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How to: Bind Data to Parameters and Output

Solver Foundation 3.0

You can use linear programming to minimize or maximize functions. In this example, an oil refinery must procure crude oil from two sources. The objective is to minimize the purchase cost of crude oils of varying quality and to meet minimum production levels of 2,000 barrels of gasoline, 1,500 barrels of jet fuel, and 500 barrels of machine lubricant. Meanwhile, the suppliers cannot exceed their maximum daily production of crude oil. The following table shows the costs and capabilities of the two different crude oils.

Source

Saudi Arabia refining

Venezuela refining

Cost

$20 per barrel

$15 per barrel

Maximum daily production

9,000 barrels

6,000 barrels

Refining percentages

30% gasoline

40% jet fuel

20% lubricant

10% waste

40% gasoline

20% jet fuel

30% lubricant

10% waste

The following example demonstrates how to use Solver Foundation to create and solve the refining model by using the Solver Foundation Services layer.

To bind data to input parameters and output variables

  1. Create a console application named PetroChem.

  2. Add a reference to Microsoft Solver Foundation on the .NET tab of the Add Reference dialog box.

  3. Add the following Imports or using statements to the top of the Program code file.

    
    using Microsoft.SolverFoundation.Common;
    using Microsoft.SolverFoundation.Services;
    
    
    
  4. Create the following class to define the information used to describe a country or region.

    
    class CountryDef {
      public string Country { get; set; }
      public double MaxProduction { get; set; }
      public double Price { get; set; }
      public double Yield { get; set; }
      public double Production { get; set; }
    
      public CountryDef(string country, double maxProduction, double price, double yield) {
        Country = country;
        MaxProduction = maxProduction;
        Price = price;
        Yield = yield;
        Production = -42;
      }
    }
    
    
    
  5. In the Main method, add the following code to instantiate the class and define the data that describes the country or region.

    
    CountryDef[] ProductionCapacity = new CountryDef[] { 
              new CountryDef("Venezuela", 9000, 15, 0.4),
              new CountryDef("Saudi Arabia", 6000, 20, 0.3)
          };
    
    
    
  6. Add the following code to get the context environment for a solver and create a new model.

    
    SolverContext context = SolverContext.GetContext();
    Model model = context.CreateModel();
    
    
    
  7. Create decision variables that represent the two sources of crude oil: Saudi Arabia and Venezuela.

    
    Decision vz = new Decision(Domain.RealNonnegative, "barrels_venezuela");
    Decision sa = new Decision(Domain.RealNonnegative, "barrels_saudiarabia");
    
    
    
  8. Bind data to the decisions by using LINQ. Then add the decisions to the model.

    
    vz.SetBinding(
      from row in ProductionCapacity where row.Country == "Venezuela" select row, 
      "Production");
    sa.SetBinding(
      from row in ProductionCapacity where row.Country == "Saudi Arabia" select row, 
      "Production");
    model.AddDecisions(vz, sa);
    
    
    
  9. Create two parameters that represent the input data for the model.

    
    Parameter maxvz = new Parameter(Domain.RealNonnegative, "maxproduction_venezuela");
    Parameter maxsa = new Parameter(Domain.RealNonnegative, "maxproduction_saudiarabia");
    
    
    
  10. Bind data to the parameters by using LINQ

    
    maxvz.SetBinding(
      from row in ProductionCapacity where row.Country == "Venezuela" select row, 
      "MaxProduction");
    maxsa.SetBinding(
      from row in ProductionCapacity where row.Country == "Saudi Arabia" select row, 
      "MaxProduction");
    model.AddParameters(maxvz, maxsa);
    
    
    
  11. Add two constraints that define the maximum daily production levels for the two refineries.

    
    model.AddConstraints("limits",
      0 <= vz <= maxvz,
      0 <= sa <= maxsa);
    
    
    
  12. Add three constraints that define the refining capabilities of each crude oil. In the following code, the constraints for the two suppliers are added as decimals. For example, the Saudi Arabian crude oil produces 30% gasoline and the Venezuelan crude oil produces 40% gasoline. The first half of the constraint is added as 0.3 * sa + 0.4 * vz. The second half of the constraint identifies the minimum production of 2,000 barrels of gasoline. Similar constraints are added for 1,500 barrels of jet fuel and 500 barrels of machine lubricant.

    
    model.AddConstraints("production",
      0.3 * sa + 0.4 * vz >= 2000,
      0.4 * sa + 0.2 * vz >= 1500,
      0.2 * sa + 0.3 * vz >= 500);
    
    
    
  13. Add the costs of the crude oils to the model. Specify that the solver should minimize the goal by setting the second parameter to GoalKind.Minimize.

    
    model.AddGoal("cost", GoalKind.Minimize, 20 * sa + 15 * vz);
    
    
    
  14. Solve the model, call the PropagateDecisions method to save the results, and then get the report.

    
    Solution solution = context.Solve(new SimplexDirective());
    
    context.PropagateDecisions();
    
    Report report = solution.GetReport();
    Console.WriteLine("vz: {0}, sa: {1}", vz, sa);
    Console.Write("{0}", report);
    
    
    
  15. Press F5 to build and run the code.

    The Command window shows the following results.

    vz: 3500, sa: 2000

    ===Solver Foundation Service Report===

    Date: Date

    Version: Version

    Model Name: Default

    Capabilities Applied: LP

    Solve Time (ms): 138

    Total Time (ms): 272

    Solve Completion Status: Optimal

    Solver Selected: Microsoft.SolverFoundation.Solvers.SimplexSolver

    Directives:

    Simplex(TimeLimit = -1, MaximumGoalCount = -1, Arithmetic = Default, Pricing = Default, IterationLimit = -1, Algorithm = Default, Basis = Default, GetSensitivity = False)

    Algorithm: Primal

    Arithmetic: Double

    Variables: 2 -> 2 + 4

    Rows: 6 -> 4

    Nonzeros: 10

    Eliminated Slack Variables: 0

    Pricing (double): SteepestEdge

    Basis: Slack

    Pivot Count: 3

    Phase 1 Pivots: 3 + 0

    Phase 2 Pivots: 0 + 0

    Factorings: 4 + 0

    Degenerate Pivots: 0 (0.00 %)

    Branches: 0

    ===Solution Details===

    Goals:

    cost: 92500

    Decisions:

    barrels_venezuela: 3500

    barrels_saudiarabia: 2000

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