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Contract - Semi-continuous variables, predefined constraint functions, combine BCL with Xpress Optimizer

Description
A small MIP-problem example demonstrating how to define semi-continuous variables, use predefined constraint functions and retrieve the problem status.

Two modified versions (documented in the 'BCL Reference Manual') show how to (1) combine BCL problem input with problem solving in Xpress Optimizer and (2) use an Xpress Optimizer solution callback with a BCL model.

Further explanation of this example: 'BCL Reference Manual', Appendix B Using BCL with the Optimizer library


Source Files





xbcontr1.cs

/********************************************************
  Xpress-BCL C# Example Problems
  ==============================

  file xbcontr1.cs
  ````````````````
  Contract allocation example.
  Combining BCL problem input with problem solving 
  in Xpress-Optimizer.

  (c) 2008 Fair Isaac Corporation
      authors: S.Heipcke, D.Brett.
********************************************************/

using System;
using System.Text;
using System.IO;
using BCL;


namespace Examples
{
    public class TestContract
    {
        const int District = 6;               /* Number of districts */
        const int Contract = 10;               /* Number of contracts */

        /**** DATA ****/
        int[] OUTPUT = {50, 40, 10, 20, 70, 50};    /* Max. output per district */
        int[] COST   = {50, 20, 25, 30, 45, 40};    /* Cost per district */
        int[] VOLUME   = {20, 10, 30, 15, 20, 30, 10, 50, 10, 20};  
        /* Volume of contracts */

        /***********************************************************************/

        public static void Main()
        {
            XPRB.init();
            int d,c;
            XPRBprob p = new XPRBprob("Contract");          /* Initialize a new problem in BCL */
            XPRBexpr l1,l2,lobj;
            XPRBvar[,] x = new XPRBvar[District,Contract];   /* Variables indicating whether a project 
            is chosen */
            XPRBvar[,] y = new XPRBvar[District,Contract];   /* Quantities allocated to contractors */

            TestContract TestInstance = new TestContract();

            /**** VARIABLES ****/
            for(d=0;d<District;d++)
                for(c=0;c<Contract;c++)
                {
                    x[d,c] = p.newVar("x_d" + (d+1) + "c" + (c+1), BCLconstant.XPRB_BV);
                    y[d,c] = p.newVar("q_d" + (d + 1) + "c" + (c + 1), BCLconstant.XPRB_SC, 0, TestInstance.OUTPUT[d]);
                    y[d,c].setLim(5);
                } 

            /****OBJECTIVE****/
            lobj = new XPRBexpr();
            for(d=0;d<District;d++)
                for(c=0;c<Contract;c++)
                    lobj += TestInstance.COST[d] * y[d,c];   

            p.setObj(p.newCtr("OBJ",lobj));  /* Set the objective function */

            /**** CONSTRAINTS ****/
            for(c=0;c<Contract;c++)
            {
                l1= new XPRBexpr(0);
                l2= new XPRBexpr(0);  
                for(d=0;d<District;d++)
                {
                    l1 += y[d,c];
                    l2 += x[d,c];
                }
                p.newCtr("Size", l1 >= TestInstance.VOLUME[c]);  /* "Size": cover the required volume */
                p.newCtr("Min", l2 >= 2 ); 	 /* "Min": at least 2 districts per contract */
            }

            for(d=0;d<District;d++)         /* Do not exceed max. output of any district */
            {
                l1=new XPRBexpr(0);
                for(c=0;c<Contract;c++)
                    l1 += y[d,c];
                p.newCtr("Output", l1 <= TestInstance.OUTPUT[d]);
            } 

            for(d=0;d<District;d++)         /* If a contract is allocated to a district,
            then at least 1 unit is allocated to it */
                for(c=0;c<Contract;c++)
                    p.newCtr("XY", x[d,c] <= y[d,c]);

            /****SOLVING + OUTPUT****/
            p.exportProb(BCLconstant.XPRB_MPS,"Contract");  /* Output the matrix in MPS format */
            p.setSense(BCLconstant.XPRB_MINIM);         /* Choose the sense of the optimization */   
            p.mipOptimize();                   /* Solve the MIP-problem */

            if((p.getMIPStat()==BCLconstant.XPRB_MIP_SOLUTION) || (p.getMIPStat()==BCLconstant.XPRB_MIP_OPTIMAL)) 
            /* Test whether an integer sol. was found */
            {              
                System.Console.WriteLine("Objective: " + p.getObjVal());  /* Get objective value */

                for(d=0;d<District;d++)        /* Print the solution values */
                {
                    for(c=0;c<Contract;c++)
                    if(x[d,c].getSol()>0)
                        System.Console.Write(y[d, c].getName() + ":" + y[d, c].getSol() + ", ");
                    System.Console.WriteLine();
                }
            } 
            return;
        } 
    }
}
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