Linear and Integer Programming Theory and Practice 2nd Edition by Gerard Sierksma ISBN 0824706730 9780824706739 by Gerard Sierksma 9780585418179, 9780824706739, 0585418179, 0824706730 instant download after payment.

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ISBN 10: 0824706730 
ISBN 13: 9780824706739
Author: Gerard Sierksma

Linear and Integer Programming Theory and Practice 2nd Table of contents:

Part I: Fundamentals of Linear Programming

• Chapter 1: Introduction to Optimization and Linear Programming
  • What is Optimization?
  • Historical Overview of Linear Programming
  • Applications of Linear Programming
  • Modeling Real-World Problems as LPs
  • Basic Definitions (Feasible Region, Optimal Solution, Objective Function)
• Chapter 2: Geometric Foundations of Linear Programming
  • Graphical Solution of 2-Variable LPs
  • Convex Sets, Polyhedra, and Extreme Points
  • Fundamental Theorem of Linear Programming (Extreme Point Solutions)
• Chapter 3: The Simplex Method: Core Algorithm
  • Standard Form of an LP
  • Basic Feasible Solutions
  • The Simplex Algorithm Steps
  • Tableau Form and Pivoting Operations
  • Handling Degeneracy, Unboundedness, and Infeasibility
• Chapter 4: Duality Theory
  • Formulating the Dual Problem
  • The Weak Duality Theorem
  • The Strong Duality Theorem
  • Complementary Slackness Conditions
  • Economic Interpretation of the Dual Variables (Shadow Prices)

Part II: Advanced Topics in Linear Programming

• Chapter 5: Sensitivity Analysis and Post-Optimality
  • Changes in Objective Function Coefficients
  • Changes in Right-Hand Side Values (Resource Availability)
  • Adding New Variables or Constraints
  • Parametric Programming
• Chapter 6: Revised Simplex Method and Computational Considerations
  • Efficiency of the Simplex Method
  • Revised Simplex Algorithm
  • Column Generation (Decomposition Methods)
  • Data Structures for Large-Scale LPs
• Chapter 7: Interior Point Methods
  • Introduction to Interior Point Algorithms
  • Primal-Dual Interior Point Method
  • Comparison with Simplex Method
  • Theoretical Foundations and Convergence
• Chapter 8: Network Optimization
  • Minimum Cost Flow Problems
  • Shortest Path Problems (Dijkstra, Bellman-Ford)
  • Maximum Flow Problems (Ford-Fulkerson)
  • Assignment Problems
  • Transshipment Problems

Part III: Integer Programming Theory

• Chapter 9: Introduction to Integer Linear Programming (ILP)
  • Modeling with Integer Variables (Binary, General Integer)
  • Applications of ILP (Knapsack, Set Covering, Facility Location)
  • The Challenge of Integer Programming (NP-Hardness)
  • Relaxation and Bounds (LP Relaxation)
• Chapter 10: Cutting Plane Algorithms
  • Gomory's Cutting Plane Algorithm
  • Strong Valid Inequalities
  • Cutting Planes for Specific Problems (e.g., Cover Inequalities for Knapsack)
• Chapter 11: Branch-and-Bound Algorithm
  • The Fundamental Principle of Branch-and-Bound
  • Branching Strategies
  • Bounding Strategies
  • Node Selection Rules
  • Fathoming Rules

Part IV: Advanced Topics and Special Structures in Integer Programming

• Chapter 12: Heuristics for Integer Programming
  • Constructive Heuristics
  • Improvement Heuristics (Local Search, Tabu Search, Simulated Annealing)
  • Metaheuristics (Genetic Algorithms, Ant Colony Optimization - possibly brief mention)
• Chapter 13: Lagrangian Relaxation
  • Formulating Lagrangian Dual Problems
  • Solving the Lagrangian Dual
  • Generating Bounds from Lagrangian Relaxation
  • Using Lagrangian Relaxation within Branch-and-Bound
• Chapter 14: Special Purpose Algorithms and Polyhedral Theory
  • The Traveling Salesperson Problem (TSP)
  • Set Covering, Partitioning, and Packing Problems
  • Knapsack Problems
  • Polyhedral Combinatorics (brief introduction to facets, valid inequalities)
• Chapter 15: Column Generation for Integer Programs
  • Branch-and-Price Algorithm
  • Applications (e.g., Cutting Stock Problem, Vehicle Routing)

Part V: Practical Considerations and Applications

• Chapter 16: Modeling Practices and Challenges
  • Discretization Techniques
  • Formulation Strategies for Complex Problems
  • Avoiding Numerical Instabilities
  • Dealing with Large-Scale Models
• Chapter 17: Software for Linear and Integer Programming
  • Overview of Commercial Solvers (CPLEX, Gurobi, Xpress-MP)
  • Open-Source Solvers (GLPK, CBC)
  • Modeling Languages (AMPL, GAMS, OPL)
  • Integration with Programming Languages (Python, R, MATLAB)
• Chapter 18: Real-World Case Studies
  • Supply Chain Optimization
  • Production Planning and Scheduling
  • Financial Portfolio Optimization
  • Logistics and Transportation
  • Crew Scheduling and Rostering

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Tags: Gerard Sierksma, Linear, Integer