**Prerequisite:** Instructor's permission

**Prerequisite:**Instructor's permission

**Contents**

Modeling of allocation and control problems in industry and social systems. Framework and overview of optimization with examples of continuous and discrete optimization, unconstrained and constrained problems. Single stage and multi stage models. Formulations and equivalences. Examples from science, engineering and business. Linear programming. Geometry and algebra of the simplex method. Duality & sensitivity. Combinatorial optimization problems with emphasis on applications, notion of large feasible spaces and neighborhood solutions, representation of solution space, search tree, search techniques, branch and bound method. Examples of mixed-integer programming models. Use of binary variables in constraint modeling. Decision problems involving network flows, assignment models, transportation models, multi-stage flows.

**References**

- Wayne L. Winston (2004) Operations Research: Applications and Algorithms, 4th edition, Thomson Learning.
- Wayne L. Winston (2003) Introduction to Mathematical Programming: Applications and Algorithms, 4th edition, Duxbury Resource Center.
- H. Paul Williams (1999) Model Building in Mathematical Programming, 4th edition, John Wiley & Sons.
- Ashok D. Belegundu, and Tirupathi R.Chandrupatla (1999) Optimization Concepts and Applications in Engineering, Pearson Education India.
- Hamdy. A. Taha (2002) Operations Research: An Introduction, 8th edition, Prentice Hall of India.
- F. Hillier and G. Lieberman (2005) Introduction to Operations Research, 8th edition, McGraw-Hill.