Optimization Models

Table of Contents:

• 1. Preface
• 2. Structured linear optimization models
• 3. Product Mix Models
  • 3.1. Dual of the product mix problem
• 4. Blending Models
  • 4.1. Dual of blending problems
  • 4.2. Dual of the diet model
• 5. Multi Period Models
• 6. Network flow models
  • 6.1. Minimum cost flow
  • 6.2. Applications of minimum cost flow models
• 7. Shortest (Minimum Cost) Path Problems
  • 7.1. The problem of arcs with negative cost
  • 7.2. Dual of the minimum cost path model
  • 7.3. Applications of the minimum cost path model
• 8. Maximum Flow
  • 8.1. Dual of the maximum flow problem
• 9. The transportation model
• 10. Assignment or bi-partite matching
• 11. Dynamic flows
• 12. Objectives and constraints in optimization models
  • 12.1. Feasibility problems (no objective function)
  • 12.2. Multiple Objectives
• 13. Some nonlinear problems that can be transformed into linear ones
  • 13.1. Minimax problems
  • 13.2. Absolute values in the objective
  • 13.3. Regression (or best approximation) models
    • 13.3.1. Minimax regression
    • 13.3.2. Absolute regression
    • 13.3.3. Quadratic (least squares) regression
  • 13.4. Rational Objectives
    • 13.4.1. Comparative efficiency evaluation
      • 13.4.1.1. Dual of the efficiency evaluation model
• 14. Constraints in linear optimization models
  • 14.1. Soft constraints
  • 14.2. Piece-wise linear convex cost functions
• 15. Uncertainty modeling: Stochastic optimization models
  • 15.1. Probabilistic constraints
  • 15.2. Stochastic linear optimization models
• 16. Mixed Integer Linear Models
  • 16.1. Introduction
  • 16.2. Modeling with integer variables
    • 16.2.1. Using binary variables in logical constraints
    • 16.2.2. Using binary variables to impose constraints
    • 16.2.3. Propositional logic and binary variables
      • 16.2.3.1. Normal forms
• 17. Structured Mixed Integer Linear Optimization Models
• 18. The fixed charge problem
• 19. Lot sizing
  • 19.1. Branch and cut - dynamical simplex method
  • 19.2. Advanced formulations for the lot sizing model
  • 19.3. Variants of production planning models
    • 19.3.1. Advanced lot sizing models
  • 19.4. Master Production Scheduling models
  • 19.5. Material Requirement Planning
• 20. Knapsack problems
  • 20.1. Introduction
    • 20.1.1. Advanced modeling: cover inequalities
  • 20.2. Multiple knapsack models, Bin Packing, Cutting Stock
    • 20.2.1. Comparison between the formulations
  • 20.3. Plant location
• 21. Set covering, packing, partition
• 22. Sequencing problems: the Traveling Salesperson Problem
  • 22.1. Sub-tour elimination constraints
• 23. Arc routing
• 24. Quadratic Optimization Models
  • 24.1. Solving linear electrical networks
  • 24.2. Elementary portfolio optimization
  • 24.3. Support Vector Machines
  • 24.4. Quadratic Assignment
• 25. Bibliographic References
• 26. Appendix
  • 26.1. Graphs: basic definitions
• 27. Version history
• 28. To do
  • 28.1. Vehicle Routing
  • 28.2. Miscellanea

Indices and tables

• Index

• Module Index

• Search Page

© Fabio Schoen 2023