Description
A simple version of a facility location problem is used to show how the solution pool and the tools associated with it work. This example is taken from the Cplex 11 User's Manual (ILOG, Cplex 11 User's Manual, 2007) A company is considering opening as many as four warehouses in order to serve nine different regions. The goal is to minimize the sum of fixed costs associated with opening warehouses as well as the various transportation costs incurred to ship goods from the warehouses to the regions. Whether or not to open a warehouse is represented by binary variable ow. Whether or not to ship goods from warehouse i to region j is represented by binary variable oa. Each region needs a specified amount of goods, and each warehouse can store only a limited quantity of goods. In addition, each region must be served by exactly one warehouse.
Small Model of Type : GAMS
Category : GAMS Test library
Main file : dumpsol.gms
$title Alternate Solutions for a Simple Facility Location Problem (DUMPSOL,SEQ=476)
$onText
A simple version of a facility location problem is used to show how the
solution pool and the tools associated with it work. This example is taken
from the Cplex 11 User's Manual (ILOG, Cplex 11 User's Manual, 2007)
A company is considering opening as many as four warehouses in order to serve
nine different regions. The goal is to minimize the sum of fixed costs
associated with opening warehouses as well as the various transportation
costs incurred to ship goods from the warehouses to the regions.
Whether or not to open a warehouse is represented by binary variable ow.
Whether or not to ship goods from warehouse i to region j is represented
by binary variable oa.
Each region needs a specified amount of goods, and each warehouse can store
only a limited quantity of goods. In addition, each region must be served
by exactly one warehouse.
The following GAMS program demonstrates how to collect the solutions
found during optimization in several GAMS solvers. GAMS will store the
individual solutions in GDX containers/files which can then be further
used by other programs or the same GAMS run. The solver links will name
these GDX containers 'soln_loc_pNN.gdx', where NN will be the serial
number of the solution found. To manage the different solutions, the
names of the GDX containers created by the solver link will be stored in
dumpsol.gdx in the set 'index' using the set elements file*.
$offText
Set i warehouses / w1*w4 /
j regions / r1*r9 /
Parameters
f(i) fixed costs / w1 130, w2 150, w3 170, w4 180 /
c(i) capacity / w1 90, w2 110, w3 130, w4 150 /
d(j) demand / r1 10, r2 10, r3 12, r4 15, r5 15,
r6 15, r7 20, r8 20, r9 30 /;
Table t(j,i) transport costs
w1 w2 w3 w4
r1 10 30 25 55
r2 10 25 25 45
r3 20 23 30 40
r4 25 10 26 40
r5 28 12 20 29
r6 36 19 16 22
r7 40 39 22 27
r8 75 65 55 35
r9 34 43 41 62;
Variables
totcost total cost
fcost fixed cost
tcost transportation cost
ow(i) indicator for open warehouse
oa(i,j) indicator for open shipment arc warehouse to region
Binary variables ow, oa;
Equations
deftotcost definition total cost
deffcost definition fixed cost
deftcost definition transportation cost
defwcap(i) limit utilization of warehouse by its capacity
onew(j) only one warehouse per region
defow(i,j) warehouse open if shipment from i to j;
deftotcost.. totcost =e= fcost + tcost;
deffcost.. fcost =e= sum(i, f(i)*ow(i));
deftcost.. tcost =e= sum((i,j), t(j,i)*oa(i,j));
defwcap(i).. sum(j, d(j)*oa(i,j)) =l= c(i);
onew(j).. sum(i, oa(i,j)) =e= 1;
defow(i,j).. ow(i) =g= oa(i,j);
Model loc /all/ ;
* --- Define sets, parameters and files to hold solutions
Sets soln possible solutions /file1*file1000,soln_loc_p1*soln_loc_p1000/
solnpool(soln) actual solutions;
Scalar cardsoln number of solutions;
* create empty dumpsol.gdx in case solver finds optimal solution right away (e.g., cbc)
execute_unload 'dumpsol.gdx', solnpool=index;
Alias (soln,s1,s2), (*,u);
Parameters
owX(soln,i) warehouse indicator by solution
oaX(soln,i,j) arc indicator by solution
totcostX(soln) total cost
fcostX(soln) fixed cost
tcostX(soln) transportation cost
xcostX(soln,*) cost structure by solution
mcostX(soln,*) cost structure by solution;
files fsoln;
option limrow=0, limcol=0, optcr=0;
loc.optfile=1; loc.solprint=%solPrint.quiet%; loc.savepoint = 1;
$if %gams.mip% == cbc $echo dumpsolutions dumpsol.gdx > cbc.opt
$if %gams.mip% == copt $echo solnpool dumpsol.gdx > copt.opt
$if %gams.mip% == cplex $echo solnpool dumpsol.gdx > cplex.opt
$if %gams.mip% == gurobi $echo solnpool dumpsol.gdx > gurobi.opt
$if %gams.mip% == scip $echo gams/dumpsolutions = "dumpsol.gdx" > scip.opt
$if %gams.mip% == xpress $echo solnpool dumpsol.gdx > xpress.opt
solve loc min totcost using mip;
execute_load 'dumpsol.gdx', solnpool=index;
cardsoln = card(solnpool); display cardsoln;
oaX(soln,i,j) = 0; owX(soln,i) = 0; xcostX(soln,u) = 0;
loop(solnpool(soln),
put_utility fsoln 'gdxin' / solnpool.te(soln);
execute_loadpoint;
oaX(soln,i,j) = round(oa.l(i,j));
owX(soln,i) = round(ow.l(i));
xcostX(soln,'totcost') = totcost.l;
xcostX(soln,'tcost') = tcost.l;
xcostX(soln,'fcost') = fcost.l;
);
* Restore the solution reported to GAMS
execute_loadpoint 'loc_p.gdx';
display xcostX;
$if %gams.mip% == cbc $echo dumpsolutionsmerged dumpsol.gdx > cbc.op2
$if %gams.mip% == copt $echo solnpoolMerge dumpsol.gdx > copt.op2
$if %gams.mip% == cplex $echo solnpoolMerge dumpsol.gdx > cplex.op2
$if %gams.mip% == gurobi $echo solnpoolMerge dumpsol.gdx > gurobi.op2
$if %gams.mip% == scip $echo gams/dumpsolutionsmerged = "dumpsol.gdx" > scip.op2
$if %gams.mip% == xpress $echo solnpoolMerge dumpsol.gdx > xpress.op2
* create empty dumpsol.gdx in case solver finds optimal solution right away (e.g., cbc)
option clear=solnpool;
execute_unload 'dumpsol.gdx', solnpool=index, oaX=oa, owX=ow, totcostX=totcost, tcostX=tcost, fcostX=fcost;
loc.optfile=2;
solve loc min totcost using mip;
execute_load 'dumpsol.gdx', solnpool=index, oaX=oa, owX=ow, totcostX=totcost, tcostX=tcost, fcostX=fcost;
mcostX(solnpool,'totcost') = totcostX(solnpool);
mcostX(solnpool,'tcost') = tcostX(solnpool);
mcostX(solnpool,'fcost') = fcostX(solnpool);
display xcostX, mcostX;