# GAMS

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GAMS is a programming language created in 1963.

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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. Read more on Wikipedia...

Example from the web:
```*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```
Example from Wikipedia:
```Sets i canning plants / seattle, san-diego / j markets / new-york, Chicago, topeka /聽; 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 /聽; 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/聽; Parameter c(i,j) transport cost in thousands of dollars per case聽; c(i,j) = f * d(i,j) / 1000聽; Variables x(i,j) shipment quantities in cases z total transportation costs in thousands of dollars聽; Positive Variable x聽; Equations cost define objective function supply(i) observe supply limit at plant i demand(j) satisfy demand at market j聽; cost .. z =e= sum((i,j), c(i,j)*x(i,j))聽; supply(i) .. sum(j, x(i,j)) =l= a(i)聽; demand(j) .. sum(i, x(i,j)) =g= b(j)聽; Model transport /all/聽; Solve transport using lp minimizing z聽; Display x.l, x.m聽;```

#### Books about GAMS from ISBNdb

title authors year publisher
Practical Financial Optimization: A Library of GAMS Models Nielson, Soren S and Consiglio, Andrea 2010 Wiley-Blackwell
Continuous Nonlinear Optimization for Engineering Applications in GAMS Technology Neculai Andrei 20171204 Springer Nature
Continuous Nonlinear Optimization For Engineering Applications In Gams Technology Andrei, Neculai (author.) Springer International Publishing :
Nonlinear Optimization Applications Using The Gams Technology (springer Optimization And Its Applications) Neculai Andrei 2013 Springer
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