\$TITLE A TRANSPORTATION PROBLEM (TRNSPORT,SEQ=1) \$OFFUPPER * This problem finds a least cost shipping schedule that meets * requirements at markets and supplies at factories * * References: * Dantzig, G B., Linear Programming and Extensions * Princeton University Press, Princeton, New Jersey, 1963, * Chapter 3-3. * * This formulation is described in detail in Chapter 2 * (by Richard E. Rosenthal) of GAMS: A Users' Guide. * (A Brooke, D Kendrick and A Meeraus, The Scientific Press, * Redwood City, California, 1988.) * * The line numbers will not match those in the book because of * these comments. 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 ;