$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. Keywords: linear programming, transportation problem, scheduling $offText option threads=2; Sets i "canning plants" / Seattle, San-Diego, Baltimore, Dallas / j "markets" / New-York, Chicago, Topeka, Boston, Miami /; Parameters a(i) "capacity of plant i in cases" / Seattle 350, San-Diego 600, Baltimore 450, Dallas 750 / b(j) "demand at market j in cases" / New-York 325, Chicago 300, Topeka 275, Boston 330, Miami 290 /; Table d(i,j) "distance in thousands of miles" New-York Chicago Topeka Boston Miami Seattle 2.5 1.7 1.8 3.1 3.3 San-Diego 2.5 1.8 1.4 3.0 2.7 Baltimore 0.2 0.7 1.8 0.4 1.1 Dallas 1.5 0.9 0.5 1.8 1.3 ; 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; Variable x(i,j) 'shipment quantities in cases' z 'total transportation costs in thousands of dollars'; Positive Variable x; Equation 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;