500:. In hindsight, one may call it a historic accident that in the 1970s mathematical economists and statisticians were assembled to address problems of development. They used the best techniques available at that time to solve multi-sector economy-wide models and large simulation and optimization models in agriculture, steel, fertilizer, power, water use, and other sectors. Although the group produced impressive research, initial success was difficult to reproduce outside their well functioning research environment. The existing techniques to construct, manipulate, and solve such models required several manual, time-consuming, and error-prone translations into different, problem-specific representations required by each solution method. During seminar presentations, modelers had to defend the existing versions of their models, sometimes quite irrationally, because of time and money considerations. Their models just could not be moved to other environments, because special programming knowledge was needed, and data formats and solution methods were not portable.
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Chicago 300 topeka 275 / ; Table d(i,j) distance in thousands of miles new-york
Chicago topeka seattle 2.5 1.7 1.8 san-diego 2.5 1.8 1.4 ; Scalar f freight in dollars per case per thousand miles /90/ ; Parameter c(i,j) transport cost in thousands of dollars per case ; c(i,j) = f * d(i,j) / 1000 ; Variables x(i,j) shipment quantities in cases z total transportation costs in thousands of dollars ; Positive Variable x ; Equations cost define objective function supply(i) observe supply limit at plant i demand(j) satisfy demand at market j ; cost .. z =e= sum((i,j), c(i,j)*x(i,j)) ; supply(i) .. sum(j, x(i,j)) =l= a(i) ; demand(j) .. sum(i, x(i,j)) =g= b(j) ; Model transport /all/ ; Solve transport using lp minimizing z ; Display x.l, x.m ;
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Sets i canning plants / seattle, san-diego / j markets / new-york, Chicago, topeka / ; Parameters a(i) capacity of plant i in cases / seattle 350 san-diego 600 / b(j) demand at market j in cases / new-york 325
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had a number of shortcomings: it could not handle large systems, problem representation was tied to an array-type data structure that required address calculations, and the system did not provide access to state-of-the art solution methods. From linear programming, GAMS learned that exploitation of
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as a powerful and elegant framework for solving real life problems in science and engineering. At the same time, these users were frustrated by high costs, skill requirements, and an overall low reliability of applying optimization tools. Most of the system's initiatives and support for new
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Combining multi-dimensional algebraic notation with the relational data model was the obvious answer. Compiler writing techniques were by now widespread, and languages like GAMS could be implemented relatively quickly. However, translating this rigorous mathematical representation into the
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problems. The system is tailored for complex, large-scale modeling applications and allows the user to build large maintainable models that can be adapted to new situations. The system is available for use on various computer platforms. Models are
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is used to provide a sample GAMS model. This model is part of the model library which contains many more complete GAMS models. This problem finds a least cost shipping schedule that meets requirements at markets and supplies at factories.
547:. The resulting system allowed the user to use automatically generated exact first and second order derivatives. This was a pioneering system and an important demonstration of a concept. However,
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The idea of an algebraic approach to represent, manipulate, and solve large-scale mathematical models fused old and new paradigms into a consistent and computationally tractable system. Using
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2012 The
Winners of the 2012 INFORMS Impact Prize included Alexander Meeraus. The prize was awarded to the originators of the five most important algebraic modeling languages.
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revealed the importance of naming rows and columns in a consistent manner. The connection to the emerging relational data model became evident. Experience using traditional
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combining different solvers. Models are described in concise, human-readable algebraic statements. GAMS is among the most popular input formats for the
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Rutherford, T. F. (1999). "Applied
General Equilibrium Modeling with MPSGE as a GAMS Subsystem: An Overview of the Modeling Framework and Syntax".
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2020 Official release of GAMS MIRO (Model
Interface with Rapid Orchestration) for deployment of GAMS models as interactive applications
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1988 Alex
Meeraus, the initiator of GAMS and founder of GAMS Development Corporation, is awarded INFORMS Computing Society Prize
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The
Mathematical Programming System for General Equilibrium analysis (MPSGE) is a language used for formulating and solving
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sparsity was key to solving large problems. Thus, the final piece of the puzzle was the use of sparse data structures.
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2012 The winners of the 2012 Coin OR Cup included
Michael Bussieck, Steven Dirkse, & Stefan Vigerske for GAMSlinks
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2019 End of support for Win7, moved 32 bit
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2020 Introduction of demo and community licensing scheme
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248:. Supported platforms: Mainframes and Unix Workstations
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algorithm-specific format required the computation of
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2017 Introduction of "Core" and "Peripheral" platforms
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2015 LaTeX documentation from GAMS source (Model2TeX)
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R E Rosenthal (1988). "Chapter 2: A GAMS Tutorial".
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2024 Purchase of CONOPT non-linear Solver IP by GAMS
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2011 End of support for Win95 / 98 / ME, and Win2000
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724:. Washington, DC, USA: GAMS Development Corporation
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2009 GAMS supports extended mathematical programs (
746:. The Scientific Press, Redwood City, California.
408:2013 Stochastic programming extension of GAMS EMP
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334:2004 Support for Quadratic Constrained programs
270:1990 GAMS moves to Georgetown, Washington, D.C.
169:(AML) and is formally similar to commonly used
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381:2010 GDXMRW interface between GAMS and Matlab
282:1995 MPSGE language is added for CGE modeling
220:GAMS allows the users to implement a sort of
702:"Phasing out of 32-bit support with GAMS 30"
145:. GAMS is designed for modeling and solving
684:Toward a General Algebraic Modelling System
311:2001 GAMS Data Exchange (GDX) is introduced
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402:2012 End of support for 32 bit on Mac OS X
305:2000 End of support for DOS & Win 3.11
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450:2019 Altered versioning scheme to XX.Y.Z
411:2013 GDXRRW interface between GAMS and R
405:2013 Support for distributed MIP (Cplex)
331:2004 Quality assurance initiative starts
604:Extended Mathematical Programming (EMP)
559:in column one are treated as comments.
171:fourth-generation programming languages
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258:1987 GAMS becomes a commercial product
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531:on very large systems. In the 1970s,
285:1996 European branch opens in Germany
27:Type of mathematical modeling system
1661:Comparison of optimization software
356:2007 Support for Solaris on Sparc64
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300:Integrated development environment
175:integrated development environment
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298:1999 Introduction of the GAMS
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715:Rosenthal, Richard E (2007).
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251:1979 Phase II: GAMS supports
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659:in Mathematical Optimization
367:Amazon Elastic Compute Cloud
340:2006 GAMS supports parallel
244:1978 Phase I: GAMS supports
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468:2024 ISO27001 certification
365:2009 GAMS available on the
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759:Computational Economics
555:Lines starting with an
438:2018 GAMS Studio (Beta)
195:COPT Cardinal Optimizer
293:Stochastic programming
718:GAMS — A user's guide
513:programming languages
253:nonlinear programming
744:GAMS: A User's Guide
491:chemical engineering
529:partial derivatives
326:Global optimization
276:1994 GAMS supports
173:. GAMS contains an
165:GAMS was the first
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1478:Gurobi Optimizer
1395:Xpress Optimizer
1360:Gurobi Optimizer
1331:Xpress NonLinear
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1093:Mathematica
1063:GLPK/GLPSOL
947:Mathematica
862:Mathematica
541:derivatives
226:NEOS Server
141:system for
106:Proprietary
1677:Categories
805:GAMS World
728:2020-12-20
639:2024-07-03
617:References
586:Subsystems
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476:Background
201:, DICOPT,
63:2024-07-01
906:APMonitor
657:Languages
655:Modeling
151:nonlinear
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1453:ANTIGONE
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1266:ANTIGONE
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887:Modeling
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598:See also
361:Mac OS X
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236:Timeline
160:portable
139:modeling
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1571:Couenne
1468:Couenne
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1407:, MISDP
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576:Dantzig
352:COIN-OR
348:solvers
328:in GAMS
191:COIN-OR
183:solvers
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112:Website
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61: (
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215:XPRESS
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147:linear
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967:Pyomo
937:LINDO
917:Gekko
896:AIMMS
889:tools
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722:(PDF)
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350:from
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302:(IDE)
291:1998
211:SNOPT
207:MOSEK
203:IPOPT
199:CPLEX
187:BARON
119:.gams
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1493:LOQO
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1370:LOQO
1341:SOCP
1316:SCIP
1237:SCIP
1118:SCIP
1088:LOQO
1058:GLOP
1005:MILP
962:PuLP
932:JuMP
922:GAMS
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901:AMPL
663:ISBN
519:and
517:sets
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185:are
135:GAMS
129:The
121:.com
89:Type
31:GAMS
1508:NAG
1443:AOA
1434:NLP
1424:NAG
1405:SDP
1385:NAG
1311:NAG
1252:QCP
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1172:CBC
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