Optimization Modeling with Spreadsheets

Kenneth R. Baker, PhD, is Nathaniel Leverone Professor of Management at the Tuck School of Business and Adjunct Professor of Engineering at Dartmouth College. A Fellow of the Institute for Operations Research and the Management Sciences (INFORMS), Dr. Baker has published extensively in his areas of research interest, which include mathematical modeling, spreadsheet engineering, and scheduling. He is also coauthor of Principles of Sequencing and Scheduling and Management Science: The Art of Modeling with Spreadsheets, Fourth Edition, both published by Wiley.

• Preface ix1 Introduction to Spreadsheet Models for Optimization 11.1 Elements of a Model 21.2 Spreadsheet Models 41.3 A Hierarchy for Analysis 71.4 Optimization Software 81.5 Using Solver 102 Linear Programming: Allocation, Covering, and Blending Models 212.1 Linear Models 222.2 Allocation Models 292.3 Covering Models 382.4 Blending Models 472.5 Modeling Errors in Linear Programming 523 Linear Programming: Network Models 653.1 The Transportation Model 663.2 The Assignment Model 713.3 The Transshipment Model 753.4 Features of Special Network Models 783.5 Building Network Models with Balance Equations 793.6 General Network Models with Yields 843.7 General Network Models with Transformed Flows 914 Sensitivity Analysis in Linear Programs 1084.1 Parameter Analysis in the Transportation Example 1094.2 Parameter Analysis in the Allocation Example 1164.3 The Sensitivity Report and the Transportation Example 1234.4 The Sensitivity Report and the Allocation Example 1274.5 Degeneracy and Alternative Optima 1294.6 Patterns in Linear Programming Solutions 1335 Linear Programming: Data Envelopment Analysis 1605.1 A Graphical Perspective on DEA 1625.2 An Algebraic Perspective on DEA 1665.3 A Spreadsheet Model for DEA 1685.4 Indexing 1735.5 Reference Sets and HCUs 1745.6 Assumptions and Limitations of DEA 1786 Integer Programming: Binary-Choice Models 1916.1 Using Solver with Integer Requirements 1936.2 The Capital Budgeting Problem 1986.3 Set Covering 2026.4 Set Packing 2056.5 Set Partitioning 2086.6 Playoff Scheduling 2116.7 The Algorithm for Solving Integer Programs 2157 Integer Programming: Logical Constraints 2277.1 Simple Logical Constraints: Exclusivity 2297.2 Linking Constraints: The Fixed Cost Problem 2317.3 Linking Constraints: The Threshold Level Problem 2377.4 Linking Constraints: The Facility Location Model 2387.5 Disjunctive Constraints: The Machine-Sequencing Problem 2467.6 Tour Constraints: The Traveling Salesperson Problem 2518 Nonlinear Programming 2708.1 One-Variable Models 2718.2 Local Optima and the Search for an Optimum 2778.3 Two-Variable Models 2808.4 Nonlinear Models with Constraints 2858.5 Linearizations 2939 Heuristic Solutions with the Evolutionary Solver 3079.1 Features of the Evolutionary Solver 3089.2 An Illustrative Example: Nonlinear Regression 3099.3 The Machine-Sequencing Problem Revisited 3179.4 The Traveling Salesperson Problem Revisited 3199.5 Budget Allocation 3229.6 Two-Dimensional Location 3249.7 Line Balancing 3279.8 Group Assignment 331Appendices1 Supplemental Files and Software 348A1.1 Supplemental Microsoft Office Excel Files 348A1.2 Analytic Solver Platform for Education Software 348A1.3 Opensolver Software 3492 Graphical Methods for Linear Programming 350A2.1 An Example 350A2.2 Generalities 3553 The Simplex Method 357A3.1 An Example 357A3.2 Variations of the Algorithm 362Index 366