First Course on Operations Research

Course Code: IM 456; ST 577 | Credits: 4 | Prerequisite: Linear Algebra, Calculus

Unit I:(Formulation) Introduction to vector spaces and matrix algebra; formulation of linear programming problems with illustrative examples; graphical method of solving an LPP in two variables.
Unit II:(Theory of Linear Programming) The linear programming model and the various forms of an LPP; foundations and theory: convex sets, feasible solution, basic solution, basic feasible solution, optimal solution; geometry of polyhedra.
Unit III:(Simplex Method and Duality) Simplex method and its demonstration, the optimal solution, dual of an LPP, fundamental theorems of duality, dual simplex method, sensitivity analysis.
Unit IV:(Assignment, Transportation and Convexity) Formation and solution of the assignment and transportation problems; convex functions and their generalizations, checking convexity of functions, optimization of convex functions.

Convert a given real world context into a linear programming problem.
Apply the graphical and simplex methods to a given LPP.
Analyze the optimal solution.
Evaluate the various methods of solving LPPs and carry out post-optimality analysis.
Model assignment and transportation problems.
Interpret the optimal solutions of linear programming, assignment and transportation problems.
Discuss the convexity of a function and find an optimal solution of a convex function.

Murty, Katta G. Operations Research: Deterministic Optimization Models. Prentice-Hall, 1995
Murty, Katta G. Linear Programming. Wiley, 1983
Bazaraa, Mokhtar S., Jarvis, John J. and Sherali, Hanif D. Linear Programming and Network Flows. 2nd ed. Wiley, 2003
Saigal, Romesh. Linear Programming: A Modern Integrated Analysis. Springer, 2012
Bertsimas, Dimitris and Tsitsiklis, John N. Introduction to Linear Optimization. Athena Scientific, 1997
Fourer, Robert, Gay, David M. and Kernighan, Brian W. AMPL: A Modeling Language for Mathematical Programming. Brooks/Cole, 1999