Linear and integer optimization : theory and practice /: theory and practice. ([2015])

• Record Type: Book
• Further Information: Note: Gerard Sierksma, Yori Zwols.
• Authors: Sierksma, Gerard, 1945-; Zwols, Yori
• Contents: Basic Concepts of Linear Optimization; The Company Dovetail; Definition of an LO-Model; Alternatives of the Standard LO-Model; Solving LO-Models Using a Computer Package; Linearizing Nonlinear Functions; Examples of Linear Optimization Models; Building and Implementing Mathematical Models; Exercises; ; LINEAR OPTIMIZATION THEORY: BASIC TECHNIQUES; ; Geometry and Algebra of Feasible Regions; The Geometry of Feasible Regions; Algebra of Feasible Regions; Feasible Basic Solutions; Exercises; ; Dantzig’s Simplex Algorithm; From Vertex to Vertex to an Optimal Solution; LO-Model Reformulation; The Simplex Algorithm; Simplex Tableaus; Discussion of the Simplex Algorithm; Initialization; Uniqueness and Multiple Optimal Solutions; Models with Equality Constraints; The Revised Simplex Algorithm; Exercises; ; Duality, Feasibility, and Optimality; The Companies Dovetail and Salmonnose; Duality and Optimality; Complementary Slackness Relations; Infeasibility and Unboundedness; Farkas’ Lemma; Primal and Dual Feasible Basic Solutions; Duality and the Simplex Algorithm; The Dual Simplex Algorithm; Exercises; ; Sensitivity Analysis; Sensitivity of Model Parameters; Perturbing Objective Coefficients; Perturbing Right Hand Side Values (Nondegenerate Case); Piecewise Linearity of Perturbation Functions; Perturbation of the Technology Matrix; Sensitivity Analysis for the Degenerate Case; Shadow Prices and Redundancy of Equality Constraints; Exercises; ; Large-Scale Linear Optimization; The Interior Path; Formulation of the Interior Path Algorithm; Convergence to the Interior Path; Maintaining Feasibility; Termination and Initialization; Exercises; ; Integer Linear Optimization; Introduction; The Branch-and-Bound Algorithm; Linearizing Logical Forms with Binary Variables; Gomory’s Cutting-Plane Algorithm; Exercises; ; Linear Network Models; LO-Models with Integer Solutions; Total Unimodularity; ILO-Models with Totally Unimodular Matrices; The Network Simplex Algorithm; Exercises; ; Computational Complexity; Introduction to Computational Complexity; Computational Aspects of Dantzig’s Simplex Algorithm; The Interior Path Algorithm Has Polynomial Running Time; Computational Aspects of the Branch-and-Bound Algorithm; Exercises; ; LINEAR OPTIMIZATION PRACTICE: ADVANCED TECHNIQUES; ; Designing a Reservoir for Irrigation; The Parameters and the Input Data; Maximizing the Irrigation Area; Changing the Input Parameters of the Model; GMPL Model Code; Exercises; ; Classifying Documents by Language; Machine Learning; Classifying Documents Using Separating Hyperplanes; LO-Model for Finding Separating Hyperplane; Validation of a Classifier; Robustness of Separating Hyperplanes; Separation Width; Models that Maximize the Separation Width; GMPL Model Code; Exercises; ; Production Planning; A Single Product Case; Model Description; Regular Working Hours; Overtime; Allowing Overtime and Idle Time; Sensitivity Analysis; GMPL Model Code; Exercises; ; Production of Coffee Machines; Problem Setting; An LO-Model that Minimizes Backlogs; Old and Recent Backlogs; Full Week Productions; Sensitivity Analysis; GMPL Model Code; Exercises; ; Conflicting Objectives: Producing Versus Importing; Problem Description and Input Data; Modeling Two Conflicting Objectives; Pareto Optimal Point; Goal Optimization for Conflicting Objective; Soft and Hard Constraints; Sensitivity Analysis; Alternative Solution Techniques; A Comparison of the Solutions; GMPL Model Code; Exercises; ; Coalition Formation and Profit Distribution; The Farmers Cooperation Problem; Game Theory; Linear Production Games; How to Distribute the Total Profit Among the Farmers?; Profit Distribution for Arbitrary Numbers of Farmers; Sensitivity Analysis; Exercises; ; Minimizing Trimloss When Cutting Cardboard; Formulating the Problem; Gilmore-Gomory’s Solution Algorithm; Calculating an Optimal Solution; Exercises; ; Off-Shore Helicopter Routing; Problem Description; Vehicle Routing Problems; Problem Formulation; ILO Formulation; Column Generation; Dual Values as Price Indicators for Crew Exchanges; A Round-Off Procedure for Determining an Integer Solution; Computational Experiments; Sensitivity Analysis; Exercises; ; The Catering Service Problem; Formulation of the Problem; The Transshipment Problem Formulation; Applying the Network Simplex Algorithm; Sensitivity Analysis; GMPL Model Code; Exercises; ; Appendix A Mathematical Proofs; Appendix B Linear Algebra; Appendix C Graph Theory; Appendix D Convexity; Appendix E Nonlinear Optimization; Appendix F Writing LO-Models in GNU MathProg (GMPL); ;
• Edition: 3rd edition
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2015
• Copyright Date: 2015
• Extent: 1 online resource
• Subjects: 519.7/2; Linear programming; Integer programming; Mathematical optimization; Integer programming; Linear programming; Mathematical optimization; Electronic books
• Languages: English
• ISBNs: 9781498743129; 1498743129
• Notes: Note: Includes bibliographical references (pages 639-644) and indexes.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.