Optimization Modeling with LINGO

Table of Contents

Go to:

Chapter 1	Chapter 2	Chapter 3
Chapter 4	Chapter 5	Chapter 6
Chapter 7	Chapter 8	Chapter 9
Chapter 10	Chapter 11	Chapter 12
Chapter 13	Chapter 14	Chapter 15
Chapter 16	Chapter 17	Chapter 18

Contents

Preface

Acknowledgments

Ch 1 What Is Mathematical Programming? (Top)
1.1 Introduction
1.2 A Simple Product Mix Problem
1.3 Linearity
1.4 Analysis of LP Solutions
1.5 Sensitivity Analysis, Reduced Costs, and Dual Prices
1.6 Unbounded Formulations
1.7 Infeasible Formulations
1.8 Multiple Optimal Solutions and Degeneracy
1.9 Problems
Ch 2 Solving Math Programs with LINGO (Top)
2.1 Introduction
2.2 LINGO for Windows
2.3 Getting Started on a Small Problem
2.4 Integer Programming with LINGO
2.5 Problems
Ch 3 Analyzing Solutions (Top)
3.1 Economic Analysis of Solution Reports
3.2 Economic Relationship Between Dual Prices and Reduced Costs
3.3 Range of Validity of Reduced Costs and Dual Prices
3.4 Sensitivity Analysis of the Constraint Coefficients
3.5 The Dual LP Problem, or the Landlord and the Renter
3.6 Problems
Ch 4 The Model Formulation Process (Top)
4.1 The Overall Process
4.2 Approaches to Model Formulation
4.3 The Template Approach
4.4 Constructive Approach to Model Formulation
4.5 Choosing Costs Correctly
4.6 Common Errors in Formulating Models
4.7 The Nonsimultaneity Error
4.8 Problems
Ch 5 The Sets View of the World (Top)
5.1 Introduction
5.2 The Sets Section of a Model
5.3 The DATA Section
5.4 Set Looping Functions
5.5 Set Based Modeling Examples
5.6 Domain Functions for Variables
5.7 Spreadsheets vs. LINGO
5.8 Summary
5.9 Problems
Ch 6 Product Mix Problems (Top)
6.1 Introduction
6.2 Example
6.3 Process Selection Product Mix Problems
6.4 Problems
Ch 7 Covering, Staffing & Cutting Stock Models (Top)
7.1 Introduction
7.2 Cutting Stock and Pattern Selection
7.3 Crew Scheduling Problems
7.4 A Generic Covering/Partitioning Model
7.5 Problems
Ch 8 Networks, Distribution and PERT/CPM (Top)
8.1 What's Special About Network Models
8.2 PERT/CPM Networks and LP
8.3 Activity-on-Arc vs. Activity-on-Node Network Diagrams
8.4 Crashing of Project Networks
8.5 Path Formulations
8.6 Path Formulations of Undirected Networks
8.7 Double Entry Bookkeeping: A Network Model of the Firm
8.8 Extensions of Network LP Models
8.9 Nonlinear Networks
8.10 Equilibrium Network Flows
8.11 Problems
Ch 9 Multi-period Planning Problems (Top)
9.1 Introduction
9.2 A Dynamic Production Problem
9.3 Multi-period Financial Models
9.4 Financial Planning Models with Tax Considerations
9.5 Present Value vs. LP Analysis
9.6 Accounting for Income Taxes
9.7 End Effects
9.8 Non-optimality of Cyclic Solutions to Cyclic Problems
9.9 Problems
Ch 10 Blending of Input Materials (Top)
10.1 Introduction
10.2 The Structure of Blending Problems
10.3 A Blending Problem within a Product Mix Problem
10.4 Proper Choice of Alternate Interpretations of Quality Requirements
10.5 How to Compute Blended Quality
10.6 Interpretation of Dual Prices for Blending Constraints
10.7 Fractional or Hyperbolic Programming
10.8 Pooling Problems
10.9 Problems
Ch 11 Formulating and Solving Integer Programs (Top)
11.1 Introduction
11.2 Exploiting the IP Capability: Standard Applications
11.3 Outline of Integer Programming Methods
11.4 Computational Difficulty of Integer Programs
11.5 Problems with Naturally Integer Solutions and the Prayer Algorithm
11.6 The Assignment Problem and Related Sequencing and Routing Problems
11.7 Problems of Grouping, Matching, Covering, Partitioning, and Packing
11.8 Linearizing Products of Variables
11.9 Representing Logical Conditions
11.10 Problems
Ch 12 Decisionmaking Under Uncertainty and Stochastic Programs (Top)
12.1 Introduction
12.2 Representing Uncertainty
12.3 The Scenario Approach
12.4 A More Complicated Two-Period Planning Problem
12.5 Expected Value of Perfect Information (EVPI)
12.6 Expected Value of Modeling Uncertainty
12.7 Risk Aversion
12.8 Choosing Scenarios
12.9 Decisions Under Uncertainty with More than Two Periods
12.10 Decisions Under Uncertainty with an Infinite Number of Periods
12.11 Chance-Constrained Programs
12.12 Problems
Ch 13 Portfolio Optimization (Top)
13.1 Introduction
13.2 The Markowitz Mean/Variance Portfolio Model
13.3 Efficient Frontier and Parametric Analysis
13.4 Important Variations of the Portfolio Model
13.5 Measures of Risk other than Variance
13.6 Scenario Model and Minimizing Downside Risk
13.7 Hedging, Matching and Program Trading
13.8 Methods for Constructing Benchmark Portfolios
13.9 Cholesky Factorization for Quadratic Programs
13.10 Problems
Ch 14 Multiple Criteria and Goal Programming (Top)
14.1 Introduction
14.2 Approaches to Multi-criteria Problems
14.3 Goal Programming and Soft Constraints
14.4 Minimizing the Maximum Hurt, or Unordered Lexico Minimization
14.5 Identifying Points on the Efficient Frontier
14.6 Comparing Performance with Data Envelopment Analysis
14.7 Problems
Ch 15 Economic Equilibria and Pricing (Top)
15.1 What is an Equilibrium?
15.2 A Simple Simultaneous Price/Production Decision
15.3 Representing Supply & Demand Curves in LPs
15.4 Auctions as Economic Equilibria
15.5 Multi-Product Pricing Problems
15.6 Transportation Equilibria
15.7 General Equilibrium Models of An Economy
15.8 Equilibria in Electrical Networks
15.9 Problems
Ch 16 Game Theory and Cost Allocation (Top)
16.1 Introduction
16.2 Two-Person Games
16.3 Two-Person Non-Constant Sum Games
16.4 Nonconstant-Sum Games Involving Two or More Players
16.5 Problems
Ch 17 Inventory, Production, and Supply Chain Management (Top)
17.1 Introduction
17.2 One Period News Vendor Problem
17.3 Multi-Stage News Vendor
17.4 Economic Order Quantity
17.5 The Q,r Model
17.6 Base Stock Inventory Policy
17.7 Multi-Echelon Base Stock, the METRIC Model
17.8 DC With Holdback Inventory/Capacity
17.9 Multiproduct, Constrained Dynamic Lot Size Problems
17.10 Problems
Ch 18 Design & Implementation of Optimization-Based Decision Support Systems (Top)
18.1 General Structure of the Modeling Process
18.2 Appropriate Level of Detail, Verification and Validation
18.3 Separation of Data and System Structure
18.4 Marketing the Model
18.5 Reducing Model Size
18.6 Matrix Generators
18.7 On-the-Fly Column Generation
18.8 Problems

INDEX
References

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