Advanced Optimization and Operations Research

This textbook provides students with fundamentals and advanced concepts in optimization and operations research. It gives an overview of the historical perspective of operations research and explains its principal characteristics, tools, and applications. The wide range of topics covered includes convex and concave functions, simplex methods, post optimality analysis of linear programming problems, constrained and unconstrained optimization, game theory, queueing theory, and related topics. The text also elaborates on project management, including the importance of critical path analysis, PERT and CPM techniques. This textbook is ideal for any discipline with one or more courses in optimization and operations research it may also provide a solid reference for researchers and practitioners in operations research.

1. Mathematical Preliminaries.- 2. Introduction of OR.- 3. Revised Simplex Method.- 4. Dual Simplex Method.- 5. Bounded Variable Technique.- 6. Post-Optimality Analysis in Linear Programming Problem.- 7. Integer Programming.- 8. Convex Function.- 9. Basics of Unconstrained Optimization. 10. Constrained Optimization with Equality Constraints.- 11. Constrained Optimization with Inequality Constraints.- 12. Quadratic Programming.- 13. Inventory Control Theory.- 14. Project Management.- 15. Queueing Theory.- 16. Flow in Networks.- 17. Theory of Game.