// (c) 2023-2024 Fair Isaac Corporation
using Optimizer.Objects;
using static Optimizer.Objects.Utils;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text.RegularExpressions;
namespace XpressExamples
{
/// <summary>Purchasing problem with price breaks using PieceWise Linear constraints</summary>
/// <remarks>
/// There are three suppliers of a good, and they have quoted various
/// prices for various quantities of product.
/// We want to buy at least total cost, yet not buy too much from any
/// one supplier.
///
/// Each supplier offers decreasing prices for increased lot size, in the
/// form of incremental discounts.
/// </remarks>
class PurchasePWL
{
static readonly String DATAFILE = (Environment.GetEnvironmentVariable("EXAMPLE_DATA_DIR") != null ? Environment.GetEnvironmentVariable("EXAMPLE_DATA_DIR") : ".") + "/purchase.cdat";
const int NB = 4; /* Number of breakpoints */
static double REQ; /* Total quantity required */
static int[] SUPPLIERS; /* Suppliers */
static double[] MAXPERC; /* Maximum percentages for each supplier */
static double[][] COST; /* Industry sector of shares */
static double[][] BREAKP; /* Breakpoints (quantities at which unit cost changes) */
public static void Main(string[] args)
{
ReadData(); // Read data from file
using (XpressProblem prob = new XpressProblem())
{
// Create the decision variables
// Quantity to purchase from supplier s
Variable[] buy = prob.AddVariables(SUPPLIERS.Length)
.WithUB(s => MAXPERC[s] * REQ / 100.0)
.WithName("buy {0}")
.ToArray();
// Cost incurred from supplier s
Variable[] cost = prob.AddVariables(SUPPLIERS.Length)
.WithName("cost {0}")
.ToArray();
// The minimum quantity that must be bought
prob.AddConstraint(Sum(buy) >= REQ);
// Function to calculate cost at breakpoints
double[][] COSTBREAK = new double[SUPPLIERS.Length][];
for (int s = 0; s < SUPPLIERS.Length; s++)
{
COSTBREAK[s] = new double[NB];
COSTBREAK[s][0] = 0;
for (int b = 1; b < NB; b++)
COSTBREAK[s][b] = COSTBREAK[s][b - 1] + COST[s][b] * (BREAKP[s][b] - BREAKP[s][b - 1]);
}
// Define relation between bought quantities and price paid per supplier
for (int s = 0; s < SUPPLIERS.Length; s++)
{
prob.AddConstraint(cost[s].PwlOf(buy[s], BREAKP[s], COSTBREAK[s]));
}
// Objective: total return
prob.SetObjective(Sum(cost));
// Solve the problem
prob.MipOptimize("");
Console.WriteLine("Problem status: " + prob.MIPStatus);
if (prob.MIPStatus != Optimizer.MIPStatus.Solution &&
prob.MIPStatus != Optimizer.MIPStatus.Optimal)
throw new Exception("optimization failed with status " + prob.MIPStatus);
// Solution printing
Console.WriteLine("Total cost: " + prob.ObjVal);
double[] sol = prob.GetSolution();
for (int s = 0; s < SUPPLIERS.Length; s++)
if (buy[s].GetValue(sol) > 0.5)
Console.WriteLine("Supp. " + SUPPLIERS[s] + ": buy:" + buy[s].GetValue(sol) + ": cost:" + cost[s].GetValue(sol));
}
}
/// <summary>Read a data vector</summary>
/// <typeparam name="T">Data type.</typeparam>
/// <param name="tokens">Token provider</param>
/// <param name="makeData">Function to turn a <c>string</c> token into an instance of <c>T</c>.</param>
/// <returns>The next vector read from <c>tokens</c>.</returns>
private static T[] ReadVector<T>(IEnumerator<string> tokens, Func<string, T> makeData)
{
List<T> data = new List<T>();
while (tokens.MoveNext())
{
string token = tokens.Current;
if (token.Equals(";")) // Semicolon terminates vector
break;
data.Add(makeData(token));
}
return data.ToArray();
}
/// <summary>Read a table of doubles.</summary>
/// <remarks>
/// Returns an <c>nrow</c> by <c>ncol</c> table of doubles.
/// </remarks>
/// <param name="tokens">Token provider.</param>
/// <param name="nrow">Number of rows.</param>
/// <param name="ncol">Number of columns.</param>
/// <returns><c>nrow</c> by <c>ncol</c> double array.</returns>
private static double[][] ReadTable(IEnumerator<string> tokens, int nrow, int ncol)
{
double[][] table = new double[nrow][];
for (int r = 0; r < nrow; ++r)
{
table[r] = new double[ncol];
table[r] = ReadVector(tokens, s => Double.Parse(s));
}
return table;
}
/// <summary>Fill the static data fields.</summary>
private static void ReadData()
{
// Split the file content into tokens
IEnumerator<string> tokens = File.ReadAllLines(DATAFILE)
.SelectMany(s => Regex.Split(s, "\\s+")) // Split tokens at whitespace
.SelectMany(s => (s.Length > 1 && s.EndsWith(";")) ? new string[] { s.Substring(0, s.Length - 1), ";" } : new string[] { s }) // Split comma into separate token
.Where(s => s.Length > 0) // filter empty strings
.GetEnumerator();
while (tokens.MoveNext())
{
string token = tokens.Current;
if (token.Equals("SUPPLIERS:"))
{
SUPPLIERS = ReadVector(tokens, s => Int32.Parse(s));
}
else if (token.Equals("MAXPERC:"))
{
MAXPERC = ReadVector(tokens, s => Double.Parse(s));
}
else if (token.Equals("REQ:"))
{
tokens.MoveNext();
REQ = Double.Parse(tokens.Current);
}
else if (token.Equals("BREAKP:"))
{
BREAKP = ReadTable(tokens, SUPPLIERS.Length, NB);
}
else if (token.Equals("COST:"))
{
COST = ReadTable(tokens, SUPPLIERS.Length, NB);
}
}
}
}
}
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// (c) 2023-2024 Fair Isaac Corporation
using Optimizer.Objects;
using static Optimizer.Objects.Utils;
using static Optimizer.Objects.SOS;
using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text.RegularExpressions;
namespace XpressExamples
{
/// <summary>Purchasing problem with price breaks using Special Ordered Set (SOS) type 2 constraints</summary>
/// <remarks>
/// There are three suppliers of a good, and they have quoted various
/// prices for various quantities of product.
/// We want to buy at least total cost, yet not buy too much from any
/// one supplier.
///
/// Each supplier offers decreasing prices for increased lot size, in
/// the form of incremental discounts.
/// </remarks>
class PurchaseSOS2
{
static readonly String DATAFILE = (Environment.GetEnvironmentVariable("EXAMPLE_DATA_DIR") != null ? Environment.GetEnvironmentVariable("EXAMPLE_DATA_DIR") : ".") + "/purchase.cdat";
const int NB = 4; /* Number of breakpoints */
static double REQ; /* Total quantity required */
static int[] SUPPLIERS; /* Suppliers */
static double[] MAXPERC; /* Maximum percentages for each supplier */
static double[][] COST; /* Industry sector of shares */
static double[][] BREAKP; /* Breakpoints (quantities at which unit cost changes) */
public static void Main(string[] args)
{
ReadData(); // Read data from file
using (XpressProblem prob = new XpressProblem())
{
// Create the decision variables
// Quantity to purchase from supplier s
Variable[] buy = prob.AddVariables(SUPPLIERS.Length)
.WithUB(s => MAXPERC[s] * REQ / 100.0)
.WithName("buy {0}")
.ToArray();
// Weights at breakpoint k for supplier s
Variable[][] weight = Enumerable.Range(0, SUPPLIERS.Length)
.Select(s => prob.AddVariables(NB)
.WithName(b => $"w({s})({b})")
.ToArray())
.ToArray();
// The minimum quantity that must be bought
prob.AddConstraint(Sum(buy) >= REQ);
// Define relation between bought quantities and price paid per supplier
for (int s = 0; s < SUPPLIERS.Length; s++)
{
// The convexity row (weight sum to 1)
prob.AddConstraint(Sum(NB, b => weight[s][b]) == 1);
// Define buy and also order the weight variables by breakpoint quantities
prob.AddConstraint(Sum(NB, b => weight[s][b] * BREAKP[s][b]) == buy[s]);
// Define the weight as SOS-2
prob.AddConstraint(Sos2(weight[s], BREAKP[s], $"sos_{s}"));
}
// Function to calculate cost at breakpoints
double[][] COSTBREAK = new double[SUPPLIERS.Length][];
for (int s = 0; s < SUPPLIERS.Length; s++)
{
COSTBREAK[s] = new double[NB];
COSTBREAK[s][0] = 0;
for (int b = 1; b < NB; b++)
COSTBREAK[s][b] = COSTBREAK[s][b - 1] + COST[s][b] * (BREAKP[s][b] - BREAKP[s][b - 1]);
}
// Objective: total return
prob.SetObjective(Sum(NB,
b => Sum(SUPPLIERS.Length, s => weight[s][b] * COSTBREAK[s][b])));
// Solve the problem
prob.MipOptimize("");
Console.WriteLine("Problem status: " + prob.MIPStatus);
if (prob.MIPStatus != Optimizer.MIPStatus.Solution &&
prob.MIPStatus != Optimizer.MIPStatus.Optimal)
throw new Exception("optimization failed with status " + prob.MIPStatus);
// Solution printing
Console.WriteLine("Total cost: " + prob.ObjVal);
double[] sol = prob.GetSolution();
for (int s = 0; s < SUPPLIERS.Length; s++)
if (buy[s].GetValue(sol) > 0.5)
Console.WriteLine("Supp. " + SUPPLIERS[s] + ": buy:" + buy[s].GetValue(sol));
}
}
/// <summary>Read a data vector</summary>
/// <typeparam name="T">Data type.</typeparam>
/// <param name="tokens">Token provider</param>
/// <param name="makeData">Function to turn a <c>string</c> token into an instance of <c>T</c>.</param>
/// <returns>The next vector read from <c>tokens</c>.</returns>
private static T[] ReadVector<T>(IEnumerator<string> tokens, Func<string, T> makeData)
{
List<T> data = new List<T>();
while (tokens.MoveNext())
{
string token = tokens.Current;
if (token.Equals(";")) // Semicolon terminates vector
break;
data.Add(makeData(token));
}
return data.ToArray();
}
/// <summary>Read a table of doubles.</summary>
/// <remarks>
/// Returns an <c>nrow</c> by <c>ncol</c> table of doubles.
/// </remarks>
/// <param name="tokens">Token provider.</param>
/// <param name="nrow">Number of rows.</param>
/// <param name="ncol">Number of columns.</param>
/// <returns><c>nrow</c> by <c>ncol</c> double array.</returns>
private static double[][] ReadTable(IEnumerator<string> tokens, int nrow, int ncol)
{
double[][] table = new double[nrow][];
for (int r = 0; r < nrow; ++r)
{
table[r] = new double[ncol];
table[r] = ReadVector(tokens, s => Double.Parse(s));
}
return table;
}
/// <summary>Fill the static data fields.</summary>
private static void ReadData()
{
// Split the file content into tokens
IEnumerator<string> tokens = File.ReadAllLines(DATAFILE)
.SelectMany(s => Regex.Split(s, "\\s+")) // Split tokens at whitespace
.SelectMany(s => (s.Length > 1 && s.EndsWith(";")) ? new string[] { s.Substring(0, s.Length - 1), ";" } : new string[] { s }) // Split comma into separate token
.Where(s => s.Length > 0) // filter empty strings
.GetEnumerator();
while (tokens.MoveNext())
{
string token = tokens.Current;
if (token.Equals("SUPPLIERS:"))
{
SUPPLIERS = ReadVector(tokens, s => Int32.Parse(s));
}
else if (token.Equals("MAXPERC:"))
{
MAXPERC = ReadVector(tokens, s => Double.Parse(s));
}
else if (token.Equals("REQ:"))
{
tokens.MoveNext();
REQ = Double.Parse(tokens.Current);
}
else if (token.Equals("BREAKP:"))
{
BREAKP = ReadTable(tokens, SUPPLIERS.Length, NB);
}
else if (token.Equals("COST:"))
{
COST = ReadTable(tokens, SUPPLIERS.Length, NB);
}
}
}
}
}
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