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import ../code/conceptPage.scroll
id general-algebraic-modeling-system
name GAMS
appeared 1963
tags pl
aka gams
isOpenSource false
fileType text
centralPackageRepositoryCount 0
country United States
originCommunity GAMS Development Corporation
example
*Basic example of transport model from GAMS model library
$Title A Transportation Problem (TRNSPORT,SEQ=1)
$Ontext
This problem finds a least cost shipping schedule that meets
requirements at markets and supplies at factories.
Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions.
Princeton University Press, Princeton, New Jersey, 1963.
This formulation is described in detail in:
Rosenthal, R E, Chapter 2: A GAMS Tutorial. In GAMS: A User's Guide.
The Scientific Press, Redwood City, California, 1988.
The line numbers will not match those in the book because of these
comments.
$Offtext
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
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 ;
$ontext
#user model library stuff
Main topic Basic GAMS
Featured item 1 Trnsport model
Featured item 2
Featured item 3
Featured item 4
Description
Basic example of transport model from GAMS model library
$offtext
wikipedia https://en.wikipedia.org/wiki/General_Algebraic_Modeling_System
example
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
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 ;
related algebraic-modeling-language
summary The General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization 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 portable from one platform to another. GAMS was the first algebraic modeling language (AML) and is formally similar to commonly used fourth-generation programming languages. GAMS contains an integrated development environment (IDE) and is connected to a group of third-party optimization solvers. Among these solvers are BARON, COIN-OR solvers, CONOPT, CPLEX, DICOPT, Gurobi, MOSEK, SNOPT, SULUM, and XPRESS. GAMS allows the users to implement a sort of hybrid algorithm combining different solvers. Models are described in concise, human-readable algebraic statements. GAMS is among the most popular input formats for the NEOS Server. Although initially designed for applications related to economics and management science, it has a community of users from various backgrounds of engineering and science.
pageId 1438314
created 2005
backlinksCount 91
revisionCount 416
dailyPageViews 89
appeared 1963
githubBigQuery GAMS
repos 49
users 43
isbndb 4
year|publisher|title|authors|isbn13
2010|Wiley-Blackwell|Practical Financial Optimization: A Library of GAMS Models|Nielson, Soren S and Consiglio, Andrea|9781405133715
20171204|Springer Nature|Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology|Neculai Andrei|9783319583563
|Springer International Publishing :|Continuous Nonlinear Optimization For Engineering Applications In Gams Technology|Andrei, Neculai (author.)|9783319583563
2013|Springer|Nonlinear Optimization Applications Using The Gams Technology (springer Optimization And Its Applications)|Neculai Andrei|9781461467960
githubLanguage GAMS
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repos 810