Optimization modelling using R. (2022)

• Record Type: Book
• Further Information: Note: Timothy R. Anderson.
• Authors: Anderson, Timothy R (Timothy Roy), 1967-
• Contents: Preface; 1 Introduction; 1.1 What is Operations Research; 1.2 Purpose of this Book; 1.3 Range of Operations Research Techniques; 1.4 Relationship between Operations Research and Analytics; 1.5 Importance of Optimization; 1.6 Why R?; 1.7 Conventions Used in this Book 2 Introduction to Linear Programming; 2.1 What is Linear Programming; 2.2 Two Variable Base Case; 2.3 Graphically Solving a Linear Program; 2.4 Implementing and Solving with ompr; 2.4.1 Preparing to Implement the Linear Program; 2.4.2 Implementing the Base Case with Piping; 2.5 Adding a Third Product (Variable); 2.5.1 Three Variable Base Case Formulation; 2.5.2 Three Variable Base Case Implementation; 2.5.3 Three Variable Case Results and Interpretation; 2.6 Linear Programming Special Cases; 2.6.1 Case 1: No Feasible Solution; 2.6.2 Case 2: Multiple Optima; 2.6.3 Case 3: Redundant Constraint; 2.6.4 Case 4: Unbounded Solution; 2.7 Abstracting the Production Planning Model; 2.8 Methods of Solving Linear Programs; 2.9 Exercises 3 More Linear Programming Models; 3.1 Types of LP Models; 3.2 The Algebraic Model; 3.2.1 Tips and Conventions for Algebraic Models; 3.2.2 Building the Generalized Model in R; 3.2.3 Examining the Results; 3.2.4 Changing the Model; 3.3 Common Linear Programming Applications; 3.3.1 Blending Problems; 3.4 Allocation Models; 3.4.1 Covering Models; 3.4.2 Transportation Models; 3.4.3 Transshipment Models; 3.4.4 Production and Inventory Planning; 3.4.5 Standard Form; 3.5 Vector and Matrix Forms of LPs; 3.6 Exercises 4 Sensitivity Analysis; 4.1 Base Case; 4.2 Shadow Prices; 4.2.1 Extraction and Interpretation; 4.2.2 Example of Adding an Hour to Assembly; 4.2.3 Shadow Prices of Underutilized Resources; 4.3 Reduced Costs of Variables; 4.3.1 Reduced Cost of Ants; 4.3.2 Reduced Price of Bats; 4.4 Using Sensitivity Analysis to Evaluate a New Product; 4.5 Exercises 5 Data Envelopment Analysis; 5.1 Introduction; 5.2 Creating the Data; 5.3 Graphical Analysis; 5.4 The Linear Programs for DEA; 5.4.1 An Explicit Linear Program for DEA; 5.4.2 A Generalized Linear Program for DEA; 5.5 Creating the LP - The Algebraic Approach; 5.6 Returns to Scale; 5.7 Multiple Inputs and Multiple Outputs; 5.8 Extracting Multiplier Weights from Sensitivity Analysis; 5.9 Slack Maximization; 5.10 DEA Packages; 5.11 DEA Model Building; 5.11.1 Selection of Inputs and Outputs; 5.11.2 Model Choices; 5.11.3 Application Area Expertise; 5.12 Further Reading; 5.13 Exercises 6 Mixed Integer Optimization; 6.1 Example of Minor Integrality Impact; 6.2 Example of Major Integality Impact; 6.3 The Branch and Bound Algorithm; 6.3.1 The LP Relaxation; 6.3.2 Subproblem I; 6.3.3 Subproblem III; 6.3.4 Subproblem IV; 6.3.5 Subproblem V ; 6.3.6 Subproblem VI; 6.3.7 Subproblem VII; 6.3.8 Subproblem VIII; 6.3.9 Subproblem II; 6.4 Computational Complexity; 6.4.1 Full Enumeration; 6.5 Binary Variables and Logical Relations; 6.6 Fixed Charge Models; 6.6.1 Fixed Charge Example-Introduction; 6.6.2 Linking Constraints with “Big M”; 6.6.3 Fixed Charge Implementation; 6.7 Model Results and Interpretation 7 More Integer Programming Models; 7.1 Overview; 7.2 Revisiting the Warehouse Location Problem; 7.2.1 Implementing the Warehouse Model; 7.2.2 Solving the Warehouse Location Problem; 7.2.3 Warehouse Discussion; 7.3 Solving MIPs with Different Solvers; 7.3.1 Performance of glpk; 7.3.2 Performance of symphony; 7.3.3 Performance of lpsolve; 7.3.4 Performance of gurobi; 7.3.5 Comparing Results across Solvers; 7.3.6 Popularity of LP Solvers; 7.4 Solving Sudoku Puzzles using Optimization; 7.4.1 Introduction to Sudoku and Optimization; 7.4.2 Formulating the Sudoku Problem; 7.4.3 Implementing Sudoku in ompr; 7.4.4 Sudoku Discussion; 7.5 Exercises; 7.6 Production Planning over Time; 7.6.1 Implementing the Model; 7.7 Additional Exercises 8 Goal Programming; 8.1 Introduction; 8.2 Preemptive Goal Programming; 8.3 Policies for Houselessness; 8.4 Mass Mailings; 8.4.1 Formulating the State Mailing Model; 8.4.2 Implementing the State Mailing Model; 8.4.3 Frontloading the Work; 8.5 Exercises Appendix; A A Very Brief Introduction to R; A.1 Purpose; A.2 Getting Started with R; A.3 Exercises B Introduction to Math Notation; B.1 Purpose; B.2 Basic Summation Notation; B.3 Using LaTeX in RMarkdown; B.4 Inline Notation; B.5 Sums; B.6 Delimiters; B.7 Summary of Mathematical Notations; B.8 Sequences and Summation Notation; B.9 Applications of Summation; B.10 Double Summation; B.11 Applications of Double Summation; B.12 Exercises C Troubleshooting; C.1 Overview; C.2 Model Building; C.2.1 Define and Formulate before Implementing; C.2.2 Failing to Look for Past Optimization Models; C.2.3 Misrendering of PDF; C.2.4 Blank Lines in LaTeX; C.2.5 Problems with PDF Creation; C.3 Implementation Troubleshooting; C.3.1 Errors in a Piped Model; C.3.2 Undefined Object in ompr; C.3.3 Unexpected Symbol in ompr; C.3.4 Name Conflicts between R and ompr; C.3.5 Blindly Reusing Code; C.4 General Debugging Tips; C.5 Getting Help D Making Good Tables 263; D.1 Importance of Tables in Modeling; D.2 Kable vs. Kbl; D.3 Table Footnotes with Kable; D.4 Setting Row and Column Names in Kable; D.5 Booktabs vs. Default; D.6 Using LaTeX in Kable Column Names; D.7 Fitting Tables to Page Width; Bibliography; Index
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2022
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 519.6; Mathematical optimization -- Data processing; R (Computer program language) -- Mathematical models
• Languages: English
• ISBNs: 9781000606898; 9781000606843; 9781003051251
• Related ISBNs: 9780367507893
• Notes: Note: Description based on CIP data; resource not viewed.
• 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.