Description
This problem finds a least cost shipping schedule that meets requirements at markets and supplies at factories where demand exceeds supply using the Cplex feature FeasOpt.
Small Model of Type : GAMS
Category : GAMS Test library
Main file : cplex03.gms
$title 'CPLEX test suite - long UEL names and large domains' (cplex03,SEQ=358)
$if not '%GAMS.lp%' == '' $set solver %GAMS.lp%
$if not set solver $set solver cplex
$onText
This problem finds a least cost shipping schedule that meets
requirements at markets and supplies at factories where demand
exceeds supply using the Cplex feature FeasOpt.
Dantzig, G B, Chapter 3.3. In Linear Programming and Extensions.
Princeton University Press, Princeton, New Jersey, 1963.
Contributor: Michael Bussieck
$offText
$set kkk k,k0,k1,k2,k3,k4,k5,k6,k7,k8,k9
Sets
i canning plants / seattle_in_washington_state_home_of_starbucks_coffee, san-diego /
j markets / new-york, chicago, topeka /
k dummy / k /
alias (%kkk%);
Parameters
a(i) capacity of plant i in cases
/ seattle_in_washington_state_home_of_starbucks_coffee 350
san-diego 600 /
b(j) demand at market j in cases
/ new-york 325
chicago 300
topeka 275 / ;
Table d(i,j) distance in thousands of miles
new-york chicago topeka
seattle_in_washington_state_home_of_starbucks_coffee 2.5 1.7 1.8
san-diego 2.5 1.8 1.4 ;
Scalar f freight in dollars per case per thousand miles /90/ ;
Parameter c(i,j) transport cost in thousands of dollars per case ;
c(i,j) = f * d(i,j) / 1000 ;
Variables
x(i,j,%kkk%) shipment quantities in cases
z total transportation costs in thousands of dollars ;
Positive Variable x ;
Equations
cost define objective function
supply(i,%kkk%) observe supply limit at plant i
demand(j,%kkk%) satisfy demand at market j ;
cost .. z =e= sum((i,j,%kkk%), c(i,j)*x(i,j,%kkk%)) ;
supply(i,%kkk%) .. sum(j, x(i,j,%kkk%)) =l= a(i) ;
demand(j,%kkk%) .. sum(i, x(i,j,%kkk%)) =g= b(j) ;
Model transport /all/ ;
* Lets make a MIP;
Binary variable xb(i,j,%kkk%);
Equation minship(i,j,%kkk%);
Equation doship(i,j,%kkk%);
minship(i,j,%kkk%).. x(i,j,%kkk%) + eps*xb(i,j,%kkk%) =g= 90;
doship(i,j,%kkk%).. x(i,j,%kkk%) =e= 0;
model miptransport /all/;
option lp=%solver%, mip=%solver%, limrow=0, limcol=0, optcr=0;
Solve transport using lp minimizing z ;
if (transport.modelstat <> %modelStat.optimal% or transport.solvestat <> %solveStat.normalCompletion%, abort 'problem solving first lp');
file fcpx Cplex Option file / %solver%.opt /; transport.optfile=1; miptransport.optfile=1;
* Indicators
putclose fcpx / 'indic minship(i,j,%kkk%)$xb(i,j,%kkk%) 1'
/ 'indic doship(i,j,%kkk%)$xb(i,j,%kkk%) 0';
Solve miptransport using mip minimizing z ;
if (transport.modelstat <> %modelStat.optimal% or transport.solvestat <> %solveStat.normalCompletion%, abort 'problem with indicators (1)');
abort$(smin((i,j,%kkk%)$(x.l(i,j,%kkk%)>1.e-6),x.l(i,j,%kkk%)) < 90) 'problems with indicators (2)';
* Indicators and BCH
putclose fcpx / 'indic minship(i,j,%kkk%)$xb(i,j,%kkk%) 1'
/ 'indic doship(i,j,%kkk%)$xb(i,j,%kkk%) 0'
/ 'usercutcall xxxdim.inc' / 'cuts no' / 'preind 0'
/ 'heurfreq -1' / 'mipinterval 1';
$onEcho > xxxdim.inc
Sets
i canning plants / seattle_in_washington_state_home_of_starbucks_coffee, san-diego /
j markets / new-york, chicago, topeka /
k dummy / k /
cut cuts / 1 /
alias (%kkk%);
* This cut cuts away the optimal solution of value 153.675
Parameters rhs_c(cut) / 1 2 /
sense_c(cut) / 1 1 /
numcuts / 0 /
xb_c(cut,i,j,%kkk%) / 1.seattle_in_washington_state_home_of_starbucks_coffee.chicago.k.k.k.k.k.k.k.k.k.k.k 1
1.san-diego.new-york.k.k.k.k.k.k.k.k.k.k.k 1
1.san-diego.topeka .k.k.k.k.k.k.k.k.k.k.k 1 /;
* Only add the cut the very first time
$if %ncalls% == 0 numcuts=1;
$offEcho
Solve miptransport using mip minimizing z ;
if (transport.modelstat <> %modelStat.optimal% or transport.solvestat <> %solveStat.normalCompletion%, abort 'problem with indicators and BCH (1)');
abort$(smin((i,j,%kkk%)$(x.l(i,j,%kkk%)>1.e-6),x.l(i,j,%kkk%)) < 90) 'problems with indicators and BCH (2)';
abort$(z.l < 156) 'problems with indicators and BCH (3)';
* Sensitivity in LST file
putclose fcpx / 'objrng all' / 'rhsrng all';
Solve transport using lp minimizing z ;
execute '=grep -q "LOWER *CURRENT *UPPER" "%gams.scrdir%gamsstat.%gams.scrext%"';
abort$errorlevel 'problem with obj/rhsrng option in lst file';
* Sensitivity in data file
putclose fcpx / 'objrng all' / 'rhsrng all' / 'rngrestart rng.txt';
Solve transport using lp minimizing z ;
execute '=grep -q "seattle_in_washington_state_home_of_starbucks_coffee.new-york.k.k.k.k.k.k.k.k.k.k.k" rng.txt';
abort$errorlevel 'problem with obj/rhsrng option in rng.txt';
* Increase demand by 20% to make model infeasible
b(j) = 1.2*b(j);
* FEASOPT
putclose fcpx / 'feasopt 1' / 'equation.feaspref 0' / 'demand.feaspref 1'
/ "demand.feaspref('new-york','k','k','k','k','k','k','k','k','k','k','k') 0";
Solve transport using lp minimizing z ;
if (transport.modelstat <> %modelStat.infeasible% or transport.solvestat <> %solveStat.normalCompletion%, abort 'problem with feasopt option');
display 'All infeasibilities should be in the demand equations', x.infeas, supply.infeas, demand.infeas;
abort$(sum((i,j,%kkk%), x.infeas(i,j,%kkk%)) + sum((i,%kkk%),supply.infeas(i,%kkk%))) x.infeas, supply.infeas, demand.infeas;
* IIS
putclose fcpx / 'iis 1';
Solve transport using lp minimizing z ;
execute '=grep -q "Number of equations in .*conflict: .*5" "%gams.scrdir%gamsstat.%gams.scrext%"';
execute '=grep -q "Number of variables in .*conflict: .*0" "%gams.scrdir%gamsstat.%gams.scrext%"';
abort$errorlevel 'problem with IIS option'