Examples

The LumiX examples demonstrate key features and best practices through practical, real-world optimization problems. Each example is fully documented with source code, mathematical formulations, and learning objectives.

Quick Start Guide

New to LumiX? Start with these examples in order:

  1. Basic LP (Basic Linear Programming Example) - The simplest introduction

  2. Production Planning (Production Planning Example) - Single-model indexing

  3. Driver Scheduling (Driver Scheduling Example) - Multi-model indexing (KEY FEATURE)

Examples by Topic

Fundamentals

Advanced Techniques

Analysis Tools

Available Examples

The LumiX repository includes 11 comprehensive examples demonstrating various features:

Basic Examples

  1. Production Planning (01_production_planning/)

    • Single-model indexing

    • Data-driven modeling

    • Resource capacity constraints

    • Profit maximization

  2. Driver Scheduling (02_driver_scheduling/)

    • Multi-dimensional indexing

    • Complex scheduling constraints

    • Assignment problems

  3. Facility Location (03_facility_location/)

    • Binary decision variables

    • Fixed costs vs. variable costs

    • Facility location optimization

  4. Basic Linear Programming (04_basic_lp/)

    • Simple LP formulation

    • Getting started example

    • Basic constraints

Assignment Problems

  1. CP-SAT Assignment (05_cpsat_assignment/)

    • Using CP-SAT solver

    • Integer programming

    • Assignment constraints

Advanced Techniques

  1. McCormick Bilinear Linearization (06_mccormick_bilinear/)

    • Bilinear term linearization

    • McCormick envelopes

    • Non-linear optimization

  2. Piecewise Linear Functions (07_piecewise_functions/)

    • Piecewise-linear approximations

    • Non-linear function modeling

    • SOS2 constraints

Analysis Examples

  1. Scenario Analysis (08_scenario_analysis/)

    • Comparing multiple scenarios

    • Scenario management

    • Side-by-side comparison

  2. Sensitivity Analysis (09_sensitivity_analysis/)

    • Parameter sensitivity

    • Shadow prices

    • Reduced costs

    • Range analysis

  3. What-If Analysis (10_whatif_analysis/)

    • Quick what-if scenarios

    • Impact analysis

    • Decision support

Goal Programming

  1. Goal Programming (11_goal_programming/)

    • Multi-objective optimization

    • Weighted goals

    • Sequential (lexicographic) goals

    • Goal priorities

Running Examples

Each example is self-contained and can be run directly:

# Clone the repository
git clone https://github.com/tdelphi1981/LumiX.git
cd LumiX

# Install LumiX with a solver
pip install -e .[ortools]

# Run an example
python examples/01_production_planning/production_planning.py

Example Structure

Each example directory typically contains:

  • Main script: The optimization model and solution

  • Sample data: Data classes and sample datasets

  • README (coming soon): Detailed explanation

What You’ll Learn

From Basic Examples

  • How to define variables with type safety

  • Building expressions and constraints

  • Creating and solving models

  • Accessing solution values

  • Working with different data structures

From Advanced Examples

  • Multi-dimensional indexing strategies

  • Automatic linearization techniques

  • Solver-specific features

  • Performance optimization

  • Complex constraint modeling

From Analysis Examples

  • Sensitivity analysis workflows

  • Scenario comparison techniques

  • What-if analysis for decision making

  • Interpreting optimization results

Example Categories

By Difficulty

Beginner

  • Basic LP (04_basic_lp/)

  • Production Planning (01_production_planning/)

Intermediate

  • Driver Scheduling (02_driver_scheduling/)

  • Facility Location (03_facility_location/)

  • CP-SAT Assignment (05_cpsat_assignment/)

Advanced

  • McCormick Bilinear (06_mccormick_bilinear/)

  • Piecewise Functions (07_piecewise_functions/)

  • Goal Programming (11_goal_programming/)

By Feature

Indexing

  • Single: Production Planning

  • Multi-dimensional: Driver Scheduling

Variable Types

  • Continuous: Production Planning, Basic LP

  • Integer: CP-SAT Assignment

  • Binary: Facility Location

Linearization

  • Bilinear: McCormick example

  • Piecewise: Piecewise functions example

Analysis

  • Sensitivity: Sensitivity Analysis example

  • Scenario: Scenario Analysis example

  • What-If: What-If Analysis example

Multi-Objective

  • Goal Programming: Goal Programming examples

Documentation Features

Each example now includes:

✓ Detailed walkthrough - Step-by-step code explanation ✓ Problem descriptions - Real-world business context ✓ Mathematical formulations - LaTeX equations and constraints ✓ Solution interpretation guides - How to read and use results ✓ Comprehensive README files - Quick reference in each example directory ✓ API cross-references - Links to relevant LumiX classes and methods

Coming Soon:

  • Jupyter notebook versions

  • Interactive visualizations

  • Performance comparisons across solvers

Contributing Examples

Have an interesting use case? We welcome example contributions!

  • Open an issue to discuss your example idea

  • Follow the existing example structure

  • Include sample data and clear comments

  • Submit a pull request

Getting Started

Step 1: Choose Your Starting Point

Step 2: Run the Examples

# Clone the repository
git clone https://github.com/tdelphi1981/LumiX.git
cd LumiX

# Install LumiX with a solver
pip install -e .[ortools]

# Run an example
python examples/04_basic_lp/basic_lp.py

Step 3: Explore and Modify

  • Read the documentation page for detailed explanations

  • Review the source code and README files

  • Try the suggested modifications

  • Adapt patterns to your own problems

Next Steps

After completing the examples:

  1. Review the User Guide for detailed feature documentation

  2. Explore the API Reference for complete API reference

  3. Join the community and share your use cases

  4. Contribute your own examples via pull request