AIMMS - Linear Programming

Linear Programming

Linear Programming (LP) problems involve the optimization of a linear objective function, subject to linear equality and inequality constraints. In addition all variables in a linear programming model are continuous. There are efficient solution methods for linear programming models and even most very large models can be solved by the available solvers.

Benefits of Using AIMMS as Linear Programming Software

Besides the general benefits of using AIMMS, there are specific functionalities that make AIMMS an excellent tool for modeling linear programming problems. Like other mathematical modeling languages AIMMS provides a full interface to the best solvers, allowing you to control the performance of solvers via option settings, callbacks, and inspection of the statistics the solvers give back, such as Reduced Cost. In addition, AIMMS is equipped with the Math Program Inspector, a tool that lets you inspect your model and solution, execute "what-if" scenarios, analyze bounds, etc.; this makes debugging your model very easy.

Teaching

AIMMS comes with an Optimization Modeling Guide in PDF format. This book contains a general introduction on modeling, a section containing linear programming tricks and various examples. The combination of AIMMS and this book are ideal for teaching linear programming courses and learning about linear programming through self-study.

Linear Programming solvers

Standard Solvers

AIMMS supports the solvers XA, CPLEX, XPRESS, and MOSEK to solve linear programming models.

Open Solver Interface

The AIMMS Open Solver Interface allows solver developers to link their own linear programming solvers to AIMMS themselves.

Linear Programming Examples

Farm Planning

This example introduces a linear programming model for a simplified farm planning problem in a developing country. Every year a farmer must decide what crops to grow, taking into account limiting resources such as land, labor and water. For a full description of the model see Chapter 11 in the Optimization Modeling Guide.

Download the Farm Planning Example

Performance Assessment

In this example the performance of a set of comparable organizational units is determined, while introducing the concept of relative efficiency of each organizational unit. Based on this concept, the underlying problem can be translated into a collection of linear programming models using relative efficiency as the optimization criteria. The efficient organizations are identified and form a reference for the other organizations. For a full description of the model see Chapter 13 in the Optimization Modeling Guide.

Download the Performance Assessment Example

Power System Expansion

This example implements a power system expansion model with uncertain electricity demand, covering a single time period. The problem is to determine new power plant design capacities in order to meet an increase in electricity demand. Yet, the future demand is uncertain and it is modeled by means of several demand scenarios. For a full description of the model see Chapter 16 in the Optimization Modeling Guide.

Download the Power System Expansion Example

Free Trial License

Download a free trial license of AIMMS to experience the benefits of using AIMMS as your linear programming software.

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