This toy problem is presented only to illustrate how GAMS lets you model in a natural way. GAMS can handle much larger and highly complex problems. Only a few of the basic features of GAMS can be highlighted here.
Here is a standard algebraic description of the problem, which is to minimize the cost of shipping goods from 2 plants to 3 markets, subject to supply and demand constraints.
$a_ = $supply of commodity of plant $i$ (cases)
$b_ = $demand for commodity at market $j$ (cases)
$d_ = $distance between plant $i$ and market $j$ (thousand miles)
$c_ = F \times d_$ shipping cost per unit shipment between plant $i$ and market $j$ (dollars per case per thousand miles)
| Distances | Markets | |||
|---|---|---|---|---|
| Plants | New York | Chicago | Topeka | Supply |
| Seattle | 2.5 | 1.7 | 1.8 | 350 |
| San Diego | 2.5 | 1.8 | 1.4 | 600 |
| Demand | 325 | 300 | 275 |
$x_=$ amount of commodity to ship from plant $i$ to market $j$ (cases), where $x_ > 0$, for all $i,j$.
The same model modeled in GAMS. The use of concise algebraic descriptions makes the model highly compact, with a logical structure. Internal documentation, such as explanation of parameters and units of measurement makes the model easy to read.
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 ;
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