/********************************************************
Xpress-BCL Java Example Problems
================================
file xbels.java
```````````````
Economic lot sizing, ELS, problem, solved by adding
(l,S)-inequalities) in several rounds looping over
the root node.
ELS considers production planning over a horizon
of T periods. In period t, t=1,...,T, there is a
given demand DEMAND[t] that must be satisfied by
production prod[t] in period t and by inventory
carried over from previous periods. There is a
set-up up cost SETUPCOST[t] associated with
production in period t. The unit production cost
in period t is PRODCOST[t]. There is no inventory
or stock-holding cost.
(c) 2008 Fair Isaac Corporation
author: S.Heipcke, 2001, rev. Mar. 2011
********************************************************/
import com.dashoptimization.*;
public class xbels
{
static final double EPS = 1e-6;
static final int T = 6; /* Number of time periods */
/****DATA****/
static final int[] DEMAND = { 1, 3, 5, 3, 4, 2}; /* Demand per period */
static final int[] SETUPCOST = {17,16,11, 6, 9, 6}; /* Setup cost / period */
static final int[] PRODCOST = { 5, 3, 2, 1, 3, 1}; /* Prod. cost / period */
static int[][] D; /* Total demand in periods t1 - t2 */
static XPRBvar[] prod; /* Production in period t */
static XPRBvar[] setup; /* Setup in period t */
static XPRB bcl;
static XPRBprob p;
/***********************************************************************/
static void modEls() throws XPRSexception
{
int s,t,k;
XPRBexpr cobj,le;
bcl = new XPRB(); /* Initialize BCL */
p = bcl.newProb("Els"); /* Create a new problem in BCL */
XPRS.init(); /* Initialize Xpress-Optimizer */
D = new int[T][T];
for(s=0;s<T;s++)
for(t=0;t<T;t++)
for(k=s;k<=t;k++)
D[s][t] += DEMAND[k];
/****VARIABLES****/
prod = new XPRBvar[T];
setup = new XPRBvar[T];
for(t=0;t<T;t++)
{
prod[t]=p.newVar("prod" + (t+1));
setup[t]=p.newVar("setup" +(t+1), XPRB.BV);
}
/****OBJECTIVE****/
cobj = new XPRBexpr();
for(t=0;t<T;t++) /* Minimize total cost */
cobj .add(setup[t].mul(SETUPCOST[t]) .add(prod[t].mul(PRODCOST[t])) );
p.setObj(cobj);
/****CONSTRAINTS****/
/* Production in period t must not exceed the total demand for the
remaining periods; if there is production during t then there
is a setup in t */
for(t=0;t<T;t++)
p.newCtr("Production", prod[t] .lEql(setup[t].mul(D[t][T-1])) );
/* Production in periods 0 to t must satisfy the total demand
during this period of time */
for(t=0;t<T;t++)
{
le = new XPRBexpr();
for(s=0;s<=t;s++) le .add(prod[s]);
p.newCtr("Demand", le.gEql(D[0][t]) );
}
}
/**************************************************************************/
/* Cut generation loop at the top node: */
/* solve the LP and save the basis */
/* get the solution values */
/* identify and set up violated constraints */
/* load the modified problem and load the saved basis */
/**************************************************************************/
static void solveEls() throws XPRSexception
{
double objval; /* Objective value */
int t,l;
int starttime;
int ncut, npass, npcut; /* Counters for cuts and passes */
double[] solprod, solsetup; /* Solution values for var.s prod & setup */
double ds;
XPRSprob op;
XPRBbasis basis;
XPRBexpr le;
starttime=XPRB.getTime();
op=p.getXPRSprob();
op.setIntControl(XPRS.CUTSTRATEGY, 0);
/* Disable automatic cuts - we use our own */
op.setIntControl(XPRS.PRESOLVE, 0);
/* Switch presolve off */
ncut = npass = 0;
solprod = new double[T];
solsetup = new double[T];
do
{
npass++;
npcut = 0;
p.lpOptimize("p"); /* Solve the LP */
basis = p.saveBasis(); /* Save the current basis */
objval = p.getObjVal(); /* Get the objective value */
/* Get the solution values: */
for(t=0;t<T;t++)
{
solprod[t]=prod[t].getSol();
solsetup[t]=setup[t].getSol();
}
/* Search for violated constraints: */
for(l=0;l<T;l++)
{
for(ds=0.0, t=0; t<=l; t++)
{
if(solprod[t] < D[t][l]*solsetup[t] + EPS) ds += solprod[t];
else ds += D[t][l]*solsetup[t];
}
/* Add the violated inequality: the minimum of the actual production
prod[t] and the maximum potential production D[t][l]*setup[t]
in periods 0 to l must at least equal the total demand in periods
0 to l.
sum(t=1:l) min(prod[t], D[t][l]*setup[t]) >= D[0][l]
*/
if(ds < D[0][l] - EPS)
{
le = new XPRBexpr();
for(t=0;t<=l;t++)
{
if (solprod[t] < D[t][l]*solsetup[t] + EPS)
le .add(prod[t]);
else
le .add(setup[t].mul(D[t][l]));
}
p.newCtr("cut" +(ncut+1), le.gEql(D[0][l]) );
ncut++;
npcut++;
}
}
System.out.println("Pass " +npass + " (" +(XPRB.getTime()-starttime)/1000.0
+ " sec), objective value " + objval + ", cuts added: " + npcut
+ " (total " + ncut +")");
if(npcut==0)
System.out.println("Optimal integer solution found:");
else
{
p.loadMat(); /* Reload the problem */
p.loadBasis(basis); /* Load the saved basis */
basis = null; /* No need to keep the basis any longer */
}
} while(npcut>0);
/* Print out the solution: */
for(t=0;t<T;t++)
System.out.println("Period " + (t+1) + ": prod " + prod[t].getSol()
+ " (demand: " + DEMAND[t] + ", cost: " + PRODCOST[t] + "), setup "
+ setup[t].getSol() + " (cost: " + SETUPCOST[t] + ")");
}
/***********************************************************************/
public static void main(String[] args) throws XPRSprobException, XPRSexception
{
modEls(); /* Model the problem */
solveEls(); /* Solve the problem */
}
}
|
/********************************************************
Xpress-BCL Java Example Problems
================================
file xbelsc.java
````````````````
Economic lot sizing, ELS, problem, solved by adding
(l,S)-inequalities) in a branch-and-cut heuristic
(using the cut manager).
ELS considers production planning over a horizon
of T periods. In period t, t=1,...,T, there is a
given demand DEMAND[t] that must be satisfied by
production prod[t] in period t and by inventory
carried over from previous periods. There is a
set-up up cost SETUPCOST[t] associated with
production in period t. The unit production cost
in period t is PRODCOST[t]. There is no inventory
or stock-holding cost.
(c) 2008 Fair Isaac Corporation
author: S.Heipcke, 2005, rev. Mar. 2011
********************************************************/
import java.util.*;
import com.dashoptimization.*;
public class xbelsc
{
static final double EPS = 1e-6;
static final int T = 6; /* Number of time periods */
/****DATA****/
static final int[] DEMAND = { 1, 3, 5, 3, 4, 2}; /* Demand per period */
static final int[] SETUPCOST = {17,16,11, 6, 9, 6}; /* Setup cost / period */
static final int[] PRODCOST = { 5, 3, 2, 1, 3, 1}; /* Prod. cost / period */
static int[][] D; /* Total demand in periods t1 - t2 */
static XPRBvar[] prod; /* Production in period t */
static XPRBvar[] setup; /* Setup in period t */
static XPRB bcl;
static XPRBprob p;
static class myobj {
XPRBprob prob;
double tol;
};
/**************************************************************************/
/* Cut generation algorithm: */
/* get the solution values */
/* identify and set up violated constraints */
/* add cuts to the problem */
/**************************************************************************/
static class CutMgrCallback implements XPRScutMgrListener
{
public int XPRScutMgrEvent(XPRSprob oprob, Object data)
{
int t,l;
boolean res;
int ncut; /* Counter for cuts */
double[] solprod, solsetup; /* Solution values for var.s prod & setup */
double ds;
XPRBexpr le;
ArrayList<XPRBcut> cutlist;
XPRBcut[] cuts;
myobj mo;
mo = (myobj)data;
ncut = 0;
cutlist = new ArrayList<XPRBcut>();
try {
/* Get the solution values */
mo.prob.beginCB(oprob);
mo.prob.sync(XPRB.XPRS_SOL);
solprod = new double[T];
solsetup = new double[T];
for(t=0;t<T;t++)
{
solprod[t]= prod[t].getSol();
solsetup[t]= setup[t].getSol();
}
/* Search for violated constraints: */
for(l=0;l<T;l++)
{
for(ds=0.0, t=0; t<=l; t++)
{
if(solprod[t] < D[t][l]*solsetup[t] + mo.tol) ds += solprod[t];
else ds += D[t][l]*solsetup[t];
}
/* Add the violated inequality: the minimum of the actual production
prod[t] and the maximum potential production D[t][l]*setup[t]
in periods 0 to l must at least equal the total demand in periods
0 to l.
sum(t=1:l) min(prod[t], D[t][l]*setup[t]) >= D[0][l]
*/
if(ds < D[0][l] - mo.tol)
{
le = new XPRBexpr();
for(t=0;t<=l;t++)
{
if (solprod[t] < D[t][l]*solsetup[t] + mo.tol)
le .add(prod[t]);
else
le .add(setup[t].mul(D[t][l]));
}
cutlist.add( mo.prob.newCut(le.gEql(D[0][l])) );
ncut++;
}
}
/* Add cuts to the problem */
if(ncut>0)
{
cuts = new XPRBcut[ncut];
for(t=0;t<ncut;t++) cuts[t] = (XPRBcut)cutlist.get(t);
mo.prob.addCuts(cuts);
System.out.println("Cuts added: " + ncut +
" (depth " + oprob.getIntAttrib(XPRS.NODEDEPTH) +
", node "+ oprob.getIntAttrib(XPRS.NODES) +
"), obj. " + oprob.getDblAttrib(XPRS.LPOBJVAL));
}
mo.prob.endCB();
}
catch(XPRSprobException e) {
System.out.println("Error " + e.getCode() + ": " + e.getMessage());
}
return 0;
}
}
/***********************************************************************/
static void modEls() throws XPRSexception
{
int s,t,k;
XPRBexpr cobj,le;
bcl = new XPRB(); /* Initialize BCL */
p = bcl.newProb("Els"); /* Create a new problem in BCL */
XPRS.init(); /* Initialize Xpress-Optimizer */
D = new int[T][T];
for(s=0;s<T;s++)
for(t=0;t<T;t++)
for(k=s;k<=t;k++)
D[s][t] += DEMAND[k];
/****VARIABLES****/
prod = new XPRBvar[T];
setup = new XPRBvar[T];
for(t=0;t<T;t++)
{
prod[t]=p.newVar("prod" + (t+1));
setup[t]=p.newVar("setup" +(t+1), XPRB.BV);
}
/****OBJECTIVE****/
cobj = new XPRBexpr();
for(t=0;t<T;t++) /* Minimize total cost */
cobj .add(setup[t].mul(SETUPCOST[t]) .add(prod[t].mul(PRODCOST[t])) );
p.setObj(cobj);
/****CONSTRAINTS****/
/* Production in period t must not exceed the total demand for the
remaining periods; if there is production during t then there
is a setup in t */
for(t=0;t<T;t++)
p.newCtr("Production", prod[t] .lEql(setup[t].mul(D[t][T-1])) );
/* Production in periods 0 to t must satisfy the total demand
during this period of time */
for(t=0;t<T;t++)
{
le = new XPRBexpr();
for(s=0;s<=t;s++) le .add(prod[s]);
p.newCtr("Demand", le.gEql(D[0][t]) );
}
}
/***********************************************************************/
static void treeCutGen() throws XPRSexception
{
XPRSprob oprob;
myobj mo;
CutMgrCallback cb;
double feastol;
int starttime,t;
starttime=XPRB.getTime();
oprob = p.getXPRSprob(); /* Get Optimizer problem */
oprob.setIntControl(XPRS.LPLOG, 0);
oprob.setIntControl(XPRS.MIPLOG, 3);
oprob.setIntControl(XPRS.CUTSTRATEGY, 0); /* Disable automatic cuts */
oprob.setIntControl(XPRS.PRESOLVE, 0); /* Switch presolve off */
oprob.setIntControl(XPRS.EXTRAROWS, 5000); /* Reserve extra rows */
feastol=oprob.getDblControl(XPRS.FEASTOL); /* Get zero tolerance */
feastol*= 10;
mo = new myobj();
mo.prob=p;
mo.tol=feastol;
p.setCutMode(1);
cb = new CutMgrCallback();
oprob.addCutMgrListener(cb, mo);
p.mipOptimize(""); /* Solve the MIP */
System.out.println("(" + (XPRB.getTime()-starttime)/1000.0 +
" sec) Global status " + p.getMIPStat() + ", best solution: " +
p.getObjVal());
/* Print out the solution: */
for(t=0;t<T;t++)
System.out.println("Period " + (t+1) + ": prod " + prod[t].getSol()
+ " (demand: " + DEMAND[t] + ", cost: " + PRODCOST[t] + "), setup "
+ setup[t].getSol() + " (cost: " + SETUPCOST[t] + ")");
}
/***********************************************************************/
public static void main(String[] args) throws XPRSprobException, XPRSexception
{
modEls(); /* Model the problem */
treeCutGen(); /* Solve the problem */
}
}
|
