CHAPTER I PROBLEM SOLVING WITH MATHEMATICAL MODELS
1.1 OR Application Stories
1.2 Optimization and the Operations Research Process
1.3 System Boundaries, Sensitivity Analysis, Tractability and Validity
1.4 Descriptive Models and Simulation
1.5 Numerical Search and Exact versus Heuristic Solutions
1.6 Deterministic versus Stochastic Models
1.7 Perspectives
Exercises
CHAPTER 2 DETERMINISTIC OPTIMIZATION MODELS IN OPERATIONS RESEARCH
2.1 Decision Variables, Constraints, and Objective Functions
2.2 Graphic Solution and Optimization Outcomes
2.3 Large-Scale Optimization Models and Indexing
2.4 Linear and Nonlinear Programs
2.5 Discrete or Integer Programs
2.6 Multiobjective Optimization Models
2.7 Classification Summary
Exercises
CHAPTER 3 IMPROVING SEARCH
3.1 Improving Search, Local and Global Optima
3.2 Search with Improving and Feasible Directions
3.3 Algebraic Conditions for Improving and Feasible Directions
3.4 Unimodel and Convex Model Forms Tractable for Improving Search
3.5 Searching and Starting Feasible Solutions
Exercises
CHAPTER 4 LINEAR PROGRAMMING MODELS
4.1 Allocation Models
4.2 Blending Models
4.3 Operations Planning Models
4.4 Shift Scheduling and Staff Planning Models
4.5 Time-Phased Models
4.6 Models with Linearizable Nonlinear Objectives
Exercises
CHAPTER 5 SIMPLEX SEARCH FOR LINEAR PROGRAMMING
5.1 LP Optimal Solutions and Standard Form
5.2 Extreme-Point Search and Basic Solutions
5.3 The Simplex Algorithm
5.4 Dictionary and Tableau Representations of Simplex
5.5 Two Phase Simplex
5.6 Degeneracy and Zero-Length Simplex Steps
5.7 Convergence and Cycling with Simplex
5.8 Doing It Efficiently: Revised Simplex
5.9 Simplex with Simple Upper and Lower Bounds
Exercises
CHAPTER 6 INTERIOR POINT METHODS FOR LINEAR PROGRAMMING
6.1 Searching through the Interior
6.2 Scaling with the Current Solution
6.3 Affine Scaling Search
6.4 Log Barrier Methods for Interior Point Search
6.5 Dual and Primal-Dual Extensions
Exercises
CHAPTER 7 DUALITY AND SENSITIVITY IN LINEAR PROGRAMMING
7.1 Generic Activities versus Resources Perspective
7.2 Qualitative Sensitivity to Changes in Model Coefficients
7.3 Quantifying Sensitivity to Changes in LP Model Coefficients: A Dual Model
7.4 Formulating Linear Programming Duals
7.5 Primal-to-Dual Relationships
7.6 Computer Outputs and What If Changes of Single Parameters
7.7 Bigger Model Changes, Reoptimization, and Parametric Programming
Exercises
CHAPTER 8 MULTIOBYECTIVE OPTIMIZATION AND GOAL PROGRAMMING
8.1 Multiobjective Optimization Models
8.2 Efficient Points and the Efficient Frontier
8.3 Preemptive Optimization and Weighted Sums of Objectives
8.4 Goal Programming
Exercises
CHAPTER 9 SHORTEST PATHS AND DISCRETE DYNAMIC
CHAPTER 10 NETWORK FLOWS
CHAPTER 11 DISCRETE OPTIMIZATION MODELS
CHAPTER 12 DISCRETE OPTIMIZATION METHODS
CHAPTER 13 UNCONSTRAINED NONLNEAR PROGRAMMING
CHAPTER 14 CONSTRAINED NONLINEAR PROGRAMMING
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SELECTED ANSWERS
INDEX
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