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This is a textbook about linear and integer linear optimization. There is a growing need in industries such as airline, trucking, and financial engineering to solve very large linear and integer linear optimization problems. Building these models requires uniquely trained individuals. Not only must they have a thorough understanding of the theory behind mathematical programming, they must have substantial knowledge of how to solve very large models in today's computing environment. The major goal of the book is to develop the theory of linear and integer linear optimization in a unified manner and then demonstrate how to use this theory in a modern computing environment to solve very large real world problems. After presenting introductory material in Part I, Part II of this book is de­ voted to the theory of linear and integer linear optimization. This theory is developed using two simple, but unifying ideas: projection and inverse projec­ tion. Through projection we take a system of linear inequalities and replace some of the variables with additional linear inequalities. Inverse projection, the dual of this process, involves replacing linear inequalities with additional variables. Fundamental results such as weak and strong duality, theorems of the alternative, complementary slackness, sensitivity analysis, finite basis the­ orems, etc. are all explained using projection or inverse projection. Indeed, a unique feature of this book is that these fundamental results are developed and explained before the simplex and interior point algorithms are presented.

Linear programming --- Mathematical optimization --- Programmation linéaire --- Optimisation mathématique --- Linear Programming --- 519.8 --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Matrices --- Production scheduling --- Programming (Mathematics) --- Substitutions, Linear --- Transformations (Mathematics) --- Vector analysis --- Operational research --- 519.8 Operational research --- Programmation linéaire --- Optimisation mathématique --- Linear programming. --- Operations research. --- Decision making. --- Mathematical optimization. --- Calculus of variations. --- Artificial intelligence. --- Operations Research/Decision Theory. --- Optimization. --- Calculus of Variations and Optimal Control; Optimization. --- Artificial Intelligence. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Fifth generation computers --- Neural computers --- Isoperimetrical problems --- Variations, Calculus of --- Operational analysis --- Industrial engineering --- Management science --- Research --- System theory --- Deciding --- Decision (Psychology) --- Decision analysis --- Decision processes --- Making decisions --- Management --- Management decisions --- Choice (Psychology) --- Problem solving --- Decision making