Key Benefits of LINGO
■ Easy Model Expression
- LINGO will help you cut your development time. It lets you formulate your linear, nonlinear and integer problems quickly in a highly readable form. LINGO's modeling language allows you to express models in a straightforward intuitive manner using summations and subscripted variables -- much like you would with pencil and paper. Models are easier to build, easier to understand, and, therefore, easier to maintain. LINGO can exploit multiple CPU cores for faster model generation.
One of LINGO's most powerful features is its mathematical modeling language. LINGO's modeling language lets you express your problems in a natural manner very similar to standard mathematical notation. LINGO allows you to do things such as quickly express a series of similar constraints in a single compact statement. Your models are compact and easy to read.

When building models, you typically find there are one or more sets of related objects (e.g., sets of factories, customers, vehicles, or employees). Often if a constraint applies to one member of a set, then a constraint of the same form also applies to each of the other set members. Rather than requiring that you express an individual constraint for each set member, LINGO allows you to express the entire group of constraints in one concise statement. Taking advantage of sets is the foundation of LINGO's modeling language, the fundamental building block of the program's most powerful capabilities. LINGO even allows you to express common sets implicitly, such as days of the week or months of the year.

LINGO's modeling language can help you drastically cut your model development time. Very large models can often be efficiently expressed with LINGO in less than a single page. The modeling language's similarity to standard mathematical notation makes it very easy to read. Models are easier for the developer to maintain and for colleagues to read and understand.

Using LINGO, you can easily make your model "scalable". This means the dimensions of your model can change without requiring changes to your expression of the problem. For example, suppose you are finding the cheapest way to supply a product from several different warehouses to several different customers. If the number of warehouses or customers change, many modeling packages would require significant changes to the problem's formulation. However, with LINGO, your problem formulation needs no modification. You can simply change the size of your data files and LINGO takes care of the rest.
■ Convenient Data Options
- LINGO takes the time and hassle out of managing your data. It allows you to build models that pull information directly from databases and spreadsheets. Similarly, LINGO can output solution information right into a database or spreadsheet making it easier for you to generate reports in the application of your choice.
Gathering the model's data and getting it in an appropriate format can be a frustrating and time-consuming task, but with LINGO you can manage your data in a variety of convenient forms. LINGO lets you keep your data:
-in an Excel or Lotus spreadsheet file
- in a database such as Access, Oracle, DB/2, Paradox, SQL Server etc
- in a separate text file in list or table form
- stored with the model expression
- entered by the user when the model is run
By providing a wide variety of data options, LINGO provides you with maximum flexibility and convenience. By allowing you to separate your expression of the problem from the data, LINGO models are easier to read and modify, and there is less chance of errors. It also makes prototyping problems on a smaller data set easy. Once you are comfortable with the model, you can easily swap in a larger set of data or several different data sets to investigate different scenarios.
LINGO's flexibility even makes creating reports easy. In addition to being able to read data from spreadsheets and databases, LINGO can also write solution information to these formats. This means that, rather than forcing you to learn some built-in report generator, you can simply output the solution to your application of choice for building reports and analysing the output.

■ Powerful Solvers
- LINGO is available with a comprehensive set of fast, built-in solvers for Linear, Nonlinear (convex & nonconvex/Global), Quadratic, Quadratically Constrained, Second Order Cone, Stochastic, and Integer optimization. You never have to specify or load a separate solver, because LINGO reads your formulation and automatically selects the appropriate one.
LINGO includes a set of built-in solvers to tackle a wide variety of problems. Unlike many modeling packages, all of the LINGO solvers are directly linked to the modeling environment. This seamless integration allows LINGO to pass the problem to the appropriate solver directly in memory rather than through more sluggish intermediate files. This direct link also minimizes compatibility problems between the modeling language component and the solver components.
Linear Solvers
LINGO is available with three state of the art solvers for linear models.

Primal and Dual Simplex Solvers
The base version includes the Primal and Dual Simplex solvers, which incorporate numerous enhancements for maximum speed and robustness. Pricing options, for instance, include partial pricing and Devex. The solver dynamically chooses the best pricing option based upon problem characteristics.

Barrier Solver
The optional Barrier solver provides an alternative means of solving linear models. The Barrier option utilizes a barrier or interior point method to solve linear models. Unlike the Simplex solvers that move along the exterior of the feasible region, the Barrier solver moves through the interior space to find the optimum. Depending upon the size and structure of a particular model, the Barrier solver may be significantly faster than the Simplex solvers and can provide exceptional speed on large linear models -- particularly on sparse models with more than 5,000 constraints or highly degenerate models. The Barrier license option is required to utilize the Barrier solver.

Integer Solver
For models with general and binary integer restrictions, LINGO includes an integer solver that works in conjunction with the linear, nonlinear, and quadratic solvers. For linear models, the integer solver includes preprocessing and dozens of constraint "cut" generation routines that can greatly improve solution times on large classes of integer models.
Nonlinear Solvers
LINGO includes a number of ways to find locally or globally optimal solutions to nonlinear models.

General Nonlinear Solver
For nonlinear programming models, the primary underlying technique used by LINGO's optional nonlinear solver is based upon a Generalized Reduced Gradient (GRG) algorithm. However, to help get to a good feasible solution quickly, LINGO also incorporates Successive Linear Programming (SLP). The nonlinear solver takes advantage of sparsity for improved speed and more efficient memory usage. The Nonlinear license option is required to solve nonlinear models.

Global Solver
Local search solvers are generally designed to search only until they have identified a local optimum. If the model is non-convex, other local optima may exist that yield significantly better solutions. Rather than stopping after the first local optimum is found, the Global solver will search until the global optimum is confirmed. The Global solver converts the original non-convex, nonlinear problem into several convex, linear subproblems. Then, it uses the branch-and-bound technique to exhaustively search over these subproblems for the global solution. The Nonlinear and Global license options are required to utilize the global optimization capabilities.

Multistart Solver
When limited time makes searching for the global optimum prohibitive, the Multistart solver can be a powerful tool for finding good solutions more quickly. This intelligently generates a set of candidate starting points in the solution space. Then, the general nonlinear solver intelligently selects a subset of these to initialize a series of local optimizations. For non-convex nonlinear models, the quality of the solution returned by the multistart solver will be superior to that of the general nonlinear solver. The Nonlinear and Global license options are required to utilize the multistartcapabilties.

Quadratic Solver
In addition to solving linear and mixed integer models, with the Barrier option LINGO can automatically detect and solve models in which the objective function and/or some constraints include quadratic terms. By taking advantage of the quadratic structure, LINGO can solve these models much more quickly than using the general nonlinear solver. LINGO can even handle quadratic models with binary and general integer restrictions. These quadratic capabilities make LINGO suitable for applications such as portfolio optimization problems, constrained regression problems, and certain classes of difficult logistics problems (e.g., layout problems, fixed-charge-network problems with quadratic objectives). The Quadratic solver is included in the Barrier license option.

Conic Solver
The Conic solver efficiently solves Second Order Cone Problems (SOCP). By expressing certain nonlinear models as SOCPs, the Conic solver can be used to solve the model substantially faster than the general nonlinear solver. The Barrier and Conic options are required to utilize the Conic solver.

Stochastic Programming Solver
Incorporate risk into multi-stage optimization models, maximize expected profit, and summarize results in histograms showing the distribution of possible profit, etc. This new option allows modeling and optimization for models with uncertain elements via multistage stochastic linear, nonlinear and integer stochastic programming (SP). Benders decomposition is used for solving large linear SP models. Deterministic equivalent method is used for solving nonlinear and integer SP models. Support is available for over 20 distribution types (discrete or continuous). The Stochastic Programming solver is included in the Stochastic Programming option.

Pre-processing
Pre-processing routines are included in all solvers. The Linear and Nonlinear solvers include scaling and model reduction techniques. Scaling procedures can improve speed and robustness on numerically difficult models. Model reduction techniques can often make models solve faster by analyzing the original formulation and mathematically condensing it into a smaller problem. The Integer solver includes extensive preprocessing and cut generation routines.
LINGO is designed, so the process of solving the model requires as little input from the user as possible. When the Solve command is initiated, LINGO analyzes the problem and, when possible, reduces the problem and even substitutes out variables. Based upon the models structure, LINGO automatically selects the appropriate solver and intelligently adjusts internal parameters.

Linearization
LINGO's Linearization capabilities can dramatically improve performance on models with common nonsmooth functions. The feature can automatically convert many nonsmooth functions and operators (e.g., @IF, @MAX and @ABS) to a series of linear, mathematically equivalent expressions. Similarly, the product of a continuous and binary variable can also be linearized. Many nonsmooth models may be entirely linearized. This allows the linear solver to quickly find a global solution to what would have otherwise been an intractable problem.

■ Model Interactively or Create Turn-key Applications
- You can build and solve models within LINGO, or you can call LINGO directly from an application you have written. For developing models interactively, LINGO provides a complete modelling environment to build, solve, and analyze your models. For building turn-key solutions, LINGO comes with callable DLL and OLE interfaces that can be called from user written applications. LINGO can also be called directly from an Excel macro or database application.
LINGO allows you to build and solve models interactively or embed the solver in another application.
Interactive Modelling
LINGO provides a complete environment in which to build and solve optimization problems interactively. The multi-windowing editor allows for easy problem entry, viewing, and modification. To aid in model creation, the "syntax aware" editor displays LINGO keywords in blue, comments in green, and all other model text in black. A toolbar is provided for fast access to frequently used commands. Solution information can be viewed in a window, graphed, or written to a spreadsheet, database or text file. While a model is solving, the user can monitor the status and has the option to interrupt the process.

Creating Turn-key Applications
Instead of running LINGO interactively, you may want to build a custom optimization application for use by a client or colleague. LINGO gives you a variety of options to incorporate its functionality into your own applications. Distribution of applications that call the LINGO solvers requires separate licensing. Contact LINGO Systems for more information.

Callable DLL and OLE Interfaces
You can seamlessly embed LINGO's functionality into your own applications using a Windows development environment such as C#.NET, VB.NET, Visual Java, Visual Basic, Visual C++, or Delphi. Your application can act as a user front-end for the optimization problem -- handling data entry and storage as well as preparing the information to be passed in memory to LINGO. It could also be set up to display the solution and produce customized reports for the user. LINGO includes both a callable DLL and OLE interfaces, which give you access to all of the features and commands available interactively.

Calling LINGO from a Spreadsheet or Database
You can even build a simple application, which can be run directly from a spreadsheet such as Excel or a database such as Access. It can be as easy as creating your own "Solve" button to call LINGO and run a series of specified commands.
■ Extensive Documentation and Help
- LINGO provides all of the tools you will need to get up and running quickly. You get the LINGO User Manual which fully describes the commands and features of the program. Also included with super versions and larger is a copy of Optimization Modelling with LINGO, a comprehensive modelling text discussing all major classes of linear, integer and nonlinear optimization problems. LINGO also comes with dozens of real-world based examples for you to modify and expand.
LINGO comes with everything you need to get started quickly and easily. Super and larger versions of LINGO include two valuable references:
The LINGO User's Manual
This 500+ page manual provides complete information on all aspects of using the LINGO package. The manual includes a full tutorial, which walks you through building and solving your first model to analyzing the solution. It explains the syntax of the modeling language thoroughly using simple examples for illustration.
The LINGO User Manual includes in depth coverage of all of the commands and features of LINGO in a well-organized manner. The manual also includes detailed discussion of how LINGO can interface with spreadsheets and databases as well as how it can be integrated into your own applications.

Optimization Modelling with LINGO
This 500+ page text thoroughly discusses all major classes of optimization models. Perhaps the book's most useful feature is its liberal use of examples to illustrate each application and modelling concept. The discussion and examples are designed to teach you the modelling techniques you need to tackle your toughest problems.
The text contains information, which will appeal to a broad spectrum of modelers. For the modelling novice, the book provides chapters to introduce basic mathematical programming concepts, examine the modelling process, explain how to analyze solutions, and discuss the intricacies of designing and implementing optimization-based decision support systems. More advanced modelers will appreciate the ability to pick and choose from the variety of chapters dedicated to applying optimization techniques to specific applications. For a complete list of topics, see Optimization Modelling with LINGO's Table of Contents.

Comprehensive Online Help
LINGO's exhaustive Help system lets you conveniently access information on the fly. Not only are the entire contents of the LINGO User Manual available at the click of your mouse, but the Help file also contains up-to-date information on any enhancements added since the documentation went to press.

Friendly, Professional Support
For times when you need a little extra assistance, LINGO Systems offers our fast, friendly technical support. If you are having problems or questions regarding a particular feature of LINGO you can contact our knowledgeable support staff by phone, email or fax. If you are having problems with some aspect of your model, we can often get you pointed in the right direction.