trnsgrid.gms : Grid Transportation Problem

**Description**

This problem finds a least cost shipping schedule that meets requirements at markets and supplies at factories. The model demonstrates how to run multiple scenarios with different demands in a parallel fashion using the GAMS Grid Facility.

**Reference**

- Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions. Princeton University Press, Princeton, New Jersey, 1963.

**Small Model of Type :** LP

**Category :** GAMS Model library

**Main file :** trnsgrid.gms

```
$title Grid Transportation Problem (TRNSGRID,SEQ=315)
$onText
This problem finds a least cost shipping schedule that meets
requirements at markets and supplies at factories.
The model demonstrates how to run multiple scenarios with different
demands in a parallel fashion using the GAMS Grid Facility.
Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions.
Princeton University Press, Princeton, New Jersey, 1963.
Keywords: linear programming, transportation problem, scheduling, GAMS grid facility,
scenario analysis
$offText
Set
i 'canning plants' / seattle, san-diego /
j 'markets' / new-york, chicago, topeka /;
Parameter
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;
Variable
x(i,j) 'shipment quantities in cases'
z 'total transportation costs in thousands of dollars';
Positive Variable x;
* Demonstrate how to restrict the model index
Set ij(i,j); ij(i,j) = yes;
Equation
cost 'define objective function with economies of scale'
supply(i) 'observe supply limit at plant i'
demand(j) 'satisfy demand at market j';
cost.. z =e= sum(ij(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 /;
$eolCom //
transport.solveLink = %solveLink.AsyncGrid%; // turn on grid option
transport.limCol = 0;
transport.limRow = 0;
transport.solPrint = %solPrint.Quiet%;
Set s 'scenarios' / 1*5 /;
Parameter
dem(s,j) 'random demand'
h(s) 'store the instance handle';
dem(s,j) = b(j)*uniform(.95,1.15); // create some random demands
loop(s,
b(j) = dem(s,j);
solve transport using lp minimizing z;
h(s) = transport.handle; // save instance handle
);
Parameter
repx(s,i,j) 'solution report'
repy 'summary report';
repy(s,'solvestat') = na;
repy(s,'modelstat') = na;
* we use the handle parameter to indicate that the solution has been collected
repeat
loop(s$handlecollect(h(s)),
repx(s,i,j) = x.l(i,j);
repy(s,'solvestat') = transport.solveStat;
repy(s,'modelstat') = transport.modelStat;
repy(s,'resusd' ) = transport.resUsd;
repy(s,'objval') = transport.objVal;
display$handledelete(h(s)) 'trouble deleting handles';
h(s) = 0; // indicate that we have loaded the solution
);
display$sleep(card(h)*0.2) 'was sleeping for some time';
until card(h) = 0 or timeelapsed > 10; // wait until all models are loaded
display repx, repy;
abort$sum(s$(repy(s,'solvestat') = na),1) 'Some jobs did not return';
```