/***********************************************************************
Goal programming example
========================
An example of lexicographic goal programming using the Xpress
multi-objective API.
A company produces two electrical products, A and B. Both require
two stages of production: wiring and assembly. The production plan
must meet several goals:
1. A profit of $200
2. A contractual requirement of 40 units of product B
3. To fully utilize the available wiring department hours
4. To avoid overtime in the assembly department
(c) 2022 Fair Isaac Corporation
***********************************************************************/
using System;
using Optimizer;
namespace XPRSExamples
{
class GoalProg
{
private static readonly int COLS = 8; // Number of columns
private static readonly int ROWS = 4; // Number of rows
private static readonly int ENTITIES = 2; // Number of entities
// Column indices
private static readonly int COL_PRODUCE_A = 0;
private static readonly int COL_PRODUCE_B = 1;
private static readonly int COL_SURPLUS_WIRING = 2;
private static readonly int COL_DEFICIT_WIRING = 3;
private static readonly int COL_SURPLUS_ASSEM = 4;
private static readonly int COL_DEFICIT_ASSEM = 5;
private static readonly int COL_DEFICIT_PROFIT = 6;
private static readonly int COL_DEFICIT_PROD_B = 7;
public static void Main(string[] args)
{
GoalProg example = new GoalProg();
example.Run();
}
private void Run()
{
try
{
XPRS.Init("");
prob = new XPRSprob();
// Tell Optimizer to call OptimizerMsg whenever a message is output
prob.AddMessageCallback(new MessageCallback(this.OptimizerMsg));
// Create two integer variables and six continuous variables
double[] ub = new double[8];
char[] coltype = new char[8];
int[] colind = new int[13];
for (int i = 0; i < 8; i++)
{
ub[i] = XPRS.PLUSINFINITY;
coltype[i] = i < 2 ? 'I' : 'C';
colind[i] = i;
}
prob.AddCols(8, 0, new double[8], new int[8], null, null, new double[8], ub);
prob.ChgColType(8, colind, coltype);
// Add one row per goal
int ncoef = 0;
char[] rowtype = new char[4];
double[] rhs = new double[4];
int[] start = new int[4];
double[] rowcoef = new double[13];
// Goal 1: profit must meet or exceed $200
colind[ncoef] = COL_PRODUCE_A; rowcoef[ncoef++] = 7;
colind[ncoef] = COL_PRODUCE_B; rowcoef[ncoef++] = 6;
colind[ncoef] = COL_DEFICIT_PROFIT; rowcoef[ncoef++] = 1;
rowtype[0] = 'G'; rhs[0] = 200;
// Goal 2: production of product B must meet or exceed 40 units
start[1] = ncoef;
colind[ncoef] = COL_PRODUCE_B; rowcoef[ncoef++] = 1;
colind[ncoef] = COL_DEFICIT_PROD_B; rowcoef[ncoef++] = 1;
rowtype[1] = 'G'; rhs[1] = 40;
// Goal 3: hours of wiring should be close to the available 120 hours
start[2] = ncoef;
colind[ncoef] = COL_PRODUCE_A; rowcoef[ncoef++] = 2;
colind[ncoef] = COL_PRODUCE_B; rowcoef[ncoef++] = 3;
colind[ncoef] = COL_SURPLUS_WIRING; rowcoef[ncoef++] = -1;
colind[ncoef] = COL_DEFICIT_WIRING; rowcoef[ncoef++] = 1;
rowtype[2] = 'E'; rhs[2] = 120;
// Goal 4: hours of assembly should be close to the available 300 hours
start[3] = ncoef;
colind[ncoef] = COL_PRODUCE_A; rowcoef[ncoef++] = 6;
colind[ncoef] = COL_PRODUCE_B; rowcoef[ncoef++] = 5;
colind[ncoef] = COL_SURPLUS_ASSEM; rowcoef[ncoef++] = -1;
colind[ncoef] = COL_DEFICIT_ASSEM; rowcoef[ncoef++] = 1;
rowtype[3] = 'E'; rhs[3] = 300;
prob.AddRows(4, ncoef, rowtype, rhs, start, colind, rowcoef);
// Define objectives to minimize deviations, in priority order
// Goal 1: minimize profit deficit
prob.ChgObj(1, new int[] { COL_DEFICIT_PROFIT }, new double[] { 1 });
// Goal 2: minimize production deficit
prob.ChgObjN(1, 1, new int[] { COL_DEFICIT_PROD_B }, new double[] { 1 });
// Goal 3: minimize deviation from wiring hours target
prob.ChgObjN(2, 2, new int[] { COL_SURPLUS_WIRING, COL_DEFICIT_WIRING }, new double[] { 1, 1 });
// Goal 4: minimize deviation from assembly hours target
prob.ChgObjN(3, 2, new int[] { COL_SURPLUS_ASSEM, COL_DEFICIT_ASSEM }, new double[] { 1, 1 });
// Set up objective priorities and tolerances
for (int i = 0; i < 4; i++)
{
prob.SetObjIntControl(i, ObjControl.Priority, 4 - i);
prob.SetObjDblControl(i, ObjControl.AbsTol, 0);
prob.SetObjDblControl(i, ObjControl.RelTol, 0);
}
// Solve the problem
prob.MipOptimize();
// Print the result
if (prob.SolveStatus == SolveStatus.Completed &&
prob.SolStatus == SolStatus.Optimal)
{
double[] sol = new double[COLS];
prob.GetMipSol(sol, null);
Console.WriteLine("Production plan:");
Console.WriteLine("Product A: " + ((int)sol[COL_PRODUCE_A]) + " units");
Console.WriteLine("Product B: " + ((int)sol[COL_PRODUCE_B]) + " units");
Console.WriteLine("Profit: $" + (int)(7 * sol[COL_PRODUCE_A] + 6 * sol[COL_PRODUCE_B]));
if (sol[COL_DEFICIT_PROFIT] > 0)
{
Console.WriteLine("Profit goal missed by $" + ((int)sol[COL_DEFICIT_PROFIT]));
}
if (sol[COL_DEFICIT_PROD_B] > 0)
{
Console.WriteLine("Contractual goal for product B missed by " + ((int)sol[COL_DEFICIT_PROD_B]) + " units");
}
if (sol[COL_SURPLUS_WIRING] > 0)
{
Console.WriteLine("Unused wiring department hours: " + ((int)sol[COL_SURPLUS_WIRING]));
}
if (sol[COL_DEFICIT_WIRING] > 0)
{
Console.WriteLine("Wiring department overtime: " + ((int)sol[COL_DEFICIT_WIRING]));
}
if (sol[COL_SURPLUS_ASSEM] > 0)
{
Console.WriteLine("Unused assembly department hours: " + ((int)sol[COL_SURPLUS_ASSEM]));
}
if (sol[COL_DEFICIT_ASSEM] > 0)
{
Console.WriteLine("Assembly department overtime: " + ((int)sol[COL_DEFICIT_ASSEM]));
}
}
else
{
Console.WriteLine("Problem could not be solved");
}
}
catch (XPRSException e)
{
Console.WriteLine(e.ToString());
throw e;
}
finally
{
prob.Destroy();
XPRS.Free();
}
}
public void OptimizerMsg(XPRSprob prob, object data, string message, int len, int msglvl)
{
switch (msglvl)
{
case 3:
case 4:
Console.WriteLine("{0}" + message, data);
break;
}
}
private XPRSprob prob;
}
}
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