M.Sc. in Applied Operational Research

Course Description : M.A. / M.Sc. in Applied Operational Research is a two year course. Annual examinations are held at the end of the academic year (April and May). Eight courses are taught in the first year and six in the second. Students also take up projects from Industries as part of their curriculum in second year.

Department of Operational Research, University of Delhi is a pioneer in teaching and research in Operational Research (O.R.). It is the only University Department in India that is dedicated solely for this purpose. To develop manpower competent to implement O.R. in Business, Industry and government organizations, a post graduate course in Applied Operational Research is run by the Department at South campus of University of Delhi. Students are encouraged to apply O.R. tools that they learn in the classrooms. Case studies and Industrial projects are the most important constituent of the course.

The curriculum lays heavy emphasis on experimental and process-oriented learning. The pedagogical tools include the use of case studies and industry oriented project work. Besides building up skills of individual decision making, lot of emphasis is laid on developing team skills and value focused decision making.

The Campus has excellent facilities with a computer laboratory with the latest software related to O.R. and a well stocked library. Students get practical training in computer programming and O.R. related software.

South Campus also has Hostels for Men and Women (selection is based on merit and requirement).

Apart from popular application software and compilers, students can work on following software packages:

SPSS 11.5
E-views 4.1
MS Project 2000
Sigma Plot 8.0

Type of Degree (Diploma/Degree) : Degree
Type of Course : Post Graduate
Duration of Course : Two years course
Venue For Teaching : Department of Operational Research South Campus
Benito Juarez Road New Delhi-110021.

Parent Department : Department of Operational Research
Parent Faculty : Faculty of MATHEMATICAL SCIENCES

Subjects :

Part 1
Course I
Computer Programming and Numerical Methods
(a) Computer Programming, (b) Numerical Methods and (c) Minor project using (a)

Course II
Statistical Methods

Course III
Linear Programming

Course IV
Inventory Management

Course V
Queueing and Simulation

Course VI
Marketing Management

Course VII
Database Management System and Visual Programming
(a) Theory (b) Practical

Course VIII
Industrial Statistics

Part II
Course IX
Network Analysis and theory of Sequencing

Course X
Theory of Reliability and Maintenance
Course XI
Mathematical Programming
Course XII
Software Engineering
Course XIII and XIV : Optionals (Any two of the following)

(i) Advanced Mathematical Programming (ii) Applied Queueing Systems (iiii) Adavanced Inventory Management (iv) Applied Reliability Methods (v) Marketing Research (vi) Financial Management (vii) Theory of Control (viii) WEB Programming using JAVA (a.Theory, b. Practical) (ix) Data Warehousing and Data Mining

Course XV

Industrial and Project Work

The work will start in the beginning of M.A. /M.Sc. Part-II under approved supervisors from amongst the members of the faculty and the report is to be submitted for evaluation by March 31. It will carry 200 marks.
Subject Syllabus


Course – I
Computer Programming and Numerical Methods
Part (a)
Introduction to UNIX / WINDOWS NT / WINDOWS Operating System, File and Memory Management. Elementary Data Structure in C++. Arrays, Stacks, Queues, Link Lists, Trees and Fundamental File Structure Concepts and its Access. Introduction to Object Oriented Programming. Object and Classes in C++. Functions, Structures, Arrays, Operator Overloading, Inheritance, Pointer, Memory Management, Polymorphism, Exceptions, Templates, Container Classes, File and Streams.
Part (b)
Theory of interpolation with error terms, Numerical integration with error terms, Trapezoidal, Simpson?s 1/3rd, 3/8th, Weddle?s and Gauss quadrature formulas, Gregory?s Euler Maclaurin?s formula.
A minor project using Course-I (a)
Course II
Statistical Methods Probability spaces, Conditional probability. Random variables, Expectation, Characteristic functions, Generating functions, Law of large numbers, Central limit Theorem. Discrete and Continuous probability distributions. Compound distribution. Linear regression analysis, Correlation, Curve-Fitting, Pearson?s System.
Sampling distribution of mean and s2 for Normal Population : t, x2 & F distributions, and tests of significance based on them. Theory of point estimation and interval estimation. Theory of testing of hypothesis: Simple and composite hypothesis, Neyman Pearson lemma and likelihood ratio tests.
Course III
Linear Programming
Convex sets and convex cones. Convex function and their properties. Theory of Simplex Method, Simplex Algorithm. Degeneracy, Duality theorem, Transportation problem, Assignment problem, Revised Simplex method, Parametric linear programming, Sensitivity analysis, Dual-simplex method, Bounded variable problem, Decomposition in linear Programming, Rectangular games: methods of solution. Equivalence of rectangular games and linear programming,
Case studies.
Course IV
Inventory Management
Concept of inventory. Estimation of different cost functions. Classification of items. Inventory control with deterministic and stochastic demands with and without lead time. Power demand pattern. Deterioration, Perishibility in inventory models. Safety Stock level. All units and incremental discounts inventory models. Multi item model with constraints. Individual and Joint Order policy, Optimum warehousing capacity. Simple periodic review model. Production Scheduling model.
Value analysis. Codifiation and standardization of items, Simulation in inventory. Computer aid in controlling inventories.
Case studies relating to inventory decisions.
Course V
Queueing and Simulation

Introduction to Stochastic Processes, Markov Chain and Markov Processes. Description of Queues; Probability description of arrivals and service times. Basic structure of Queueing models.

Mathematical Queueing Models: M/M/1, M/M/C, M/G/1, G/M/1, M/D/1, M/D/C, M/Ek/1 and Ek/M/1. Solutions for the Queue length, waiting time and busy period. Basic idea of priority and other queue disciplines. Simulation and Monte Carlo Techniques. Book-keeping aspects of Simulation. Monte Carlo method applied to Queueing Theory. Application of Queueing Theory to Machine interference problem.
Case studies.
Course VI

Marketing Management

Concept of marketing and its role in business and public organisations, Marketing decisions, Need for scientific marketing analysis, Uses and limitations of mathematical models in marketing, Classifications of market structure depending upon the nature of competitive conditions. Demand elasticities and elasticity theorem; Factors affecting pricing decision, Pricing methods; Joint optimization of price, quality and promotional effort, Purchasing under fluctuating prices.

Introduction of a new product, Consumer behaviour, Utility measure for product search, Break-even analysis for product evaluation, PERT and CPM in product development. Promotional decisions in the presence of competition, Game theory models for promotional effort, Spatial allocation of promotional effort, Media allocation for advertisement. Brand switching analysis.

Channels of distribution, Transportation decision, Locating company?s wholesale dealers and warehouses.
Case studies relating to marketing decisions.
Course VII
Database Management System and Visual programming
Part (a) Theory
Introduction to Database Systems. Data Models, Relational Model. The ER Methodology for Logical Design. Relational Algebra, SQL, Design Theory for Relational Databases. Object Oriented Database Systems. Physical Level Organization, Query Processing & Optimization, Security and Integrity, Concurrency Control and Crash Recovery, Distributed Systems.

Introduction to Client Server Programming : Visual programming environment, iconic systems and their specifications including syntactic and semantic aspects, Messages and message passing, Programming with graphic devices, Implementation with visual systems. Introduction to Visual Basic.
Course (b)
Practical based on VII (a)
Course VIII
Industrial Statistics Time-series : Components of time series, Measurement of trend, seasonal and cyclical components, Forecasting techniques.

Statistical Quality control. Control Charts. Sampling acceptance plans. Properties and determination of parameters of single and double sampling plans for LTPD, AQL requirements, OC-curve scheme for determination of parameters for single sampling plan.
Econometrics : Theory of regression for single equation models and simultaneous equation models. Distributed lag-models. Multicollinearity.

Case studies in application of econometric models and other specialised aspects of Econometrics.
Course IX

Network Analysis and Theory of Sequencing

Flows in networks, Maximal flow, Distribution and General Minimal Cost Flow problems. Shortest Path and Travelling Salesman Problem, Construction of minimal spanning tree and its applications.
PERT and CPM with activity times known and probabilistic, Various types of floats, Updating of PERT charts, Project crashing, Formulation of CPM as a linear programming problem, Resource leveling and Resource Scheduling.

Sequencing Problems, Flow shop problem and general n/m job-shop problem.
Numerical solution of ordinary differential equations. One step methods for initial value problems and boundary value problems. Numerical solution of ordinary differential equations. One step methods for initial value problems and boundary value problems.

Course X
Theory of Reliability and Maintenance
Part – A
Basics of Reliability including structured function. Classes of life distributions, Series, Parallel, Standby configurations, Bridge structure. Reliability models of maintained & nonmaintained systems. Availability theory and its modelling for various configurations.

Part – B
Renewal theory and its application to one-unit repairable systems with simple different maintenance policies (Age, Block, Preventive & Corrective). Minimal repair replacement policies, ordering policies. Notions of Ageing.

Optimization problems with respect to system reliability. Overhaul and repair decisions. Reliability allocations problems.

Case Studies.
Course XI
Mathematical Programming
Convex sets, Convex functions and their properties, Fritz-John?s optimality conditions, Kuhn ? Tucker?s optimality conditions. Quadratic Programming: Methods due to Beale and Wolfe. Duality in quadratic programming.

Elements of Dynamic Programming, Integer Programming: Dantzig?s Method, Gomory?s method for all integer and mixed integer Programming, Branch and bound technique, E. Balas? Algorithim for 0-1 Programming.

Goal Programming : Lexico-graphic and Weighting Vector Approach for Multiobjective Linear Programming Problems.
Course XII

Software Engineering

A historical overview of software technology. Software production and its difficulties, Software life cycle models. Stepwise Refinement, CASE, and Other Tools of the Trade. Modularity and Objects. Requirements analysis, Requirements specification methods. Software planning and project management, Software design.
Software verification, validation, and testing. Introduction to Software Reliability, Importance of Software testing, Difference between hardware and software reliability, Software Reliability and Availability, Modelling Software Reliability and its uses. Markovian models, NHPP models, Parameter estimation. Reliability of Modular software, Introduction to COTS.

Release time problems, Release time problem based on cost criterion, Reliability criterion, Cost-reliability criteria, Penalty cost, Testing effort, Random lifecycle, Warranty and risk costs, Bicriterion release policy.
Software implementation and integration, Software maintenance.

Case Studies.
Course XIII & XIV
(i) Advanced Mathematical Programming
Feasible direction method, Rosen?s gradient Projection method, Generalized convexity and their properties. Fritz-John?s generalized optimality conditions. Duality in convex programming. Stochastic, Fractional, Indefinite and Geometic Programming. Non-differentiable Programming : Optimality conditions and duality relations. Multi-objective linear programming : Vector maximum and Interactive approaches.
Course XIII to XIV

(ii) Applied Queueing Systems

Probability distribution of phase type. Quasi Birth and Death processes, G/PH/1 queueing models and their algorithmic solution. Combinatorial method and its application in queueing theory. Duality principle of queueing theory. Introduction to different queueing network models. Use of queueing theory in manufacturing systems. Queueing theory in practice.
Individual and social optimization of Markovian queueing models. M/G/1 model with server?s vacations and different priorities.

Case Studies.
Chapters XIII to XIV
(iii) Advanced Inventory Management
Dynamic inventory models. Probabilistic reorder Point inventory models with and without lead time. Distribution free analysis. Minmax solution of inventory model. Capacity expansion and warehousing problem. Periodic review and continuous review models. Two bin inventory system. Inventory management of items with deterioration. Production and production functions. Production planning and inventory management. Planning and control in multiechelon inventory management. Planning and control in multiechelon inventory system. Material management, material planning and handling. Purchasing function. Material Requirement Planning.

Course XIII to XIV
(iv) Applied Reliability Methods

Part – A
System Modelling : Markov Renewal Process (Semi-Markov Process) Applications to analyse 2-unit and multiunit systems, Preventive maintenance/corrective maintenance policies for these systems. Generalized availability measures. Replacement policies and Ordering Policies under extended Minimal Repair, Application of these policies to Computing Systems.

Part – B
Reliability in Design : Failure Mode Effects & Criticality Analysis (FMECA), Fault Tree Analysis (FTA)
Probability Plotting : Probability plotting techniques, Straight line fitting, Censored data. Probability plots for Lognormal, Weibull, Extreme value and Binomial distributions.
Quality Systems: Principles & concepts of Quality Management, and its implementation. Total Quality Management, Quality motivation & reward, Quality system standards (ISO-9000). Human Reliability Modelling : Concept of human error, types & causes of human error. Human reliability modelling in continuous time. Human error prediction technique.

Computerised Methods : Reliability evaluation software.

Courses XIII to XIV (v)

Marketing Research

Marketing Research and its objectives, Methods of collecting Primary and Secondary data; Marketing Research as a Cost-incurring function-Bayesian approach. Analysis of the data. Consumer behaviour Marketing strategies. Application of Cluster analysis, Discriminant Analysis and Factor analysis and Automatic Interaction Detection to marketing problems. Studies relating to Pricing, Promotion(Diffusion models), Purchasing and distribution decisions.
Conjoint Analysis, Multidimensional Scaling.
Experimental design and Analysis of variance.

Course XIII to XIV

(vi) Financial Management

Elements of Financial Management: Financial Analysis and Planning. Capital Budgeting Decisions under certainty and uncertainty. Application of Goal Programming in Capital Budgeting Decisions. Cost of Capital, Capital Structure and Dividend Policies. Working Capital Management. Short term and Long term Financial Planning. Introduction to Portfolio Management. Application of Stochastic Processes in Finance.
Case studies.

Courses XIII to XIV (vii)

Theory of Control

Fundamentals of optimal control Problem formulation, Indentification and control, Mathematical models of continuous and discrete time optimal control problems, and Necessary and sufficient conditions for optimality (discrete and continuous), Some special continuous time optimal control problems, Relationship of the Maximum Principal to Dynamic Programming, Computational methods, stochastic control.
Case studies.

Course XIII to XIV (viii)

WEB Programming using JAVA

Part-(a) Theory

Introduction to Java Programming. Basic Syntax & Structures, Applets, Control Structures, Methods, Arrays, Strings, Object Oriented Programming Concepts (Objects, Classes, Inheritance), GUI Component (Panels and Frames), Multimedia (Sound, Graphics, Images and Animation), Error and Exception Handling, Multithreading and Input/Output Streams.

Introduction to Internet, HTML and E-commerce

Part (b) Practical based on part (a)

Course XIII to XIV

(ix) Data Warehousing and Data Mining Overview of Data Warehouse, Online analytical Processing (OLAP). Introduction to Data Mining, The Knowledge in Databases (KDD) process, Limitation of traditional query tools. Association rules, Classification, Clustering, Regression, Patterns, Time series. Measuring predictive performance, Efficiency, Data preparation, Data Reduction, Mathematical Solutions, Statistical Methods, Distance Solutions, Decision Trees, Decision Rules, Neural Networks, Genetic Algorithms. Text mining, Text categorization. Mining Web Logs.
Case Studies.

Admission Eligibility :

i) M.A./M.Sc.in Mathematics/Statistics/ Physics/Electronics/ Economics/Business Economics/ M.C.A.
ii) B.A./B.Sc.(Hons.) Mathematics/ Statistics/Physics/ Electronics/Economics or B.E.
iii) B.A.(Pass)/B.Sc.(Gen.)with Mathematics/ Statistics/Computer Science/Operational Research.
(b) For Students of other Universities recognised by University of Delhi:
(i) M.A./M.Sc. in Mathematics/Statistics/M.C.A.
(ii) B.A./B.Sc.(Hons.) in Mathematics/Statistics/ Physics/Economics or B.E.
(iii) B.A.(Pass)/ B.Sc.(Gen.) with Mathematics/Statistics./ Computer Science.
Admission to M.A. / M.Sc. Applied Operational Research is strictly on merit. Graduates with Mathematics as a subject are eligible to apply. Preference is given to honours degrees in Mathematics and Statistics and B.Sc. Mathematical Sciences.
For further details kindly refer to the admission brochure.
Admission brochure and application forms are available at South Campus, University of Delhi from June 25, 2003.
For queries on the admission procedure only please contact

Office of the Assistant Registrar (General),
University of Delhi – South Campus,
Benito Juarez Road,
New Delhi – 110021
Phone: 26111955, 26876180
Other Info:

The placement activities are managed by the Students. The Department also arranges placement talks and campus interviews. Many students have secured good jobs in Indian and Multinational Organizations and with the Government institutions. For further information please contact

Dr. A.K. Bardhan

Room no. 108, Arts Faculty Building

University of Delhi – South Campus
Benito Juarez Road
New Delhi – 110 021

Phone: 26111955 Extn. 295 (Office) 27662479 (Res.) E-mail: amit@du.ac.in amitb9@yahoo.co.in
The Head
Department of Operational Research
University of Delhi
Delhi – 110 007
Phone: 27666960, 27666672 (Telefax)
E-mail: pkkapur@du.ac.in

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