// (c) 2023-2024 Fair Isaac Corporation
using System;
using Optimizer;
using Optimizer.Objects;
using static Optimizer.Objects.Utils;
namespace XpressExamples
{
/// <summary>Contract allocation example.</summary>
class ContractAllocation
{
static readonly int NDISTRICT = 6; /* Number of districts */
static readonly int NCONTRACT = 10; /* Number of contracts */
private static readonly double[] output = new double[]{ /* Max. output per district */
50, 40, 10, 20, 70, 50
};
private static readonly double[] cost = new double[]{ /* Cost per district */
50, 20, 25, 30, 45, 40
};
private static readonly double[] volume = new double[]{ /* Volume of contracts */
20, 10, 30, 15, 20, 30, 10, 50, 10, 20
};
public static void Main(string[] args)
{
using (XpressProblem prob = new XpressProblem())
{
// Output all messages.
prob.callbacks.AddMessageCallback(DefaultMessageListener.Console);
/**** VARIABLES ****/
/* Variables indicating whether a project is chosen */
Variable[,] x = prob.AddVariables(NDISTRICT, NCONTRACT)
.WithType(ColumnType.Binary)
.WithName((d, c) => $"x_d{d + 1}_c{c + 1}")
.ToArray();
/* Quantities allocated to contractors */
Variable[,] y = prob.AddVariables(NDISTRICT, NCONTRACT)
.WithType(ColumnType.SemiContinuous)
.WithUB((d, c) => output[d])
.WithName((d, c) => $"q_d{d + 1}_c{c + 1}")
.WithLimit(5) // Set limit for the semi-continous variable
.ToArray();
/**** CONSTRAINTS ****/
// Cover the required volume
// for all c in [0,NCONTRACT[
// sum(d in [0,NDISTRICT[) y[d][c] >= volume[c]
prob.AddConstraints(NCONTRACT,
c => Sum(NDISTRICT, d => y[d, c]).Geq(volume[c]).SetName($"Size_{c}")
);
// "Min": at least 2 districts / contract
// for all c in [0,NCONTRACT[
// sum(d in [0,NDISTRICT[) x[d][c] >= 2
prob.AddConstraints(NCONTRACT,
c => Sum(NDISTRICT, d => x[d, c]).Geq(2.0).SetName($"Min_{c}")
);
// Do not exceed max. output
// for all d in [0,NDISTRICT[
// sum(c in [0,NCONTRACT[) y[d][c] <= output[d]
prob.AddConstraints(NDISTRICT,
d => Sum(NCONTRACT, c => y[d, c]).Leq(output[d]).SetName($"Output_{d}")
);
// If a contract is allocated to a district, then at least 1 unit is allocated to it
// for all d in [0,NDISTRICT[
// for all c in [0,NCONTRACT[
// x[d][c] <= y[d][c]
prob.AddConstraints(NDISTRICT, NCONTRACT,
(d, c) => x[d, c].Leq(y[d, c]).SetName($"XY_{d}{c}")
);
/****OBJECTIVE****/
prob.SetObjective(
Sum(
NCONTRACT,
c => Sum(NDISTRICT, d => y[d, c] * cost[d])),
Optimizer.ObjSense.Minimize
);
// Output the matrix in LP format
prob.WriteProb("Contract.lp", "l");
// Solve
prob.MipOptimize();
if (prob.SolStatus != Optimizer.SolStatus.Optimal &&
prob.SolStatus != Optimizer.SolStatus.Feasible)
throw new Exception("optimization failed with status " + prob.SolStatus);
// Print out the solution
double[] sol = prob.GetSolution();
Console.WriteLine("Objective: {0}", prob.MIPObjVal);
foreach (Variable v in y)
{
if (v.GetValue(sol) > 0.5)
Console.WriteLine($"{v.GetName()}:{v.GetValue(sol)} ");
}
}
}
}
}
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