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Mixed Integer Programming
Mixed integer programming (MIP) problems involve the optimization of a linear objective function, subject to linear equality and inequality constraints. Some or all of the variables are required to be integer. Mixed integer programming problems are in general more difficult to solve than linear programming problems but AIMMS is equipped with the best high-performance solvers available.
Benefits of Using AIMMS as Mixed Integer Programming Software
Besides the general benefits of using AIMMS, there are specific functionalities that make AIMMS an excellent tool for modeling mixed integer programming problems. Like other mathematical modeling languages AIMMS provides a full interface to the best solvers which allow you to control the performance of solvers via option settings and inspect the statistics the solvers give back. 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. AIMMS also supports the solver control callbacks, which one may want to use to influence the solver, e.g., for branching, adding cuts, heuristics and incumbent solutions.
Teaching
AIMMS comes with an Optimization Modeling Guide in PDF format. This book contains a general introduction on modeling, a section containing 
integer programming tricks and various examples. The combination of AIMMS and this book are ideal for teaching mixed integer programming courses and learning about mixed integer programming through self-study.
Mixed Integer Programming solvers
Standard Solvers
AIMMS supports the solvers XA, CPLEX, XPRESS, and MOSEK to solve mixed integer programming models.
Open Solver Interface
The AIMMS Open Solver Interface allows solver developers to link their own mixed integer programming solvers to AIMMS themselves.
Mixed Integer Programming Examples
Employee Training
An airline company must decide how many flight attendants to hire and train over the next six months. The model includes a (stock) balance constraint which is typical in multi-period models involving state and control type decision variables. A time lag notation is introduced for the backward referencing of time periods. For a full description of this model see Chapter 8 in the Optimization Modeling Guide.
Download the Employee Training Example
Media Selection
A company wants to set up an advertising campaign in preparation for the launch of new products. There are six different types of target audiences for the new products. Furthermore, there are eight different media types that will reach various audiences. Since there isn't any single media that will reach all of the target audiences at once, multiple media types need to be selected in order to reach all of the target audiences. The goal of this example is to minimize the total cost of selecting the different types of media that will cover all of the target audiences. For a full description of this model see Chapter 9 in the Optimization Modeling Guide.
Download the Media Selection Example
Bandwidth Allocation
As a result of the growing number of mobile communication systems, there is an increasing need to allocate and re-allocate bandwidth for point-to-point communications. During operational periods the volume of traffic usually changes significantly, which causes point-to-point capacity and interference problems. Consequently, bandwidth allocation is a recurring process in practice. In this example a specific bandwidth allocation problem is examined. For a full description of this model see Chapter 15 in the Optimization Modeling Guide.
Download the Bandwidth Allocation Example
Free Trial License
Download a free trial license of AIMMS to experience the benefits of using AIMMS as your mixed integer programming software.
