// (c) 2023-2025 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, k + 1, (p, 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.Optimize(""); 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]); } } } }