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Coco - A full production planning example

Description
The Coco productional planning problem: multi-item, multi-period, multi-site production planning. A sequence of model versions show how the model was developed, to (a) use more sophisticated modeling features and (b) to extend the model, taking it from a simple linear model to one with fixed prices and logical decisions.
  1. xbcoco1: initial formulation, data, variables and constraints fixed
  2. xbcoco2: use parameters, data tables and subscripted variables.

    read data tables in from text data files (short-term planning).
  3. xbcoco3: like xbcoco2.c, but several time periods (mid-term planning).
  4. xbcoco : complete problem, data defined in the model definition (long-term planning).

xbcocojava.zip[download all files]

Source Files

Data Files





xbcoco.java

/********************************************************
  Xpress-BCL Java Example Problems
  ================================

  file xbcoco.java
  ````````````````
  Complete Coco Problem. 
  Specify phase by PHASE parameter. 
  Data input in the model, not via data files.

  (c) 2008 Fair Isaac Corporation
      author: S.Heipcke, Jan. 2000, rev. Mar. 2011
********************************************************/

import com.dashoptimization.*;

public class xbcoco
{
 static final int PHASE = 5;
/* Phase = 3: Multi-period parameterised model; mines always open
 * Phase = 4: Mines may open/closed freely; when closed save 20000 per month
 * Phase = 5: Once closed always closed; larger saving */
 
 static final int NP = 2;            /* Number of products (p) */
 static final int NF = 2;            /*           factories (f) */
 static final int NR = 2;            /*           raw materials (r) */
 static final int NT = 4;            /*           time periods (t) */

/****DATA****/
 static final double[][] REV =
        {{400, 380, 405, 350},
         {410, 397, 412, 397}};
                      /* Unit selling price of prod. p in period t */
 static final double[][] CMAK = 
        {{150, 153},
         { 75,  68}}; /* Unit cost to make product p at factory f */
 static final double[][] CBUY = 
        {{100,  98,  97, 100},
         {200, 195, 198, 200}};
                      /* Unit cost to buy raw material r in period t */
 static final double[] COPEN = {50000, 63000}; 
                      /* Fixed cost of factory f being open for one period */
 static final double CPSTOCK = 2.0; /* Unit cost to store any product p */
 static final double CRSTOCK = 1.0; /* Unit cost to store any raw material r */
 static final double[][] REQ =   
        {{1.0, 0.5},
         {1.3, 0.4}}; /* Requirement by unit of prod. p for raw material r */
 static final double[][] MXSELL = 
        {{650, 600, 500, 400},
         {600, 500, 300, 250}};
                      /* Max. amount of p that can be sold in period t */
 static final double[] MXMAKE = {400, 500};
                      /* Max. amount factory f can make over all products */
 static final double MXRSTOCK = 300;  
                      /* Max. amount of r that can be stored each f and t */
 static final double[][] PSTOCK0 = 
        {{50, 100},
         {50,  50}};  /* Initial product p stock level at factory f */
 static final double[][] RSTOCK0 = 
        {{100, 150},
         { 50, 100}}; /* Initial raw material r stock level at factory f*/
 
/***********************************************************************/

 public static void main(String[] args)
 {
  XPRB bcl;
  XPRBvar[][][] make, sell, pstock, buy, rstock; 
  XPRBvar[][] openm;
  XPRBexpr lobj, lc;
  int p,f,r,t; 
  XPRBprob pb;

  bcl = new XPRB();              /* Initialize BCL */
  pb = bcl.newProb("Coco");      /* Create a new problem in BCL */

/****VARIABLES****/
  make = new XPRBvar[NP][NF][NT];
  sell = new XPRBvar[NP][NF][NT]; 
  pstock = new XPRBvar[NP][NF][NT+1];
  buy = new XPRBvar[NR][NF][NT];
  rstock = new XPRBvar[NR][NF][NT+1];
  openm = new XPRBvar[NF][NT];
  for(p=0;p<NP;p++)
   for(f=0;f<NF;f++)
   {
    for(t=0;t<NT;t++)
    {
     make[p][f][t] = pb.newVar("make_p" + (p+1) + "_f" + (f+1));
        /* Amount of prod. p to make at factory f in period t */
     sell[p][f][t] = pb.newVar("sell_p" + (p+1) + "_f" + (f+1));
        /* Amount of prod. p sold from factory f in period t */
    }        
    for(t=0;t<NT+1;t++)
     pstock[p][f][t] = pb.newVar("pstock_p" + (p+1) + "_f" + (f+1));
        /* Stock level of prod. p at factory f at start of period t */
   }     
  for(r=0;r<NR;r++)
   for(f=0;f<NF;f++)
   {
    for(t=0;t<NT;t++)
    buy[r][f][t] = pb.newVar("buy_r" + (r+1) + "_f" + (f+1)); 
        /* Amount of raw material r bought for factory f in period t */
    for(t=0;t<NT+1;t++)
     rstock[r][f][t] = pb.newVar("rstock_r" + (r+1) + "_f" + (f+1));
        /* Stock level of raw mat. r at factory f at start of per. t */
   }
   
  for(f=0;f<NF;f++)
   for(t=0;t<NT;t++)
    openm[f][t] = pb.newVar("open_f" + (f+1), XPRB.BV);
        /* 1 if factory f is open in period t, else 0 */
            
/****OBJECTIVE****/
  lobj = new XPRBexpr();
  for(f=0;f<NF;f++)        /* Objective: maximize total profit */
  {
   for(p=0;p<NP;p++)
   {
    for(t=0;t<NT;t++)
     lobj.add(sell[p][f][t].mul(REV[p][t])) 
         .add(make[p][f][t].mul(-CMAK[p][f]));
    for(t=1;t<NT+1;t++)  lobj.add(pstock[p][f][t].mul(-CPSTOCK));    
   } 
   if(PHASE==4)
    for(t=0;t<NT;t++)  lobj.add(openm[f][t].mul(20000-COPEN[f]));
   else if(PHASE==5)
    for(t=0;t<NT;t++)  lobj.add(openm[f][t].mul(-COPEN[f]));
   for(r=0;r<NR;r++)
   {
    for(t=0;t<NT;t++)  lobj.add(buy[r][f][t].mul(-CBUY[r][t]));
    for(t=1;t<NT+1;t++)  lobj.add(rstock[r][f][t].mul(-CRSTOCK));    
   }
  } 
  pb.setObj(lobj);         /* Set objective function */  
 
/****CONSTRAINTS****/
  for(p=0;p<NP;p++)        /* Product stock balance */  
   for(f=0;f<NF;f++)
    for(t=0;t<NT;t++)
     pb.newCtr("PBal", pstock[p][f][t].add(make[p][f][t]) 
                       .eql(sell[p][f][t].add(pstock[p][f][t+1])) ); 
     
  for(r=0;r<NR;r++)        /* Raw material stock balance */
   for(f=0;f<NF;f++)
    for(t=0;t<NT;t++)
    {                 
     lc = new XPRBexpr();
     for(p=0;p<NP;p++)  lc.add(make[p][f][t].mul(REQ[p][r]));
     pb.newCtr("RBal", rstock[r][f][t].add(buy[r][f][t]) 
                       .eql(lc.add(rstock[r][f][t+1])) );
    }

  for(p=0;p<NP;p++)
   for(t=0;t<NT;t++)
   {                       /* Limit on the amount of product p to be sold */
    lc = new XPRBexpr();
    for(f=0;f<NF;f++)  lc.add(sell[p][f][t]);
    pb.newCtr("MxSell", lc.lEql(MXSELL[p][t]) );  
   }
    
  for(f=0;f<NF;f++)
   for(t=0;t<NT;t++)
   {                       /* Capacity limit at factory f */
    lc = new XPRBexpr();
    for(p=0;p<NP;p++)  lc.add(make[p][f][t]);
    pb.newCtr("MxMake", lc.lEql(openm[f][t].mul(MXMAKE[f])) );
   }

  for(f=0;f<NF;f++)
   for(t=1;t<NT+1;t++)
   {                       /* Raw material stock limit */        
    lc = new XPRBexpr();
    for(r=0;r<NR;r++) lc.add(rstock[r][f][t]);
    pb.newCtr("MxRStock", lc.lEql(MXRSTOCK) );    
   }

  if(PHASE==5)
   for(f=0;f<NF;f++)
    for(t=0;t<NT-1;t++)    /* Once closed, always closed */
     pb.newCtr("Closed", openm[f][t+1].lEql(openm[f][t]) ); 

/****BOUNDS****/
  for(p=0;p<NP;p++)
   for(f=0;f<NF;f++)
    pstock[p][f][0].fix(PSTOCK0[p][f]);    /* Initial product levels */

  for(r=0;r<NR;r++)
   for(f=0;f<NF;f++)
    rstock[r][f][0].fix(RSTOCK0[r][f]);    /* Initial raw mat. levels */

  if(PHASE<=3)
   for(f=0;f<NF;f++)
    for(t=0;t<NT;t++)
     openm[f][t].fix(1);
   
/****SOLVING + OUTPUT****/
  pb.setSense(XPRB.MAXIM);  /* Choose the sense of the optimization */
  pb.mipOptimize("");       /* Solve the MIP-problem */
  System.out.println("Objective: " + pb.getObjVal()); /* Get objective value */
     
                            /* Uncomment to print out the solution values */
/* for(p=0;p<NP;p++)        
   for(f=0;f<NF;f++)
    for(t=0;t<NT;t++)
     System.out.print(make[p][f][t].getName() + ":" + make[p][f][t].getSol() 
      + " " + sell[p][f][t].getName() +":" + sell[p][f][t].getSol());
  System.out.println(); 

  for(p=0;p<NP;p++)      
   for(f=0;f<NF;f++)
    for(t=0;t<NT+1;t++)
     System.out.print(pstock[p][f][t].getName() +":" + pstock[p][f][t].getSol() + " ");
  System.out.println(); 
 
  for(r=0;r<NR;r++)      
   for(f=0;f<NF;f++)
   {
    for(t=0;t<NT;t++)
     System.out.print(buy[r][f][t].getName() +":" + buy[r][f][t].getSol() 
      + " ");
    for(t=0;t<NT+1;t++)
     System.out.print(rstock[r][f][t].getName() +":" + rstock[r][f][t].getSol() 
      + " ");
   }
  for(f=0;f<NF;f++)
   for(t=0;t<NT;t++)
    System.out.print(openm[f][t].getName() +":" + openm[f][t].getSol() + " ");
  System.out.println(); 
*/
 }
} 

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