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Case studies from AIMMS

Welcome to AMPL (A Mathematical Programming Language), a powerful and intuitive modeling language designed specifically for large-scale optimization problems. If you are new to modeling languages or AMPL, this page will guide you through what AMPL is, its benefits, and why it stands out in the landscape of programming and modeling languages.

Optimization problems in businesses using AMPL

The CVRPLIB team announces the CVRPLIB BKS Challenge, a 30-day competition aimed at finding extremely high-quality solutions for the new XL benchmark set, 100 challenging CVRP instances ranging from 1,000 to 10,000 customers.

The CG:SHOP Challenge (Computational Geometry: Solving Hard Optimization Problems) is an annual competition dedicated to tackling specific, difficult geometric optimization problems. Originally established as a workshop at Computational Geometry Week (CG Week) in 2019, the Challenge provides a unique platform where the success of proposed solutions is measured based on computational performance on a set of carefully selected benchmark instances. This focus on empirical evaluation marks a shift from traditional computational geometry research, which often emphasizes theoretical approaches.

Consortium for Mathematics and its applications

COMAP's Mathematical Contest in Modeling (MCM) and Interdisciplinary Contest in Modeling (ICM) are international contests for high school students and college undergraduates. The contests challenge teams of up to three students to analyze, model, solve, and present solution reports to an open-ended application problem. In these contests research, analytics, and applied intelligence are just as important as time management and problem selection. Are you and your team up to it?

Customer success stories from Coupa including optimization problems

CVXPY is an open source Python-embedded modeling language for convex optimization problems. It lets you express your problem in a natural way that follows the math, rather than in the restrictive standard form required by solvers.

Community for Decision Management, including Machine Learning and Optimization

A track record of successful deployments in several countries across the globe from DecisionBrain

Challenges from the Center for Discrete Mathematics and Theoretical Computer Science

The Resource Center of use cases done with FICO

GAMS is a modeling system for mathematical optimization that lets users formulate complex problems in a high-level language and run them with different commercial and open-source solvers. All solvers are packaged in a single distribution, making it easy to switch between them and giving customers one point of contact for licensing and support. It also has a Python interface -GAMSPy- for building and solving mathematical optimization models using the GAMS technology stack. It keeps the modeling concepts of GAMS (sets, parameters, variables, equations) but exposes them as Python classes and functions. This allows modelers to stay in the Python ecosystem while using mature GAMS solvers and workflows.

A selection of case studies that demonstrate the diverse application areas of mathematical optimization with GAMS.

Open source software suite for optimization, tuned for tackling the world's toughest problems in vehicle routing, flows, integer and linear programming, and constraint programming.

Grid Optimization challenges for electric systems

Insights from different case studies of companies using Gurobi

Success stories from different companies using Hexaly

Use cases from IBM

JuMP is a domain-specific modeling language for mathematical optimization embedded in Julia. JuMP makes it easy to formulate and solve a range of problem classes, including linear programs, integer programs, conic programs, semidefinite programs, and constrained nonlinear programs.

Challenges around TSP variant with Santa Claus

The 2026 Land-Doig MIP Competition is a computational competition hosted by the 2026 Mixed Integer Programming Workshop, offering an opportunity for teams to showcase their practical and computational prowess and fostering innovation in computational MIP. It is named in honor of Ailsa H. Land and Alison G. Harcourt (née Doig), who proposed the first LP-based branch-and-bound algorithm.

MiniZinc is a high-level constraint modelling language that allows you to easily express and solve discrete optimisation problems.

Annual challenges from the University of Lehigh

Real life examples from More Optimal

Challenges with different optimization problems

Case studies from Optimal Dynamics

Case studies from Optimal Solutions focused on food & beverage, pharmaceuticals, airlines, and finance

Optlang is a Python package implementing a modeling language for solving mathematical optimization problems, i.e. maximizing or minimizing an objective function over a set of variables subject to a number of constraints. Optlang provides a common interface to a series of optimization tools, so different solver backends can be changed in a transparent way.

Customer success stories from ORTEC

Challenge from Parameterized Algorithms and Computational Experiments Challenge to bridge the gap between theory and practice of algorithms

An LP modeler written in Python

Python-based, open-source optimization modeling language with a diverse set of optimization capabilities.

PyOptInterface is an open-source Python library to provide a unified API to construct and solve optimization models with various optimizers.

Bi-annual challenges from the French Operational Research (OR) and Decision Support Society. 2026: https://gitlab.com/Orange-OpenSource/network-optimization-tools/challenge-roadef-2026/-/tree/main/sprint_results

Annual challenges organized by Shell AI team.

Optimization competition organized by the Mexican Society of Operations Research (SMIO).

Business cases highlighted by The OR Society

Customer stories of companies using Timefold for planning problems

Vehicle Routing and Logistics work group from EURO