Spreadsheet-based introduction to mathematical programming concepts and applications, intended for undergraduate and graduate students in management and engineering. Its emphasis on model building and its focus on formulation principles are key features that reinforce its practical approach. The text also includes a comprehensive tutorial on the use of Excel's Solver, and, at a more advanced level, Frontline Systems' Premium Solver.
1. Introduction to Spreadsheet Modeling for Optimization. Elements of a Model. Spreadsheet Models. A Hierarchy for Analysis. Optimization Software. Using Solver. Summary. Homework.2. Linear Programming Formulations: Allocation, Covering, and Blending Models.Linear Models. Allocation Models. Blending Models. Modeling Errors in Linear Programming. Summary. Homework.3. Linear Programming Formulations: Network Models. The Transportation Model. The Assignment Model. The Transshipment Model. Features of Special Network Models. Building Network Models with Balance Equations. General Network Models with Expanding Flows. General Network Models with Transformed Flows. Summary. Homework. 4. Sensitivity Analysis Linear Programs.Sensitivity Analysis Transportation Example. Sensitivity Analysis in the Allocation Example. The Sensitivity Report and the Transportation Example. The Sensitivity Report and the Allocation Example. Degeneracy and Alternative Optima. Patterns in Linear Programming Solutions.Summary. Homework.5. Linear Programming Formulations: Data Envelopment Analysis.A Graphical Perspective on DEA. An Algebraic Perspective on DEA. A Spreadsheet Model for DEA. Indexing. Finding Reference Sets and HCUs. Assumptions and Limitations of DEA. Summary. Homework.6. Integer Programming.Using Solver with Integer Requirements. Models with Binary Choice. Models with Qualitative Constraints. The Facility Location Model. The Algorithm for Solving Integer Programs. Summary. Homework.7. Nonlinear Programming.One-Variable Models. Local Optima and Search for an Optimum. Two-Variable Models. Nonlinear Models with Constraints. Linearizations. Summary. Homework. 8. Heuristic Solutions with the Evolutionary Solver.Features of the Evolutionary Solver. An Illustrative Example: Nonlinear Regression. The Machine-Sequence Problem Revisited. The Traveling Salesperson Problem Revisited. Multi-Machine Scheduling. Two-Dimensional Location. Group Assignment. Summary. Homework.Appendix I. Software.Appendix II. Graphical Methods in Linear Programming.Appendix III. The Simplex Method.Appendix IV. Stochastic Programming.