Course Archives    Theoretical Statistics and Mathematics Unit

Course: Operations Research I Level: Postgraduate Time: Currently not offered

Syllabus Past Exams Syllabus 1. Introduction to Optimization (2) Origin of Operations Research (OR) and its definitions - Operations Research with special emphasis on interdisciplinary and systems approach, Stages of OR project, problem formulations. Developing a model. Testing the adequacy of the model, Deriving a solution, Evaluation of the solution and implementation. Basic tools for optimization. 2. Linear Programming (18) Linear programming (LP): examples and modeling. LP formulations using matrix notation, Standard and canonical forms, Row operations, and pivoting. Convex sets, Polyhedral sets, Extreme points and basic feasible solutions, the connection to extreme points. Graphical method for solving LP. Existence of optimal basic feasible solutions. The simplex method. Two-phase and the Big-M method. Degeneracy in LP and its resolution. The revised simplex method and its significance. 3. Duality Theorem (10) Formulations, The fundamental theorems of duality and proofs, Complementary slackness conditions, The dual simplex algorithm, The sensitivity analysis. 4. Applications of LP (10) The transportation and the assignment model, the LPP with bounded variables. Case studies on industrial applications of OR and DSS. Game theory: Two-person zerosum games. Saddle points graphical methods. 5. Advanced techniques in Project Management (10) PERT/CPM, Sequencing and scheduling, Dependency structure matrix analysis, M7 tools, Decision analysis. Reference texts: 1. Ravindran, A. R. (2016). Operations research and management science handbook. CRC Press. 2. Hillier, F. S., & Lieberman, G. J. (2015). Introduction to operations research. McGrawHill Education. 3. Taha, H. A. (2013).Operations research: An introduction. Pearson Education India. Top of the page Past Exams

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