How to: Bind Data to Parameters
You can use linear programming to minimize or maximize functions. In this data binding 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 procedure 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 create the model
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Create a console application named PetroChem.
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Add a reference to Microsoft Solver Foundation on the .NET tab.
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Add the following Imports or using statements to the top of the Program code file.
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Create the following class to define the information used to describe a locale or region.
Class CountryDef Public Property Country() As String Get Return m_Country End Get Set(ByVal value As String) m_Country = value End Set End Property Private m_Country As String Public Property MaxProduction() As Double Get Return m_MaxProduction End Get Set(ByVal value As Double) m_MaxProduction = value End Set End Property Private m_MaxProduction As Double Public Property Price() As Double Get Return m_Price End Get Set(ByVal value As Double) m_Price = value End Set End Property Private m_Price As Double Public Property Yield() As Double Get Return m_Yield End Get Set(ByVal value As Double) m_Yield = value End Set End Property Private m_Yield As Double Public Property Production() As Double Get Return m_Production End Get Set(ByVal value As Double) m_Production = value End Set End Property Private m_Production As Double Public Sub New(ByVal country As String, ByVal maxProduction As Double, ByVal price As Double, ByVal yield As Double) m_Country = country m_MaxProduction = maxProduction m_Price = price m_Yield = yield m_Production = -42 End Sub End Class
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In the Main method, add the following code to instantiate the class and define the data that describes the country or region.
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Add the following code to get the context environment for a solver and to create a new model.
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Create new decision variables that represent the two sources of crude oil: Saudi Arabia and Venezuela. Then add the decisions to the model.
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Add parameters that represent the data input to the model.
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Bind data to the parameters by using LINQ.
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Add two constraints that define the maximum daily production levels for the two refineries.
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Add three constraints that define the refining capabilities of each crude oil. In the following code, 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.
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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.
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Solve the model and get the report.
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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