GAMS is a programming language created in 1988.
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The General Algebraic Modeling System (GAMS) is a high-level modeling system for mathematical programming and optimization. It consists of a language compiler and a stable of integrated high-performance solvers. GAMS is tailored for complex, large scale modeling applications, and allows you to build large maintainable models that can be adapted quickly to new situations. GAMS is specifically designed for modeling linear, nonlinear and mixed integer optimization problems.
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 variables 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 ;