linear programming, GAMS learned that exploitation of sparsity was key to solving large problems. Thus, the final piece of the puzzle was the use of sparse data structures. Lines starting with an * in column one are treated as comments. A sample model A transportation problem from George Dantzig 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. Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey, 1963. 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 ; Subsystems The Mathematical Programming System for General Equilibrium analysis (MPSGE) is a language used for formulating and solving Arrow–Debreu economic equilibrium models and exists as a subsystem within GAMS. See also Extended Mathematical Programming (EMP) – an extension to mathematical programming languages available within GAMS GNU MathProg – an open-source mathematical programming language based on AMPL References External links GAMS Development Corporation GAMS Software GmbH GAMS World Computer algebra systems Mathematical optimization software