// (c) 2023-2024 Fair Isaac Corporation
using System;
using Optimizer;
using Optimizer.Objects;
using static Optimizer.Objects.Utils;
namespace XpressExamples
{
/// <summary>Capital budgeting example, solved using three multi-objective approaches</summary>
/// <remarks>
/// <list type='number'>
/// <item><description>
/// Lexicographic approach, solving first to minimize capital expended
/// and second to maximize return
/// </description></item>
/// <item><description>
/// Blended approach, solving a weighted combination of both objectives
/// simultaneously
/// </description></item>
/// <item><description>
/// Lexicographic approach, with the objective priorities reversed
/// </description></item>
/// </list>
class CapitalBudgeting : IDisposable
{
/// Required capital for each project
static readonly double[] CAPITAL = { 104000, 53000, 29000, 187000, 98000, 32000, 75000, 200000 };
/// Required personnel for each project
static readonly double[] PERSONNEL = { 22, 12, 7, 36, 24, 10, 20, 41 };
/// Expected return of each project
static readonly double[] RETURN = { 124000, 74000, 42000, 188000, 108000, 56000, 88000, 225000 };
/// Target capital to invest
static readonly double CAPITAL_TARGET = 478000;
/// Target return on investment
static readonly double ROI_TARGET = 550000;
/// Available personnel
static readonly int PERSONNEL_MAX = 106;
private readonly XpressProblem prob;
/// Binary decision variables indicating which projects will be implemented
private Variable[] select;
/// Constraint for the number of personnel available
private Inequality personnel;
/// Primary objective: minimize capital expended
private LinExpression capital;
/// Secondary objective: maximize return on investment
private LinExpression roi;
public CapitalBudgeting()
{
prob = new XpressProblem();
}
public void Dispose()
{
prob.Dispose();
}
public static void Main(string[] args)
{
using (CapitalBudgeting capBudget = new CapitalBudgeting())
{
capBudget.Solve();
}
}
public void Solve()
{
// Binary decision variables indicating which projects will be implemented
select = prob.AddVariables(CAPITAL.Length)
.WithType(ColumnType.Binary)
.WithName("select_{0}")
.ToArray();
// Constraint: at least 3 projects must be implemented
prob.AddConstraint(Sum(select) <= 3);
// Constraint for the number of personnel available
personnel = prob.AddConstraint(ScalarProduct(select, PERSONNEL) <= PERSONNEL_MAX);
// Primary objective: minimize capital expended
capital = ScalarProduct(select, CAPITAL);
// The first objective has priority=1 (weight=1 by default)
prob.SetObjective(capital, ObjSense.Minimize);
prob.SetObjIntControl(0, ObjControl.Priority, 1);
// Secondary objective: maximize return on investment
roi = ScalarProduct(select, RETURN);
// The second objective has weight=-1 to maximize this expression, and priority=0
// to cause this objective to be solved in a second optimization
prob.AddObjective(roi, 0, -1);
prob.Optimize();
PrintSolution("Higher priority for 'Minimize Capital' objective:");
// Now set the same priority for both objectives. This will result in a single solve
// using the weighted sum of the two objectives.
prob.SetObjIntControl(1, ObjControl.Priority, 1);
prob.Optimize();
PrintSolution("Equal priority for objectives:");
// Finally, give the first objective a lower priority
prob.SetObjIntControl(0, ObjControl.Priority, 0);
prob.Optimize();
PrintSolution("Higher priority for 'Maximize Return' objective:");
}
/// <summary>
/// Prints the current solution to the problem.
/// </summary>
/// <param name="title">a title to print before the solution</param>
private void PrintSolution(String title)
{
Console.WriteLine(title);
if (prob.SolveStatus != SolveStatus.Completed ||
prob.SolStatus != SolStatus.Optimal)
{
Console.WriteLine(" Problem not solved");
}
else
{
Console.WriteLine($" Objectives: {prob.Objectives}, solved objectives: {prob.SolvedObjs}");
double[] sol = prob.GetSolution();
double capitalUsed = capital.Evaluate(sol);
double roiGained = roi.Evaluate(sol);
if (capitalUsed > CAPITAL_TARGET)
{
Console.WriteLine(" Unable to meet Capital target");
}
if (roiGained < ROI_TARGET)
{
Console.WriteLine(" Unable to meet Return target");
}
Console.Write(" Projects undertaken:");
for (int p = 0; p < select.Length; p++)
{
if (select[p].GetSolution() >= 0.99)
{
Console.Write($" {p}");
}
}
Console.WriteLine();
Console.WriteLine($" Used capital: ${capitalUsed}," +
(CAPITAL_TARGET >= capitalUsed ? " unused: $" : " overused: $") +
Math.Abs(CAPITAL_TARGET - capitalUsed));
Console.WriteLine($" Total return: ${roiGained}");
Console.WriteLine($" Unused personnel: {(int)personnel.GetSlack()} persons");
}
}
}
}
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