Introduction: The origin, nature and impact of OR; Defining the problem and gathering data; Formulating a mathematical model; Deriving solutions from the model; Testing the model; Preparing to apply the model; Implementation . Introduction to Linear Programming: Prototype example; The linear programming (LP) model.
Assumptions of LP; Additional examples. The essence of the simplex method; Setting up the simplex method; Algebra of the simplex method; the simplex method in tabular form; Tie breaking in the simplex method
Adapting to other model forms; Post optimality analysis; Computer implementation Foundation of the simplex method.
The revised simplex method, a fundamental insight. The essence of duality theory; Economic interpretation of duality, Primal dual relationship; Adapting to other primal forms
The role of duality in sensitive analysis; The essence of sensitivity analysis; Applying sensitivity analysis. The dual simplex method; Parametric linear programming; The upper bound technique.
The transportation problem; A streamlined simplex method for the transportation problem; The assignment problem; A special algorithm for the assignment problem.
Game Theory: The formulation of two persons, zero sum games; Solving simple games- a prototype example;Games with mixed strategies; Graphical solution procedure; Solving by linear programming, Extensions. Decision Analysis: A prototype example; Decision making without experimentation; Decision making with experimentation; Decision trees.
The nature of Metaheuristics, Tabu Search, Simulated Annealing, Genetic Algorithms.