// (c) 2023-2024 Fair Isaac Corporation
using Optimizer;
using Optimizer.Objects;
using static Optimizer.Objects.Utils;
using System;
using System.Linq;
namespace XpressExamples
{
/// <summary>Project planning: MIP example</summary>
/// <remarks>
/// A company has several projects that it must undertake in the next
/// few months.
/// Each project lasts for a given time (its duration) and uses up one
/// resource as soon as it starts.
/// The resource profile is the amount of the resource that is used in
/// the months following the start of the project.
/// For instance, project 1 uses up 3 units of resource in the month it
/// starts, 4 units in its second month, and 2 units in its last month.
/// The problem is to decide when to start each project, subject to not
/// using more of any resource in a given month than is available.
/// The benefit from the project only starts to accrue when the project
/// has been completed, and then it accrues at BEN[p] per month for
/// project p, up to the end of the time horizon.
/// </remarks>
class Pplan
{
static readonly string[] PROJ = { "A", "B", "C" }; /* Set of projects */
const int NM = 6; /* Time horizon (months) */
static readonly int[] MONTHS = System.Linq.Enumerable.Range(1, NM).ToArray(); /* Set of time periods (months) to plan for */
static readonly int[] DUR = { 3, 3, 4 }; /* Duration of project p */
static readonly int[] RESMAX = { 5, 6, 7, 7, 6, 6 }; /* Resource available in month m */
static readonly double[] BEN = { 10.2, 12.3, 11.2 }; /* Benefit per month once project finished */
static readonly int[][] RESUSE = /* Res. usage of proj. p in its t'th month */
new int[][] { new int[] { 3, 4, 2, 0, 0, 0 }, new int[] { 4, 1, 5, 0, 0, 0 }, new int[] { 3, 2, 1, 2, 0, 0 } };
public static void Main(string[] args)
{
using (XpressProblem prob = new XpressProblem())
{
Variable[,] start = prob.AddVariables(PROJ.Length, NM)
.WithType(ColumnType.Binary)
.WithName((p, m) => $"start({PROJ[p]})({MONTHS[m]})")
.ToArray();
// Each project starts once and only once
prob.AddConstraints(PROJ.Length, p => Sum(NM, m => start[p, m]) == 1);
// Resource availability. A project starting in month m is in its k-m month in month k:
// sum(p in PROJ, m in 0..k) RESUSE(p,k-m)*start(p,m) <= RESMAX(k)
prob.AddConstraints(NM, k => Sum(PROJ.Length, p => Sum(k + 1, m => start[p, m] * RESUSE[p][k - m])) <= RESMAX[k]);
/* Objective: Maximize Benefit
If project p starts in month m, it finishes in month m+DUR(p)-1 and
contributes a benefit of BEN(p) for the remaining NM-(m+DUR(p)-1) months: */
LinExpression obj = LinExpression.Create();
for (int p = 0; p < PROJ.Length; p++)
{
for (int m = 0; m < NM - DUR[p]; m++)
{
obj.AddTerm(start[p, m], BEN[p] * (NM - m - DUR[p]));
}
}
prob.SetObjective(obj, ObjSense.Maximize);
// Solve the problem
prob.MipOptimize("");
System.Console.WriteLine("Problem status: " + prob.MIPStatus);
if (prob.MIPStatus != Optimizer.MIPStatus.Solution &&
prob.MIPStatus != Optimizer.MIPStatus.Optimal)
throw new System.Exception("optimization failed with status " + prob.MIPStatus);
// Solution printing
System.Console.WriteLine("Solution value is: " + prob.ObjVal);
double[] sol = prob.GetSolution();
for (int p = 0; p < PROJ.Length; p++)
for (int m = 0; m < NM; m++)
if (start[p, m].GetValue(sol) > 0.5)
System.Console.WriteLine("Project " + PROJ[p] + " starts in month " + MONTHS[m]);
}
}
}
}
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// (c) 2023-2024 Fair Isaac Corporation
using Optimizer;
using Optimizer.Objects;
using static Optimizer.Objects.Utils;
using static Optimizer.Objects.SOS;
using System;
using System.Linq;
namespace XpressExamples
{
/// <summary>Project planning: Defining SOS1</summary>
/// <remarks>
/// A company has several projects that it must undertake in the next
/// few months.
/// Each project lasts for a given time (its duration) and uses up one
/// resource as soon as it starts.
/// The resource profile is the amount of the resource that is used in
/// the months following the start of the project.
/// For instance, project 1 uses up 3 units of resource in the month it
/// starts, 4 units in its second month, and 2 units in its last month.
/// The problem is to decide when to start each project, subject to not
/// using more of any resource in a given month than is available.
/// The benefit from the project only starts to accrue when the project
/// has been completed, and then it accrues at BEN[p] per month for
/// project p, up to the end of the time horizon.
/// </remarks>
class Pplan2
{
static readonly string[] PROJ = { "A", "B", "C" }; /* Set of projects */
const int NM = 6; /* Time horizon (months) */
static readonly int[] MONTHS = System.Linq.Enumerable.Range(1, NM).ToArray(); /* Set of time periods (months) to plan for */
static readonly int[] DUR = { 3, 3, 4 }; /* Duration of project p */
static readonly int[] RESMAX = { 5, 6, 7, 7, 6, 6 }; /* Resource available in month m */
static readonly double[] BEN = { 10.2, 12.3, 11.2 }; /* Benefit per month once project finished */
static readonly int[][] RESUSE = /* Res. usage of proj. p in its t'th month */
new int[][] { new int[] { 3, 4, 2, 0, 0, 0 }, new int[] { 4, 1, 5, 0, 0, 0 }, new int[] { 3, 2, 1, 2, 0, 0 } };
public static void Main(string[] args)
{
using (XpressProblem prob = new XpressProblem())
{
// Create the decision variables
// 1 if proj p starts in month m, else 0
Variable[][] start = System.Linq.Enumerable.Range(0, PROJ.Length)
.Select(p => prob.AddVariables(NM)
.WithName(m => $"start({PROJ[p]})({MONTHS[m]})")
.ToArray())
.ToArray();
// Each project starts once and only once
prob.AddConstraints(PROJ.Length, p => Sum(start[p]) == 1);
// Resource availability. A project starting in month m is in its k-m month in month k:
// sum(p in PROJ, m in 0..k) RESUSE(p,k-m)*start(p,m) <= RESMAX(k)
prob.AddConstraints(NM, k => Sum(PROJ.Length, p => Sum(k + 1, m => start[p][m] * RESUSE[p][k - m])) <= RESMAX[k]);
/* Define SOS-1 sets that ensure that at most one start(p,m) is non-zero
for each project p. Use month index to order the variables */
prob.AddConstraints(PROJ.Length, p => Sos1(start[p], null, $"sos_{p}"));
/* Objective: Maximize Benefit
If project p starts in month m, it finishes in month m+DUR(p)-1 and
contributes a benefit of BEN(p) for the remaining NM-(m+DUR(p)-1) months: */
LinExpression obj = LinExpression.Create();
for (int p = 0; p < PROJ.Length; p++)
{
for (int m = 0; m < NM - DUR[p]; m++)
{
obj.AddTerm(start[p][m], BEN[p] * (NM - m - DUR[p]));
}
}
prob.SetObjective(obj, ObjSense.Maximize);
// Solve the problem
prob.MipOptimize("");
System.Console.WriteLine("Problem status: " + prob.MIPStatus);
if (prob.MIPStatus != Optimizer.MIPStatus.Solution &&
prob.MIPStatus != Optimizer.MIPStatus.Optimal)
throw new System.Exception("optimization failed with status " + prob.MIPStatus);
// Solution printing
System.Console.WriteLine("Solution value is: " + prob.ObjVal);
double[] sol = prob.GetSolution();
for (int p = 0; p < PROJ.Length; p++)
for (int m = 0; m < NM; m++)
if (start[p][m].GetValue(sol) > 0.5)
System.Console.WriteLine("Project " + PROJ[p] + " starts in month " + MONTHS[m]);
}
}
}
}
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