: On successful completion of this course, the students will be able to
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.
Books Recommended:
1. Siegel, A. F. and Morgan, C. J. (1995): Statistics and Data Analysis: An Introduction, 2nd
Edition, John Wiley & Sons, Inc. New York
2. Freund, J. E. and Perles, B. M. (2006): Modern Elementary Statistics, 12th
Edition, Pearson
Higher Education.
3. Snedecor, G. W. and Cochran, W. G. (1989): Statistical Methods, 8th
Edition, Wiley.
4. R. Lyman Ott and Michael Longnecker (2001): An Introduction to Statistical Methods and
Data Analysis, 5th
Edition, Thomson Learning, Inc.
5. Hogg R.V., Tanis E.A. & Zimmerman, D. (2014): Probability and Statistical Inference, 9th
Edition, Pearson Education.
Last Updated 28.12.2019