/********************************************************
BCL Example Problems
====================
file xbels.c
````````````
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
********************************************************/
#include <stdio.h>
#include "xprb.h"
#include "xprs.h"
#define EPS 1e-6
#define T 6 /* Number of time periods */
/****DATA****/
int DEMAND[] = { 1, 3, 5, 3, 4, 2}; /* Demand per period */
int SETUPCOST[] = {17,16,11, 6, 9, 6}; /* Setup cost per period */
int PRODCOST[] = { 5, 3, 2, 1, 3, 1}; /* Production cost per period */
int D[T][T]; /* Total demand in periods t1 - t2 */
XPRBvar prod[T]; /* Production in period t */
XPRBvar setup[T]; /* Setup in period t */
/***********************************************************************/
void mod_els(XPRBprob prob)
{
int s,t,k;
XPRBctr ctr;
for(s=0;s<T;s++)
for(t=0;t<T;t++)
for(k=s;k<=t;k++)
D[s][t] += DEMAND[k];
/****VARIABLES****/
for(t=0;t<T;t++)
{
prod[t]=XPRBnewvar(prob,XPRB_PL, XPRBnewname("prod%d",t+1),0,XPRB_INFINITY);
setup[t]=XPRBnewvar(prob,XPRB_BV, XPRBnewname("setup%d",t+1),0,1);
}
/****OBJECTIVE****/
ctr = XPRBnewctr(prob,"OBJ",XPRB_N); /* Minimize total cost */
for(t=0;t<T;t++)
{
XPRBaddterm(ctr, setup[t], SETUPCOST[t]);
XPRBaddterm(ctr, prod[t], PRODCOST[t]);
}
XPRBsetobj(prob,ctr);
/****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++)
{
ctr = XPRBnewctr(prob,"Production",XPRB_L);
XPRBaddterm(ctr, setup[t], -D[t][T-1]);
XPRBaddterm(ctr, prod[t], 1);
}
/* Production in periods 0 to t must satisfy the total demand
during this period of time */
for(t=0;t<T;t++)
{
ctr = XPRBnewctr(prob,"Demand",XPRB_G);
for(s=0;s<=t;s++)
XPRBaddterm(ctr, prod[s], 1);
XPRBaddterm(ctr, NULL, 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 */
/**************************************************************************/
void solve_els(XPRBprob prob)
{
double objval; /* Objective value */
int t,l;
int starttime;
int ncut, npass, npcut; /* Counters for cuts and passes */
double solprod[T], solsetup[T]; /* Solution values for var.s prod & setup */
double ds;
XPRBbasis basis;
XPRBctr cut;
starttime=XPRBgettime();
XPRSsetintcontrol(XPRBgetXPRSprob(prob),XPRS_CUTSTRATEGY, 0);
/* Disable automatic cuts - we use our own */
XPRSsetintcontrol(XPRBgetXPRSprob(prob),XPRS_PRESOLVE, 0);
/* Switch presolve off */
ncut = npass = 0;
do
{
npass++;
npcut = 0;
XPRBlpoptimize(prob,"p"); /* Solve the LP */
basis=XPRBsavebasis(prob); /* Save the current basis */
objval = XPRBgetobjval(prob); /* Get the objective value */
/* Get the solution values: */
for(t=0;t<T;t++)
{
solprod[t]=XPRBgetsol(prod[t]);
solsetup[t]=XPRBgetsol(setup[t]);
}
/* 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)
{
cut = XPRBnewctr(prob,XPRBnewname("cut%d",ncut+1), XPRB_G);
XPRBaddterm(cut, NULL, D[0][l]);
for(t=0;t<=l;t++)
{
if (solprod[t] < D[t][l]*solsetup[t] + EPS)
XPRBaddterm(cut, prod[t], 1);
else
XPRBaddterm(cut, setup[t], D[t][l]);
}
ncut++;
npcut++;
}
}
printf("Pass %d (%g sec), objective value %g, cuts added: %d (total %d)\n",
npass, (XPRBgettime()-starttime)/1000.0, objval, npcut, ncut);
if(npcut==0)
printf("Optimal integer solution found:\n");
else
{
XPRBloadmat(prob); /* Reload the problem */
XPRBloadbasis(basis); /* Load the saved basis */
XPRBdelbasis(basis); /* No need to keep the basis any longer */
}
} while(npcut>0);
/* Print out the solution: */
for(t=0;t<T;t++)
printf("Period %d: prod %g (demand: %d, cost: %d), setup %g (cost: %d)\n",
t+1, XPRBgetsol(prod[t]), DEMAND[t], PRODCOST[t], XPRBgetsol(setup[t]),
SETUPCOST[t]);
}
/***********************************************************************/
int main(int argc, char **argv)
{
XPRBprob prob;
prob=XPRBnewprob("Els"); /* Initialize a new problem in BCL */
mod_els(prob); /* Model the problem */
solve_els(prob); /* Solve the problem */
return 0;
}
|
/********************************************************
BCL Example Problems
====================
file xbelsc.c
`````````````
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.
*** This model cannot be run with a Community Licence ***
(c) 2008 Fair Isaac Corporation
author: S.Heipcke, 2005, rev. Mar. 2011
********************************************************/
#include <stdio.h>
#include <stdlib.h>
#include "xprb.h"
#include "xprs.h"
#define T 6 /* Number of time periods */
/****DATA****/
int DEMAND[] = { 1, 3, 5, 3, 4, 2}; /* Demand per period */
int SETUPCOST[] = {17,16,11, 6, 9, 6}; /* Setup cost per period */
int PRODCOST[] = { 5, 3, 2, 1, 3, 1}; /* Production cost per period */
int D[T][T]; /* Total demand in periods t1 - t2 */
XPRBvar prod[T]; /* Production in period t */
XPRBvar setup[T]; /* Setup in period t */
struct myobj
{
XPRBprob prob;
double tol;
};
/***********************************************************************/
void mod_els(XPRBprob prob)
{
int s,t,k;
XPRBctr ctr;
for(s=0;s<T;s++)
for(t=0;t<T;t++)
for(k=s;k<=t;k++)
D[s][t] += DEMAND[k];
/****VARIABLES****/
for(t=0;t<T;t++)
{
prod[t]=XPRBnewvar(prob,XPRB_PL, XPRBnewname("prod%d",t+1),0,XPRB_INFINITY);
setup[t]=XPRBnewvar(prob,XPRB_BV, XPRBnewname("setup%d",t+1),0,1);
}
/****OBJECTIVE****/
ctr = XPRBnewctr(prob,"OBJ",XPRB_N); /* Minimize total cost */
for(t=0;t<T;t++)
{
XPRBaddterm(ctr, setup[t], SETUPCOST[t]);
XPRBaddterm(ctr, prod[t], PRODCOST[t]);
}
XPRBsetobj(prob,ctr);
/****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++)
{
ctr = XPRBnewctr(prob,"Production",XPRB_L);
XPRBaddterm(ctr, setup[t], -D[t][T-1]);
XPRBaddterm(ctr, prod[t], 1);
}
/* Production in periods 0 to t must satisfy the total demand
during this period of time */
for(t=0;t<T;t++)
{
ctr = XPRBnewctr(prob,"Demand",XPRB_G);
for(s=0;s<=t;s++)
XPRBaddterm(ctr, prod[s], 1);
XPRBaddterm(ctr, NULL, D[0][t]);
}
}
/**************************************************************************/
/* Cut generation loop at the tree node: */
/* get the solution values */
/* identify and set up violated constraints */
/* add cuts to the matrix */
/**************************************************************************/
int XPRS_CC cb_node(XPRSprob oprob, void *mobj)
{
struct myobj *mo;
double objval; /* Objective value */
int t,l;
int ncut; /* Counters for cuts */
double solprod[T], solsetup[T]; /* Solution values for var.s prod & setup */
double ds;
int depth,node;
XPRBcut cut[T];
mo=(struct myobj *)mobj;
XPRBbegincb(mo->prob, oprob);
ncut = 0;
XPRSgetintattrib(oprob,XPRS_NODEDEPTH, &depth);
XPRSgetintattrib(oprob,XPRS_NODES, &node);
/* Get the solution values */
XPRBsync(mo->prob, XPRB_XPRS_SOL);
for(t=0;t<T;t++)
{
solprod[t]=XPRBgetsol(prod[t]);
solsetup[t]=XPRBgetsol(setup[t]);
}
/* 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)
{
cut[ncut] = XPRBnewcut(mo->prob, XPRB_G, 1);
XPRBaddcutterm(cut[ncut], NULL, D[0][l]);
for(t=0;t<=l;t++)
{
if (solprod[t] < D[t][l]*solsetup[t] + mo->tol)
XPRBaddcutterm(cut[ncut], prod[t], 1);
else
XPRBaddcutterm(cut[ncut], setup[t], D[t][l]);
}
ncut++;
}
}
/* Add cuts to the problem */
if(ncut>0)
{
XPRBaddcuts(mo->prob, cut, ncut);
XPRSgetdblattrib(oprob, XPRS_LPOBJVAL, &objval);
printf("Cuts added : %d (depth %d, node %d, obj. %g)\n",
ncut, depth, node, objval);
}
XPRBendcb(mo->prob);
return 0;
}
/***********************************************************************/
void tree_cut_gen(XPRBprob prob)
{
XPRSprob oprob;
struct myobj mo;
double feastol;
int starttime,t;
starttime=XPRBgettime();
oprob = XPRBgetXPRSprob(prob); /* Get Optimizer problem */
XPRSsetintcontrol(oprob, XPRS_LPLOG, 0);
XPRSsetintcontrol(oprob, XPRS_MIPLOG, 3);
XPRSsetintcontrol(oprob, XPRS_CUTSTRATEGY, 0); /* Disable automatic cuts */
XPRSsetintcontrol(oprob, XPRS_PRESOLVE, 0); /* Switch presolve off */
XPRSsetintcontrol(oprob, XPRS_EXTRAROWS, 5000); /* Reserve extra rows */
XPRSgetdblcontrol(oprob, XPRS_FEASTOL, &feastol); /* Get zero tolerance */
feastol*= 10;
mo.prob=prob;
mo.tol=feastol;
XPRBsetcutmode(prob,1);
XPRSsetcbcutmgr(oprob, cb_node, &mo);
XPRBmipoptimize(prob,""); /* Solve the MIP */
printf("(%g sec) Global status %d, best solution: %1.3f\n",
(XPRBgettime()-starttime)/1000.0, XPRBgetmipstat(prob), XPRBgetobjval(prob));
for(t=0;t<T;t++)
printf("Period %d: prod %g (demand: %d, cost: %d), setup %g (cost: %d)\n",
t+1, XPRBgetsol(prod[t]), DEMAND[t], PRODCOST[t], XPRBgetsol(setup[t]),
SETUPCOST[t]);
}
/***********************************************************************/
int main(int argc, char **argv)
{
XPRBprob prob;
prob=XPRBnewprob("Els"); /* Initialize a new problem in BCL */
mod_els(prob); /* Model the problem */
tree_cut_gen(prob); /* Solve the problem */
return 0;
}
|
