THE OR-PATH STUDY GUIDE

Your path through
Operations Research.

Build your knowledge from mathematical modeling to advanced optimization, with a clear sequence of topics and trusted references.

8 learning stages12 core referencesAt your own pace
Explore the path Browse references

Follow the path. Go deeper.

FOUNDATIONS · STAGES 01–03
01Linear ProgrammingTranslate decisions into mathematical models

Start with the building blocks of an optimization model.

WHAT YOU WILL STUDY
  • Decision variables and linear objectives
  • Constraints in algebraic form
  • Feasible regions and graphical solutions
CORE REFERENCES
Hillier & Lieberman · Introduction to OR Taha · Operations Research
02The Simplex MethodUnderstand the algorithm behind linear programming
WHAT YOU WILL STUDY
  • Standard form, slack and artificial variables
  • Two-phase and Big-M methods
  • Pivot operations, degeneracy and multiple optima
CORE REFERENCES
Hillier & Lieberman · Simplex Taha · Simplex & Sensitivity Winston · Applications and Algorithms
03Duality & SensitivityConnect optimal solutions with economic interpretation
WHAT YOU WILL STUDY
  • Dual problems and strong duality
  • Complementary slackness
  • Shadow prices and post-optimal analysis
CORE REFERENCES
Hillier & Lieberman · Duality Taha · Post-Optimal Analysis Bazaraa, Jarvis & Sherali
DISCRETE DECISIONS & NETWORKS · STAGES 04–05
04Integer & Mixed-Integer ProgrammingModel discrete choices and logical constraints
WHAT YOU WILL STUDY
  • Binary decisions and logical constraints
  • Fixed charges and combinatorial structures
  • Branch-and-bound, cutting planes and hybrid approaches
CORE REFERENCES
Hillier & Lieberman · Integer Programming Taha · Integer Linear Programming Nemhauser & Wolsey
05Network OptimizationExplore specialized models and algorithms
WHAT YOU WILL STUDY
  • Shortest paths and minimum spanning trees
  • Maximum flow and minimum-cost flow
  • Transportation and assignment models
CORE REFERENCES
Hillier & Lieberman · Network Models Ahuja, Magnanti & Orlin Winston · Network chapters
ADVANCED METHODS · STAGES 06–08
06Decomposition MethodsUse problem structure to scale optimization
WHAT YOU WILL STUDY
  • Dantzig–Wolfe decomposition and column generation
  • Benders decomposition
  • Lagrangian relaxation
CORE REFERENCES
Bazaraa, Jarvis & Sherali Conejo et al. · Decomposition Techniques
07Heuristics & MetaheuristicsExplore structured search for difficult problems
WHAT YOU WILL STUDY
  • GRASP and simulated annealing
  • Tabu search
  • Genetic algorithms
CORE REFERENCES
Hillier & Lieberman · Metaheuristics Gendreau & Potvin Resende & Ribeiro · GRASP
08Computational ComplexityUnderstand limits and choose your approach
WHAT YOU WILL STUDY
  • P vs NP and NP-completeness
  • Polynomial reductions
  • Approximation algorithms
CORE REFERENCES
Kleinberg & Tardos Garey & Johnson Papadimitriou & Steiglitz
Core reference libraryAll 12 books, in one place
Introduction to Operations Research Hillier & Lieberman · 10th edition · Foundations Operations Research: An Introduction Hamdy Taha · 10th edition · Foundations Operations Research: Applications and Algorithms Wayne Winston · 4th edition · Foundations Linear Programming and Network Flows Bazaraa, Jarvis & Sherali · 4th edition Integer and Combinatorial Optimization Nemhauser & Wolsey · Integer programming Network Flows: Theory, Algorithms, and Applications Ahuja, Magnanti & Orlin · Networks Decomposition Techniques in Mathematical Programming Conejo et al. · Decomposition Handbook of Metaheuristics Gendreau & Potvin · Metaheuristics Optimization by GRASP Resende & Ribeiro · Metaheuristics Algorithm Design Kleinberg & Tardos · Algorithms Computers and Intractability Garey & Johnson · Complexity Combinatorial Optimization: Algorithms and Complexity Papadimitriou & Steiglitz · Complexity

Some links may be affiliate links. OR-Path may earn a small commission at no additional cost to you.