Useful for CSIR NET · ASRB NET · ISS
This is the complete study package for Operations Research — the science of optimal decision-making using mathematical models. The course covers Linear Programming Problems (LPP) from formulation through graphical, simplex, Big-M, two-phase and dual-simplex methods, and concludes with the powerful theory of duality. Each topic has two worked examples.
Origin and development of OR, scientific method, modelling, advantages & limitations; introduction to LPP and mathematical formulation with illustrative problems.
UNIT 2Graphical solution for max & min objectives up to 3 variables; convex / non-convex hull; alternative, unbounded and infeasible solutions.
UNIT 3General LPP, matrix form, slack & surplus variables, standard & canonical forms; basic feasible solution; simplex algorithm for max and min problems.
UNIT 4Artificial variable techniques — Big-M penalty method, Two-Phase simplex; degeneracy & how to resolve it; special cases via simplex; solving simultaneous equations.
UNIT 5Concept of duality, primal-dual conversion rules, relation between primal and dual solutions; solving primal via dual; the dual simplex method.
PRACTICALWorked LPP labs: graphical method, simplex, Big-M, Two-Phase, special cases, primal-dual, dual simplex.
REFERENCECourse outline, textbooks, references and exam blueprint.