trnsgrid.gms : Grid Transportation Problem
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
<![CDATA[
$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.
$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/ ;
$eolcom //
transport.solvelink = 3; // turn on grid option
transport.limcol = 0;
transport.limrow = 0;
transport.solprint = 2;
set s scenarios / 1*5 /;
parameter dem(s,j) random demand
h(s) store the instance handle;
dem(s,j)= b(j)*uniform(.95,1.15); // create some random demands
loop(s,
b(j) = dem(s,j)
Solve transport using lp minimizing z;
h(s) = transport.handle ); // save instance handle
parameter repx(s,i,j) solution report
repy summary report;
repy(s,'solvestat') = na;
repy(s,'modelstat') = na;
* we use the handle parameter to indicate that the solution has been collected
repeat
loop(s$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';
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