**Preface.**
**1. Introduction to Operations Research.**

1.1 What is Deterministic Operations Research?

1.2 Introduction to Optimization Modeling.

1.3 Common Classes of Mathematical Programs.

1.4 About the Book.

Exercises.

**2. Linear Programming Modeling.**

2.1 Resource Allocation Models.

2.2 Work Scheduling Models.

2.3 Models and Data.

2.4 Blending Models.

2.5 Production Process Models.

2.6 Multiperiod Models: Work Scheduling and Inventory.

2.7 Linearization of Special Nonlinear Models.

2.8 Various Forms of Linear Programs.

2.9 Network Models.

Exercises.

**3. Integer and Combinatorial Models.**

3.1 Fixed-Charge Models.

3.2 Set Covering Models.

3.3 Models Using Logical Constraints.

3.4 Combinatorial Models.

3.5 Sports Scheduling and an Introduction to IP Solution Technques.

Exercises.

**4. Real-World Operations Research Applications: An Introduction.**

4.1 Vehicle Routing Problems.

4.2 Facility Location and Network Design Models.

4.3 Applications in the Airline Industry.

Exercises.

**5. Introduction to Algorithm.**

5.1 Exact and Heuristic Algorithms.

5.2 What to Ask When Designing Algorithms?

5.3 Constructive versus Local Search Algorithms.

5.4 How Good is our Heuristic Solution?

5.5 Example of a Local Search Method.

5.7 Other Heuristic Methods.

5.8 Designing Exact Methods: Optimality Conditions.

Exercises.

**6. Improving Search Algorithms and Comvexity.**

6.1 Improving Search and Optimal Solutions.

6.2 Finding Better Solutions.

6.3 Convexity: When Does Improving Search Imply Global Optimality?

6.4 Farkas’ Lemma: When Can No Improving Feasible Direction be Found?

Exercises.

**7. Geometry and Algebra of Linear Programs.**

7.1 Geometry and Algebra of “Corner Points”.

7.2 Fundamental Theorem of Linear Programming.

7.3 Linear Programs in Canonical Form.

Exercises.

**8. Solving Linear Programs: Simplex Method.**

8.1 Simplex Method.

8.2 Making the Simplex Method More Efficient.

8.3 Convergence, Degeneracy, and the Simplex Method.

8.4 Finding an Initial Solution: Two-Phase Method.

8.5 Bounded Simplex Method.

8.6 Computational Issues.

Exercises.

**9. Linear Programming Duality.**

9.1 Motivation: Generation Bounds.

9.2 Dual Linear Program.

9.3 Duality Theorems.

9.4 Another Interpretation of the Simplex Method.

9.5 Farkas’ Lemma Revisited.

9.6 Economic Interpretation of the Dual.

9.7 Another Duality Approach: Lagrangian Duality.

Exercises.

**10. Sensitivity Analysis of Linear Programs.**

10.1 Graphical Sensitivity Analysis.

10.2 Sensitivity Analysis Calculations.

10.3 Use of Sensitivity Analysis.

10.4 Parametric Programming.

Exercises.

**11. Algorithmic Applications of Duality.**

11.1 Dual Simplex Method.

11.2 Transportation Problem.

11.3 Column Generation.

11.4 Dantzig-Wolfe Decomposition.

11.5 Primal-Dual Interior Point Method.

Exercises.

**12. Network Optimization Algorithms.**

12.1 Introduction to Network Optimization.

12.2 Shortest Path Problems.

12.3 Maximum Flow Problems.

12.4 Minimum Cost Network Flow Problems.

Exercises.

**13. Introduction to Integer Programming**.

13.1 Basic Definitions and Formulations.

13.2 Relaxations and Bounds.

13.3 Preprocessing and Probing.

13.4 When are Integer Programs “Easy?’

Exercises.

**14. Solving Integer Programs: Exact Methods.**

14.1 Complete Enumeration.

14.2 Branch-and Bound Methods.

14.3 Valid Inequalities and Cutting Planes.

14.4 Gomory’s Cutting Plane Algorithm.

14.5 Valid Inequalities for 0-1 Knapsack Constraints.

14.6 Branch-and-Cut Algorithms.

14.7 Computational Issues.

Exercises.

**15. Solving Integer Programs: Modern Heuristic Techniques.**

15.1 Review of Local Search Methods: Pros and Cons.

15.2 Simulated Annealing.

15.3 Tabu Search.

15.4 Genetic Algorithms.

15.5 GRASP Algorithms.

Exercises.

**Appendix A: Background Review.**

A.1 Basic Notation.

A.2 Graph Theory.

A.3 Linear Algebra.

**Reference.**

**Index.**