GAMS is an acronym that stands for General Algebraic Modeling System, a high level Computer programming language for modeling and solving optimization problems - linear, nonlinear, and mixed integer. It is especially useful for handling large, complex, "one of a kind" problems, which may require many revisions of the model to get the formulation right. GAMS enables you to model problems in a natural way, so that you can easily change your formulation - even convert a model from linear to nonlinear with little trouble.

GAMS was developed primarily by optimization experts Dr. Anthony Brooke and Dr. Alexander Meeraus, formerly of The World Bank. Their goal was to create a powerful but easy-to-use computer programming language that would greatly simplify the modeler's task of formulating and solving complex optimization problems. Recogn izing the excellence of GAMS, the Computer Science Technical Section of the Operations Research Society of America awarded its 1987 prize to The World Bank's GAMS development team. Previous versions of GAMS are widely used by academic institutions and in dustry around the world.

Documentation that accompanies the CD ROM containing the software explains in detail with examples how to make best use of the several algorithms available. Some of the well known codes are MINOS, CONOPT (two versions), DICOPT (for mixed integer problems), OLS (an IBM code), and MILES (for systems of nonlinear equations). CACHE provides a code for PCs running under DOS, Windows 3.1, Windows 95, and Windows NT.

GAMS is designed to use machine resources in a flexible way, and acquires memory as needed to store your data structures. Therefore, it is not possible to specify precise limits for "what will fit". There are some fixed limits built into GAMS and the solvers, but they are large and generally will not in terfere with the user.

GAMS software comes with a 286 page manual GAMS: A User's Guide, written by the principal authors of GAMS, along with GAMS - The Solver Manuals that provides full documentation of the GAMS programming language and solvers: 18 chapters, 6 appendices, glossary, bibliography, and index.

Also included in the manual is an in-depth but easy-to-follow tutorial, which covers the major features of GAMS, using examples from an actual model that comes with the software.

GAMS offers many advantages over conventional computer optimization systems. It enables you to:

*Describe your model to a computer nearly as easily as you can describe it to a colleague.*

In GAMS, you formulate your model using concise algebraic statements, so your model is easy to read for computers and humans alike. This feature makes GAMS a "natural" programming language - many of the advantages described below derive from this key feature.

*Create whole sets of closely related constrains in one statement.*

Most other optimization software requires you to enter each individual constraint explicitly into your model - which means you do a lot of calculations and data entry yourself. In GAMS, however, the power of algebraic expression relieves you from this task - GAMS automatically generates each constraint equation, based on your input of general algebraic formulae and specific data values. This significantly cuts development time and reduces the potential for errors in data entry and transformations. (NOTE: GAMS lets you make any exceptions in cases where such generality isn't desired).

*Enter data only once, in their most elemental form.*

You need only enter your most basic data, in list and table form (i.e. the way data most often come to you), and specify data transformations algebraically. Not only does this save time and reduce the possibility of making mistakes, but it allows any user of the model to readily inspect all transformations made in constructing the model and in reporting.

*Reuse statements in your model when new instances of the same or related problem arise.*

This is another instance of how the use of general algebraic descriptions saves you time and effort. You can enter new data into your model without having to change the algebra. GAMS simply uses the new data values to compute the new set of related constraints - an especially useful feature if you are constantly updating or otherwise changing data in your model.

**B****uild models independent of the solution algorithms of specific solvers.**

In GAMS, you formulate linear, nonlinear, and integer problems following the same format whatever the solution algorithm. You can use this feature to great advantage - for example, to develop and test alternate versions of a model within one document: one formulation might be linear, another nonlinear.

*Solve your model on different types of machines without having to change your formulation.*

GAMS models are fully portable from one computer environment to another, and an entire model is contained in just a single document. A model developed on a PC running DOS, for instance, can later be solved on a VAX running the VMS operating system, without any need for reformulation (assuming, of course, that GAMS is loaded onto both machines).

*Create self-documenting models.*

With GAMS, you develop and document your model simultaneously, because GAMS allows you to include explanatory text as party of the definition of any symbol or equation. So your documentation is accurate and up-to-date, and it resides in the model itself. Furthermore, GAMS automatically incorporates your comments into your output report, making the results easy to understand for anyone who might need to inspect your model.

*Avoid whole classes of errors common in many other computer optimization systems.*

Many of the typical errors made with conventional optimization programming languages (e.g. FORTRAN) involve concepts that do not even exist in GAMS. A GAMS user never has to worry about making errors in things like address calculations, storage assignments, subroutine linkages, and input-output and flow control. GAMS handles all these in the background, completely out of the modeler's way.

*Quickly pinpoint errors in your model - where they are, and of what type - before a solution has been attempted.*

As GAMS compiles your model, it searches exhaustively for errors. The software "knows" optimization logic and mathematical programming. It checks for errors in syntax, numerical operations (e.g. division by zero), and mathematical consistency (e.g. a model designated as linear but contains nonlinearities). If errors are detected, GAMS does not try to solve the model. Instead, it tells you where the errors occur in your model and what sort they are. You can then easily correct your model and avoid wasting time and resources on a useless solution attempt.

*Perform sensitivity analysis on your model with ease.*

In GAMS, you can easily program your model to solve for different values of an element and generate an output report listing the solution characteristics for each case.

*Implement large-scale models efficiently.*

GAMS includes advanced features to handle large models. For example, it allows you to: screen out unnecessary rows and columns to keep the size of the problem within the range of solvability; build complex summations and products, which can then be used in equations or customized reports; and issue warning messages upon context-specific data edits.

*Construct dynamic model concisely.*

Several built-in features of GAMS allow you to handle dynamic models with a minimum of programming complexity. Problems involving time sequences, lags, leads, and the treatment of temporal endpoints can be concisely modeled in GAMS.

*Concentrate on the art of modeling rather than on the cumbersome engineering requirements of a matrix generator or conversational solver.*

By simplifying the task of computer formulation of your model, GAMS frees you to focus on the conceptual aspects of modeling. You increase your productivity - time spent on conceptualizing your problem, running your models, and analyzing the results - and decrease the "downtime" spent on making your model machine-readable.

The basic GAMS system is file-oriented, and no special editor or graphical input and output routines exist. Rather than burden the user with having to learn yet another set of editing commands, GAMS offers an open architecture in which each user can use his word processor or editor of choice. This basic user interface facilitates the integration of GAMS with a variety of existing and future user environments.

These problems are modeled as linear, nonlinear and mixed-integer optimization problems. This case study describes in detail the formulation and solution of a total of 22 optimization problems that cover the different areas cited above.

The new version of GAMS that is available on the CD-ROM can solve problems with the following size limits: 300 rows (constraints), 300 columns (variables), 50 binary variables, 2,000 non zero elements (1,000 nonlinear non zero elements).

The case study Volume 6 is supplied with the following:

- Binder with a brief introduction to GAMS, and description of the 22 application problems.
- CD-ROM with new GAMS version, and GAMS input files for the 22 problems
- GAMS User's Guide
- GAMS Solver Manual

This new version of GAMS is now available from the CACHE office. The cost for Process Design Case Study No. 6, along with GAMS: A User's Guide, and GAMS - The Solver Manuals, and a CD-ROM is $110 per CACHE supporting departments, and $150 per non-CACHE supporting departments.

CACHE Corporation

P.O. Box 511

Williamsburg, MA 01096-0511

Phone: (386) 256-2165

Fax: (386) 256-2168

cache@umass.edu

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