Practical Mathematical Models of Optimization Problems
Practical Mathematical Models of Optimization Problems
Using Google OR-Tools
About the Book
This book is an introduction to the art and science of optimization
modelling. It covers the creation and analysis of practical
algebraic models of optimization problems. Typical problems
include:
- What is the best route to go from home to work?
- What is the best way to produce cars?
- What is the best way to distribute groceries?
- What is the best way to pack a container?
- What is the best fuel to use in rocket boosters?
- What is the best placement of transistors on a chip?
- What is the best basketball schedule?
To answers such questions, researchers and practitioners have
established a framework into which they mold the questions,
clarifying meaning and enforcing precision; that is a model.
Many textbooks cover the theory behind such models, along with their
solution techniques. This book, the product of the author's decades
of teaching and consulting, stresses the model creation aspect;
contrasting alternate approaches and practical variations.
The text can be used as an undergraduate text or a practitioner's
reference. Each model is explained thoroughly and written to be
executed. The source code from all examples in the book is
available, written in Python using Google's OR-Tools library.
Web site: http://www.practicalopt.com/
Also available is a random problem generator, useful for individual
study or class assignements.
Table of Contents
Introduction
- What is this book about?
- Features of the text
- Getting our feet wet: Bacterial coexistence
Linear continuous models (LP)
- Diet problem
- Blending crude oils
- Project management
- Minimax problems
- Absolute value problems
- Multi-stage (multi-period) models
Non obviously linear continuous models (LP)
- Maximum flow problem
- Minimum cost flow problem
- Flow problems (Transshipment)
- Shortest paths (and longest and all-pairs)
-- Critical tasks finder
- Piecewise linear functions
- Non-linear function minimization via linear approximations
- Non-convex piecewise linear functions
- Curve fitting
Pure linear integer models (IP)
- Set Cover
- Set Packing
- Bin Packing
- TSP
Mixed models (MIP)
- Facility Location
- Multi-Commodity Flow
- All-pairs shortest paths (revisited)
- Staffing levels
- Cutting Stock
- Non-convex objective and other non-convex trickery
-- Selecting k variables out of n to be non-zero.
-- Selecting k adjacent variables out of n to be non-zero..
-- Selecting k constraints out of n.
- Staff Scheduling
- Sport scheduling
- Puzzles
-- Pseudo-chess
-- Sudoku
-- Send more money
-- Ladies and tigers
- Quick reference guide for OR-Tools MPSolver
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