// (c) 2023-2024 Fair Isaac Corporation
using System;
using System.Linq;
using Optimizer;
using static Optimizer.Objects.Utils;
using Variable = Optimizer.Objects.Variable;
using XpressProblem = Optimizer.Objects.XpressProblem;
using Optimizer.Maps;
using System.Collections.Generic;
namespace XPRSexamples
{
/// <summary>Solve a facility location problem for which data is given as collections.</summary>
public class FacilityLocationCollection
{
/// <summary>Customer descriptor.</summary>
private sealed class Customer
{
/// <summary>Customer name.</summary>
public readonly String name;
/// <summary>Demand for this customer.</summary>
public readonly double demand;
public Customer(String name, double demand)
{
this.demand = demand;
this.name = name;
}
}
/// <summary>Facility descriptor.</summary>
private sealed class Facility
{
/// <summary>Facility name.</summary>
public readonly String name;
/// <summary>Capacity of this facility.</summary>
public readonly double capacity;
/// <summary>Cost for opening this facility.</summary>
public readonly double cost;
public Facility(String name, double capacity, double cost)
{
this.name = name;
this.capacity = capacity;
this.cost = cost;
}
}
/// <summary>The customers in this example.</summary>
private static readonly Customer[] customers = new Customer[]{
new Customer("Customer 1", 80),
new Customer("Customer 2", 270),
new Customer("Customer 3", 250)
};
/// <summary>The facilityies in this example.</summary>
private static readonly Facility[] facilities = new Facility[]{
new Facility("Facility 1", 500, 1000),
new Facility("Facility 2", 500, 1000),
new Facility("Facility 3", 500, 1000)
};
/// <summary>Cost for transporting one unit between a customer and a facility.</summary>
private static readonly HashMap2<Facility, Customer, double> transportCost = new HashMap2<Facility, Customer, double>();
static FacilityLocationCollection()
{
transportCost.Add(facilities[0], customers[0], 4.0);
transportCost.Add(facilities[0], customers[1], 5.0);
transportCost.Add(facilities[0], customers[2], 6.0);
transportCost.Add(facilities[1], customers[0], 6.0);
transportCost.Add(facilities[1], customers[1], 4.0);
transportCost.Add(facilities[1], customers[2], 3.0);
transportCost.Add(facilities[2], customers[0], 9.0);
transportCost.Add(facilities[2], customers[1], 7.0);
transportCost.Add(facilities[2], customers[2], 4.0);
}
public static void Main(String[] args)
{
using (XpressProblem prob = new XpressProblem())
{
// Create a 1-dimensional map of y variables, indexed by Facility instances.
var y = prob.AddVariables(facilities)
.WithType(ColumnType.Binary)
.WithName(f => f.name)
.ToMap();
// Create a 2-dimensional map of x variables, indexed by (Facility,Customer) pairs
var x = prob.AddVariables(facilities, customers)
.WithType(ColumnType.Binary)
.WithName((f, c) => String.Format("x[{0},{1}]", f.name, c.name))
.ToMap();
// for each customer c
// sum(f=1..m) x[f,c] = d
prob.AddConstraints(customers,
c => Sum(facilities, (Facility f) => x[f, c]).Eq(c.demand)
);
// for each facility f
// sum(c=1..n) x[f,c] <= capacity[j] * y[f]
prob.AddConstraints(facilities,
f => Sum(customers, (Customer c) => x[f, c]).Leq(y[f] * f.capacity)
);
// minimize sum(j=1..m) cost[j] * y[j] +
// sum(i=1..n) sum(j=1..m) cost[f,c] * x[f,c]
prob.SetObjective(Sum(Sum(facilities, (Facility f) => y[f] * f.cost),
Sum(customers,
(Customer c) => Sum(facilities, (Facility f) => x[f, c] * transportCost[f, c]))));
prob.WriteProb("facilitylocationcollection.lp", "l");
prob.Optimize("");
double[] sol = prob.GetSolution();
foreach (var f in facilities)
{
if (y[f].GetValue(sol) > 0.5)
{
Console.WriteLine("Facility " + f.name + " is open, serves");
foreach (var c in customers)
{
if (x[f, c].GetValue(sol) > 0.0)
Console.WriteLine(" " + c.name + ": " +
x[f, c].GetValue(sol));
}
}
}
}
}
}
}
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