- Algorithms on Graphs and Networks (G&N)
The course aims to introduce students to graph and network algorithms. The takeaways from this course will be useful to students in a variety of courses in logistics and supply chain management.
- Applied Multivariate Analysis (AMA)
This course gives a balanced emphasis on theory and applications. It covers the following broad areas: Multivariate Normal Distribution and Related Inference Problems, Assessing Normality, Outlier Detection, Multiple Linear Regression Analysis, Variable Selection Problems, Multicollinearlity, Heteroscedasticity, Regression Plots, Regression Diagnostics, Model Specification Tests, Auto correlated and Longitudinal Data Analysis.
- Applied Regression Analysis (ARA)
This course is designed to provide a comprehensive exposition on the scope and applicability of regression modelling techniques in solving real-life problems. In doing so, the aim will be to inculcate a sound understanding of both the underlying theoretical aspects of modelling as well as various issues that are encountered in applying the models in real-life scenarios. Real datasets and cases from diverse areas (like business administration, economics, engineering and social, biological and ecological sciences) will be analysed which will help the participants in reinforcing their methodological and conceptual understanding. It is expected that by the end of the course, the participants will gain a thorough understanding of various aspects of regression models and their applicability in analyzing datasets they may encounter during their FPM coursework/programme and beyond. Since all applications will be carried out in the R programming language, this course can also aid the participants in learning this important statistical programming language at some length.
- Applied Statistical Inference (ASI)
This course will explore the concepts of statistical inference with applications in management research in mind. This course will start with basic inference but will also cover situations where assumptions about situations being ‘nice' do not work, and one needs to go beyond the obvious. Estimation techniques, both theoretical and empirical, will be covered. Asymptotic as well as data-driven estimates will be derived. Examples will be discussed in detail. The theoretical discussions will be backed up by hands-on training to apply the methodology to data sets using R. Both standard packages and non-standard coding will be discussed.
- Approximate Methods in Solving Real World Complexities (AMS)
Exact approaches in solving problems are highly dependent on definitive problem structuring and on computational sophistication. They generate superior solutions, but with huge computational time and overhead. In solving real-world problems, very often heuristic procedures are applied as a trade-off for acceptable, but quick solutions. Meta-heuristic procedures are standardized and advanced procedures that operate iteratively to generate improved solutions under dynamic system variations. In fact, most of the problems in real world are prone to dynamic and uncertain changes that are difficult to solve using standard and bespoke heuristics. This course discusses a host of meta-heuristic algorithms that can effectively address the real world complexities and inter-dependencies. Discussions shall cover some of the distinctive characteristics of these meta-heuristics such as learning, self-correction and adaption.
- Bayesian Methodology for Business Research (BMBR)
Application of Bayesian methodology in solving business research problems is a fast growing area of research. In this course we will start from the scratch assuming no prior knowledge of Bayesian Methodology. Before getting into deeper issues of Bayesian modelling, we plan to devote adequate number of sessions at the beginning to acquaint the students with the basic tools and concepts of Bayesian inference. In this course, our emphasis will be on the modelling aspect of business data arising in different functional areas of management from a Bayesian perspective. In this context, we will discuss hierarchical Bayesian models, model checking (both data model consistency and model selection) and implementation of the methodologies through Bayesian computation.
- Convexity & Optimization (CO)
Convex analysis is the analysis of properties of convex functions and convex sets in a normed vector space. In optimization, convexity plays a very important role in proving optimality results in both linear and nonlinear optimization. For instance, the concept of a separating hyperplane between two disjoint convex sets helps establish the sufficiency of KKT conditions for optimality of convex programming problem. However, to prove the existence of a separating hyperplane between two disjoint convex sets requires knowledge of continuous functions, affine transformations, dimension of sets, hyperplanes and uses other topological properties of sets such as closure, relative interior, relative boundary and compactness, amongst others. This course is aimed at establishing these results from basic results in set theory and topology. Among the topics discussed are basic properties of convex sets (extreme points, facial structure of polytopes), separation theorems, duality and polars, propertes of convex functions, mimima and maxima of convex functions over a convex set and various optimization problems.
- Game Theory for Operations Management (GTOM)
Game Theory deals with problems of strategic interaction between two or more players, wherein each player needs to decide its best action, while anticipating the reaction from the other(s). In business, such strategic interactions occur at various levels. If the decision making within a firm is decentralized, then such interactions may manifest between two of its functions; for example, between marketing and production for price and leadtime decisions (Pekgun et al., 2008). This also often manifests between two retailers deciding the stocking (newsvendor) quantity of a limited shelf-life product for the next period (Lipman and McCardle, 1997), or between two manufacturers/service providers for price and delivery leadtime (So, 2000), or between a retailer and a manufacturer in a supply chain (Tsay and Agarwal, 2000; Camdereli and Swaminathan, 2005; Wang and Zipkin, 2009), or between two supply chains (Liu & Tyagi, 2011). The objective of this course is to prepare students to analyze such problems of strategic interactions that are pertinent to Operations Managers. It also covers such problems that lie at the interface between Operations and other functions like, IT (Camdereli and Swaminathan, 2005); Marketing (Pekgun et al., 2008; Goic et al., 2011); Environment (Orsmedir et al., 2015; Zhou et al., 2016; Park et al., 2015); and Finance (Dada and Hu, 2008; Lai et al., 2011; Lai et al., 2012).
The course assumes no prior background on Game Theory. It will, therefore, begin with the basic concepts of elimination of dominated strategies and Nash Equilibrium to arrive at the outcome of a game. We will discuss four classes of games: static games of complete information; dynamic games of complete (perfect/imperfect) information; static games of incomplete information; and dynamic games of incomplete information. Corresponding to these four classes of games, we will discuss the four notions of equilibrium in games: Nash equilibrium, subgame-perfect Nash equilibrium, Bayesian Nash equilibrium, and perfect Bayesian equilibrium. After developing the idea of corresponding equilibrium concept, we will study one or two problems of strategic interactions arising in each of the four categories of the games, which are relevant to Operations/Supply chain Managers. We will see how to arrive at the corresponding equilibrium for each of the games, and derive useful insights for Operations managers. To this end, the course will also introduce Bilevel Mathematical programming & its solution methods for Stackelberg Games (2-stage Dynamic games with complete and perfect information).
- Large Scale Optimization (LSO)
Real world optimization problems often tend to be large Integer Program/ Mixed Integer Program (IP/MIP) problems, often to an extent that even the standard IP/MIP solvers, which use Branch & Bound and Branch and Cut algorithms, fail to solve them in reasonable time. In this course, students learn how to take advantage of the often hidden special structures of such problems either by relaxation or by decomposition into relatively easier/smaller problems, which can be solved efficiently using their special structures. The challenge then is how to recover the solution to the original problem from the solution to its relaxation/decomposition. To this end, the introduces several decomposition techniques, namely, Cutting Plane Method, Lagrangian Relaxation, Benders Decomposition, Column Generation, and Dantzig-Wolfe Decomposition methods. The course also introduces linearization techniques for non-linear IP/MIP problems and their solutions using cutting plane techniques. Towards the end, the course also introduces Stochastic Optimization and Database Optimization Interface.
This is an applied course, and hence its focus is more on understanding and applications of the techniques rather than on formal proofs. The course introduces several practical applications from Hub-and-Spoke Network Design, Facility Location, Telecommunication Network Design, etc.
- Non-linear Optimization (NLO)
The course introduces students to the fundamentals of non-linear optimization and then builds on it to introduce other advanced topics in the area of optimization. It enables students to enhance their understanding of optimization methods that may be suitable for problems with complexities such as non-linearity, non-convexity, discontinuity and non-differentiability.
Around 50% of the course focuses on the conventional techniques for solving non-linear optimization problems. 20% of the course focuses on non-traditional optimization techniques. Remaining 30% of the course discusses extensions of single objective optimization to multiobjective optimization, bilevel optimization and robust optimization.
- Problem Solving With Heuristics (PSH)
Many real-world optimization problems belong to the class of NP-hard problems, which mean that there are no methods that guarantee optimal solutions to large instances of such problems within reasonable time. However obtaining good quality solutions to such problems are important in practice, and research has focused on developing heuristic methods for such problems. In this course the participant is exposed to the current state of knowledge about heuristic techniques to solve large instances of combinatorial optimization problems.
- Queuing Models (QM)
The participants will be able to appreciate the various queuing modelling constructs and solution algorithms as an analytical toolkit. Further, the participant will be able to develop customized models to analyse the performance of a practical system, and obtain design insights. No prior working knowledge of measure theory or stochastic processes is required. However, participants should have a prior course on basic probability theory.
- Revenue Management and Dynamic Pricing (RMDP)
Revenue Management and Dynamic Pricing (RMDP) is the method of selling right product to the right customer at the right price at the right time. It is the scientific way of dynamically managing prices, inventories, and capacities of perishable services. Although core of RM is related to OR/Statistics, it has relationship with economics, marketing, information technology, human resources and legal dimension. In this doctoral courses, we plan to discuss those topics that cuts across four disciplines, PQM (OR/OM/Statistics), economics, marketing and information technology. Conceptually the course focuses on two three aspects, economics of pricing, optimization of perishable resources and forecasting of demand of perishable products. We discuss several aspects related to design of revenue management system. At end we discuss emerging research areas on the topic.
- Real Analysis (RA)
The course analyses basic concepts in certain areas of mathematics and prepares students to take advanced courses. The topics covered include : structure of the real number system, infinite sequence- convergence and divergence, subsequence – Bolzano-Weierstrass Theorem, Cantor intersection property, Cauchy sequences, infinite series - convergence and divergence, tests for convergence, Metric Spaces - limits, continuity, Compactness – Heine-Borel theorem, connectedness and uniform continuity.
- Statistics II (Stat-II)
The course will provide an understanding of the statistical methods that are useful for carrying out research in management.
- Stochastic Processes (SP)
The objective of this course is to provide the theoretical foundation for modelling and analysis of variety of processes in service and manufacturing environments that are characterized by uncertainty. Topics include birth and death processes, Markov chains, Markov processes, renewal theory, martingales and optimal stopping, processes with independent increments (e.g. Poisson, Wiener processes), Brownian motion and the theory of weak convergence, application of stochastic processes in logistics, inventory, manufacturing, marketing, and finance.
- Systems Analysis and Simulation (SAS)
To introduce the participant to the idea of simulation in management, and to expose them to the latest software and statistical techniques in simulation. The broad topics that will be covered are: Introduction to Simulation, Building Simulation Models, Input Modelling, Generating Random Input, Output Analysis, Comparing and Optimizing Systems, and Variance Reduction.
- Survey of Statistical Methods Used in Management Research (SSMMR)
This is close to a comprehensive review of major statistical methods that are used extensively in management research. This course should serve the purpose of exposing the student to these prolifically used statistical/empirical methods. While all attempts have been made to make the course comprehensive enough to include major techniques, it is not necessarily exhaustive. Additionally, this is a generic survey course to provide exposure to the methods to FPM students. Students are advised to acquire additional expertise in any specific topic by choosing advanced courses offered by various relevant academic Areas of the institute.
- Time Series Analysis (TSA)
This course introduces the theory and methods of time series analysis for research in economics and finance. The objective of the course is two-fold. First is to give participants enough technical background to enable them to read research papers in applied time series analysis. The second is to introduce select advanced topics useful for analysis of macroeconomic and financial time series. After introducing fundamental concepts in time series analysis, the course covers the theory of stationary ARMA processes and reviews the relevant asymptotic distribution theory. This forms the bulk of roughly half the course and the basis for studying Vector Autoregressions (VARs) which is discussed next. Moving on from considering covariance stationary processes, the course next introduces the econometrics of unit roots. The core of the remaining portion consists of studying linear combinations of unit root processes, i.e. Cointegrated Systems (VECMs) and models with conditional heteroskedasticity (GARCH). We end the course by introducing State Space representations of time series models and Bayesian methods.