Course Description
Syllabus
Operations Research/Optimization
Basic concepts of Linear Programming (LP), Simplex Method, Big-M Method, Duality, Dual Simplex Problem, Sensitivity Analysis, Ideas of KKT condition, Ideas of Network Analysis, Non-Linear Programming (NLP), Quadratic Programming (QP), Reliability Optimization, Robust Optimization, etc.
Multi Criteria Decision Making
Multiple Objective Decision Making (MODM), Multiple Criteria Decision Making (MCDM); Decisions under uncertainty
Statistics and Multivariate Statistics
Multivariate Data Analysis, Multivariate Distribution, Multiple Regression models, Principle Component Analysis (PCA), Factor Analysis (FA), Multivariate Analysis of Variance (MANOVA), Conjoint Analysis, Canonical Correlation, Cluster Analysis, Multidimensional Scaling, Structural Equation Modelling (SEM), etc.
Non-parameter Techniques
Data Envelopment Analysis (DEA), Analytical Hierarchy Process (AHP); Statistical Decision Trees; Utility analysis and its significance to MCDM and MODM; Concepts of heuristic approaches with introduction to variety of examples of heuristics methods
Course Content
Course Content
Operations Research
- Introduction to Operations Research, Frederick S. Hillier, Gerald J. Lieberman, Bodhibroto Nag, Preetam Basu, McGraw Hill, 2017, ISBN-10: 9354601200, ISBN-13 : 978-9354601200
- Operations Research : Applications and Algorithms, W. Winston, Duxbury Press, 2003, ISBN-10: 0534423620, ISBN-13: 978-0534423629
- Optimization in Operations Research, Ronald L. Rardin, Pearson Prentice Hall, 1997, ISBN-10: 0023984155, ISBN-13: 978-0023984150
Probability & Statistics
- Introduction to Mathematical Statistics, R. V. Hogg, and A. T. Craig, Pearson Education, 2004, ISBN (10): 81-7808-630-1.
- Introduction to the Theory of Statistics, A. M. Mood, F. A. Graybill and D. E. Boes, Tata McGraw Hill Publication, 2001, ISBN (10): 0-07-044520-6.
- Mathematical Statistics, J. Shao., Springer, 2003, ISBN (10): 0387953825/ISBN (13): 978-0387953823
- Statistical Inference, G. Casella and R. L. Berger, Cengage India Private Limited, 2007, ISBN (10): 8131755371/ISBN (13): 978-8131503942
Multivariate Statistics
- Applied Multivariate Statistical Analysis, Richard A. Johnson and Dean W. Wichern, Prentice Hall India, 2012, ISBN-10: 8120345878, ISBN-13: 978-8120345874
- Multivariate Statistical Analysis, Narayan C. Giri, CRC Press, 2003, ISBN-10: 0824747135, ISBN-13: 978-0824747138
Forecasting
Forecasting: Methods and Applications, Spyros G. Makridakis, Steven C. Wheelwright, Rob J. Hyndman, Wiley,1998, ISBN-13: 978-0471532330
Linear Regression
- Introduction to Linear Regression Analysis, Douglas C Montgomery, Elizabeth A Peck, G. Geoffrey Vining, Wiley, 2006, ISBN-13: 978-8126510474
- Applied Regression Analysis, N. R. Draper and H. Smith, Wiley & Sons, 1981, ISBN (10): 0471170828.
MACBETH
- Bana e Costa, Carlos A. and Chagas, Manuel P. (2004). A career choice problem: An example of how to use MACBETH to build a quantitative value model based on qualitative value judgments, European Journal of Operational Research, 153, 323-331.
- Bana e Costa Carlos A. and Vansnick, Jean-Claude. (1995). General overview of the MACBETH approach in Advances in Multicriteria Analysis: P.M. Pardalos, Y. Siskos, C. Zopounidis (Edited), Non-convex Optimization and its Applications, Kluwer Academic Publishers, 93-100, ISBN: 0-7923-3671-2.
PROMETHEE
- Behzadian, M., Kazemzadeh, R. B., Albadvi, A. and Aghdasi, M. (2010). PROMETHEE: A comprehensive literature review on methodologies and applications, European Journal of Operational Research, 200, 198-215.
- Brans, J. P. and Vincke, Ph. (1985). A preference ranking organization method, Management Science, 31, 647-656.
- Brans, J. P, Mareschal, B. (2005). PROMETHEE Methods (Chapter 5, pp: 163-195) in J. Figueira, S. Greco, and M. Ehrgott (Edited). Multiple attributes decision analysis: State of the art survey, Springer, ISBN: 9780387230818,
- Brans, J. P, Mareschal, B. and Vincke, Ph. (1984). Promethee: A new family of outranking methods in multicriteria analysis (OR'84: Edited by J. P. Brans), 408-421, North Holland.
MCDM
- Charnes, A. and Cooper, W. W. (1961). Management Models and Industrial Applications of Linear Programming, John Wiley & Sons, ISBN: 9780471148500.
- Ehrgott, M., Figueira, J. R. and Greco, S. (Eds). (2010). Trends in Multiple Criteria Decision Analysis, Springer, ISBN: 978-1-4419-5903-4.
- Figueira, J., Greco, S. and Ehrgott, M. (2005). Multiple attributes decision analysis: State of the art survey, Springer, ISBN: 9780387230818.
- Hwang, Ching-Lai. and Yoon, Kwangsun. (1981). Multiple Attribute Decision Making Methods and Applications A State-of-the-Art Survey in Lecture notes in Economics and Mathematical Systems, 186, Springer-Verlag, Berlin, ISBN: 978-3-540-10558-9.
- Gal, T., Stewart T. J. and Hanne T. (1999). Multicriterion Decision Making, Springer Verlag, ISBN: 978-1-4613-7283-7.
- Opricovic, S. and Tzeng, Gwo-Hshiung. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS, European Journal of Operational Research, 156, 445–455.
- Parlos, P. M. (Eds) (2000). Multi-Criteria Decision Making Methods: A Comparative Study, Kluwer Academic Publishers, ISBN: 0-7923-6607-7.
- Tzeng, Gwo-Hshiung. and Huang Jih-Jeng. (2011). Multiple Attribute Decision Making: Methods and Applications, CRC Press Taylor & Francis, ISBN: 978-1-4398-6157-8.
- Zeleny, M. (1982). Multi Criterion Decision Making, McGraw Hill, ISBN: 978-0070727953.
Utility Theory/Analysis
- Fishburn, Peter C. (1970). Utility Theory for Decision Making, John Wiley & Sons, ISBN: 0-88275-736-9.
- Kreps, David M. (1988). Notes on the Theory of Choice, West View Press, ISBN: 0-8133-7553-3.
ELECTRE
Roy, Bernard. (1968). Classement et choix en présence de points de vue multiples (la méthode ELECTRE), La Revue d'Informatique et de Recherche Opérationelle (RIRO), 8, 57–75.AHP
- Saaty, Thomas L. (1994). How to make a decision: The Analytic Hierarchy Process, Interfaces, 24, 19–43.
- Saaty, Thomas L. (1996). Decision Making with Dependence and Feedback: The Analytic Network Process, RWS Publications, ISBN: 0-9620317-9-8.
- Saaty, Thomas, S. (2003). Decision-making with the AHP: Why is the principal eigenvector necessary, European Journal of Operational Research, 145, 85-91.
- Saaty, Thomas L. (2004). Fundamentals of the analytic network process — Dependence and feedback in decision-making with a single network, Journal of Systems Science and Systems Engineering, 13, 129-157.
- Saaty, Thomas L. (2005). Theory and Applications of the Analytic Network Process: Decision Making with Benefits, Opportunities, Costs and Risks, RWS Publications, ISBN: 1-888603-06-2.
Fuzzy Logic
Zimmermann, H.-J. (1996). Fuzzy set Theory and its Applications, Kluwer Academic Publishers, ISBN: 0792374355.
Discussion of many of the topics covered in this course
Decision Sciences: Theory and Practice, Raghu Nandan Sengupta, Aparna Gupta, Joydeep Dutta, CRC Taylor & Francis, 2016, ISBN-13: 978-1466564305.
Course Audience
Course Audience
Audience
01) MTech/MS/MSc (1st and 2nd year of any branch)
02) MBA (2nd year IME Department)
03) BTech/BS/BSc (final year of any branch)
Class timing/Venue
01) IMEC5: Monday 0900-1015 hrs (IST)
02) IMEC5: Wednesday 0900-1015 hrs (IST)
Outcomes of this Course
Objective
In all domain of data analysis and multiple levels decision making considering variety of information, large of data, numerous alternative and conflicting criterion, it becomes imperative for the decision maker (DM)/set of decision makers (DMs) to come up with the best solution using the data and utilizing different techniques in multi criteria decision making. Thus fundamental techniques/ideas of Data Analysis/Multi Criteria decision making (MCDM) (comprising of multi-variate statistics, multi objective optimization (MOO) and multi attributive decision making (MADM)) help DMs to make rational as well mathematical well grounded decision to solve these set of problems. Furthermore in many cases/situations when stakes are high and one has non-commensurable units of measurement as well multiple conflicting objectives, multi variate statistics/MCDM definitely aids better decision making. This course will benefit students in their masters and doctoral programs and working in a variety of areas like engineering (electrical, mechanical, civil, chemical, etc.), mathematics & statistics, economics, management (SCM, quantitative finance, etc.) to tackle and solve interesting problems both from theoretical as well as practical view points.
Note: It is strongly recommended that students are conversant with any code statistics/optimization simulation packages like MATLAB <https://www.mathworks.com/>, R <https://www.r-project.org/>, Python <https://www.python.org/>, SAS <https://www.sas.com/>, Statistica <https://www.statistica.com>, Mathematica <https://www.wolfram.com/mathematica/>, etc. Of course a good knowledge in C, C++ would be best
Key learning take away
01) Will help students master the rich repertoire of tools for scientifically/rationally data analysis, optimization and multi criteria decision making.
02) Will facilitate students with both the basic and advanced theoretical background in Statistics, Multivariate Statistics and MCDM.
03) Will equip learners with the requisite skills in utilizing different techniques through practical applications.
04) Will help improve decision-making in myriad of decision and data analysis processes be it engineering, management science, psychology, biological sciences, environment, social sciences, etc.
Evaluation/Grading Policy
01) Assignments (group): 15%
02) Quizzes (individual): 25%
03) Mid-Sem (individual): 25%
04) End -sem (individual): 35%
05) Attendance (includes regular class/quiz/mid-sem/end-sem/extra class, etc.): Maximum marks deduction is 07 from normalized total of (01, 02, 03, 04). 80% and above attendance 00 marks deduction, 60% to 79% attendance 03 marks deduction, 40% to 59% attendance 05 marks deduction, 00% to 39% attendance 07 marks deduction
Note: For any one absent for assignment/quiz/mid-sem/end-sem, with valid reason/document, the respective assignment/quiz/mid-sem/end-sem will be pro-rated as per norms based on average performance/class performance, etc.