1\. Introduction 1.1 Variants of the linear programming problem 1.2 Examples of linear programming problems 1.3 Piecewise linear convex objective functions 1.4 Graphical representation and solution 1.5 Linear algebra background and notation 1.6 Algorithms and operations counts 2\. The geometry of linear programming 2.1 Polyhedra and convex sets 2.2 Extreme points, vertices, and basic feasible solutions 2.3 Polyhedra in standard form 2.4 Degeneracy 2.5 Existence of extreme points 2.6 Optimality of extreme points 2.7 Representation of bounded polyhedra 2.8 Projections of polyhedra: Fourier-Motzkin elimination 3\. The simplex method 3.1 Optimality conditions 3.2 Development of the simplex method 3.3 Implementations of the simplex method 3.4 Anticycling: lexicography and Bland’s rule 3.5 Finding an initial basic feasible solution 3.6 Column geometry and the simplex method 3.7 Computational efficiency of the simplex method 4\. Duality theory 4.1 Motivation 4.2 The dual problem 4.3 The dual theorem 4.4 Optimal dual variables as marginal costs 4.5 Standard form problems and the dual simplex method 4.6 Farkas’ lemma and linear inequalities 4.7 From separating hyperplanes to duality 4.8 Cones and extreme rays 4.9 Representation of polyhedra 4.10 General linear programming duality 5\. Sensitivity analysis 5.1 Local sensitivity analysis 5.2 Global dependence on the right-hand side vector 5.3 The set of all dual optima solutions 5.4 Global dependence on the cost vector 5.5 Parametric programming 6\. Large scale optimization 6.1 Delayed column generations 6.2 The cutting stock problem 6.3 Cutting plane methods 6.4 Dantzig-Wolfe decomposition 6.5 Stochastic programming and Benders decomposition 7\. Network flow problems 7.1 Graphs 7.2 Formulation of the network flow problem 7.3 The network simplex algorithm 7.4 The negative cost cycle algorithm 7.5 The maximum flow problem 7.6 Duality in network flow problems 7.7 Dual ascent methods 7.8 The assignment problem and the auction algorithm 7.9 The shortest path problem 7.10 The minimum spanning tree problem 8\. Complexity of linear programming and the ellipsoid method 8.1 Efficient algorithms and computational complexity 8.2 The key geometric result behind the ellipsoid method 8.3 The ellipsoid method for the feasibility problem 8.4 The ellipsoid method for optimization 8.5 Problems with exponentially many constraints 9\. Interior point methods 9.1 The affine scaling algorithm 9.2 Convergence of affine scaling 9.3 The potential reduction algorithm 9.4 The primal path following algorithm 9.5 The primal-dual path following algorithm 9.6 An overview 10\. Integer programming formulations 10.1 Modeling techniques 10.2 Guidelines for strong formulations 10.3 Modeling with exponentially many constraints 11\. Integer programming methods 11.1 Cutting plane methods 11.2 Branch and bound 11.3 Dynamic programming 11.4 Integer programming duality 11.5 Approximation algorithms 11.6 Local search 11.7 Simulated annealing 11.8 Complexity theory 12\. The art in linear optimization 12.1 Modeling languages for linear optimization 12.2 Linear optimization libraries and general observations 12.3 The fleet assignment problem 12.4 The air traffic flow management problem 12.5 The job shop scheduling problem PREFACE objective 1.Insight: interplay btw algebra and geometry 2.comprehensive, but economical 3.up to date wrt state of the art