A linear optimizer is a mathematical optimization tool that can identify the best possible solutions to questions where the outcome has a linear relationship with the variables of interest. It is also known as a linear programming solver.
Linear optimizers are often the first solvers people use in their optimization journeys, as the mathematical concepts are relatively basic (i.e., linear algebra and college-level calculus). This allows users to master optimization concepts before moving to more complicated mathematical concepts.
While linear optimizers solve (relatively) straightforward problems, they are also powerful. Small startups to Fortune 100 companies use linear optimizers to solve pressing business challenges, such as workforce scheduling, resource allocation, and supply chain optimization. If your team is interested in linear optimization, check out Gurobi’s Linear Programming Tutorial.
All problems have constraints, such as budgets, timelines, or production limits. A linear optimizer works by utilizing the linear constraints to define the boundaries of any possible solution. It then explores the feasible region (i.e., the region of solutions that fit within the constraints) until it identifies the optimal solution. How it explores the feasible region for the optimal solution depends on the specific algorithm teams employ. For example, the Simplex Method starts at an initial feasible solution and then follows the exterior of the feasible region until it reaches the most optimal point. The Interior Point Method, however, explores the interior of the feasible region.
For an in-depth explanation of how linear programming models are developed, be sure to read the Gurobi LP Models Primer.
Linear optimizers are appropriate for pure linear programs (i.e., programs in which variables are continuous and have linear relationships with the outcome and constraints). Most business challenges have at least some integer variables, which means that most models will require at least mixed-integer linear solvers. However, linear optimizers can still solve many problems.
When deployed appropriately, a linear optimizer can help your team identify the best possible solution in a timely manner. For example, with Gurobi, Lyft was able to reduce their time spent per linear problem by 80% and improve their overall end-to-end time by 92%. This played a key role in helping them be more responsive to changing conditions and scale up driver incentive programs.
The main weakness of linear optimizers is the relative rarity of purely linear optimization problems. To determine if a linear optimizer is appropriate for your challenge, you must determine:
If the answer to any of these questions is “no,” then a linear optimizer may not be the appropriate tool for your challenge and you will need to explore other optimizers.
Yes, the Gurobi Optimizer is a linear optimizer. As noted above, that may not always be the right tool for the job. Luckily, Gurobi is not just a linear optimizer. In addition to linear programming, Gurobi can solve:
A linear optimizer is specifically designed to solve linear problems (i.e., problems in which variables are continuous and have linear relationships with the objective function) by taking advantage of the geometry of the solution space. Other optimizers include:
Operations researchers and data scientists need three key skills to use a linear optimizer:
Gurobi has many resources to learn more about linear optimization, including:
Choose the evaluation license that fits you best, and start working with our Expert Team for technical guidance and support.
Request free trial hours, so you can see how quickly and easily a model can be solved on the cloud.