trnsport.gms : A Transportation Problem

**Description**

This problem finds a least cost shipping schedule that meets requirements at markets and supplies at factories.

**References**

- Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey, 1963.
- Rosenthal, R E, Chapter 2: A GAMS Tutorial. In GAMS: A User's Guide. The Scientific Press, Redwood City, California, 1988.

**Small Model of Type :** LP

**Category :** GAMS Model library

**Main file :** trnsport.gms

$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 ;