The concepts that are covered in this tutorial, that are essential to practical optimization modeling, include: using vectors and indexes; separating data from the model; special types of constraints, such as balance constraints; and various data management issues, such as the difference between using sparse and dense data.
The MPL Modeling System has a highly advanced integrated model development environment, which allows the user to quickly formulate and solve models. Within that system is the MPL Modeling Language which has a full-featured algebraic language for formulating optimization models.
We strongly believe that MPL has some unique features that make it the ideal choice for teaching optimization modeling, such as an easy-to-use graphical user interface, straightforward easy-to-learn syntax, and powerful data management capabilities. This tutorial can either be used as a stand-alone course on modeling, or as supplementary material to standard textbooks on Operations Research and Linear Programming.
In addition, MPL has extensive flexibility when working with subsets of indexes, functions of indexes, and compound or multi-dimensional index sets.
This allows the model formulator, for example, to index only over products that are made by each machine in a specific plant instead of having to go through all the products for all the machines and all the plants, which would be considerable slower.
MPL can easily handle very large matrices with millions of variables and constraints. This is especially important when dealing with large supply-chain optimization models over multiple time periods that can grow very quickly.
MPL has its own memory manager that can dynamically store models of any size, giving it a full scalability. The only limitation the model developer faces is how much memory is available on his or her machine. Typically, MPL uses only MB of memory per 10, variables, which puts a minimal additional burden on the machine capacity needed to generate and solve the matrix.
The matrix generation in MPL is extremely fast and efficient which is important since it contributes to the overall time needed to obtain the solution of the model. As a result, we can now run models with millions of variables and generate a matrix for them in less than one minute.
This is very important, because if the matrix generation takes too long it can seriously add to the time needed to reach the solution even if the fastest optimization solvers are used. MPL provides the fastest and most scalable matrix generation capabilities available in a modeling system on the market today. Importing data from a variety of corporate database systems into optimization models is frequently an essential requirement for optimization projects.
One of the advanced features of MPL is the database connection option that directly links MPL with relational databases and other data sources. This option enables the model developer to gather both indexes and data values from various data sources and import them directly into the model. After the model has been optimized, the solution output can be exported back into the database. This, along with the run-time features of MPL , allows the model developer to easily create customized end-user applications for optimization using the built-in data entry and reporting capabilities of the database.
The database connection in MPL has the ability to access data from many different sources, such as databases, Excel spreadsheets, external data files, and the Internet. In addition, academic users will still be able to use free Gurobi academic licenses through these modeling systems.
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