Course Description
Syllabus
Basic concepts of Linear Programming (LP), Simplex Method, Big-M Method, Duality, Dual Simplex Problem, Sensitivity Analysis, Ideas of Network Analysis, Non-Linear Programming (NLP), Quadratic Programming (QP), Reliability Optimization, Robust Optimization, etc; Multiple Objective Decision Making (MODM), Multiple Criteria Decision Making (MCDM); Decisions under uncertainty; Multivariate Data Analysis, Multiple regression models, Principle Component Analysis (PCA), Factor Analysis, Multivariate Analysis of Variance (MANOVA), Conjoint Analysis, Canonical Correlation, Cluster Analysis, Multidimensional Scaling, Structural Equation Modelling, etc. Non-parameter techniques like 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
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.
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
Audience
MTech (1st and 2nd year), BTech/BS (final year), MBA (2nd year)
Evaluation
01) Assignments
02) Quiz
03) Mid-Sem
04) End -sem
Outcomes of this Course
Objective
In all domain of multiple levels decision making considering 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. Ideas of Multi Criteria decision making (MCDM) (comprising of 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. In many cases when stakes are high and one has non-commensurable units of measurement as well multiple conflicting objectives, 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 (Multiple Bayesian Decision making), economics, management (SCM, quantitative finance, etc.) to tackle and solve interesting problems both from theoretical as well as practical view points.
Key learning take away
01) Will help students master the rich repertoire of tools for scientifically/rationally multi criteria decision making.
02) Will facilitate students with both the basic and advanced theoretical background in 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 process be it engineering, management science, psychology, biological sciences, environment, etc.