Create the Model-class

Prerequisites

• The Instantiation of Business Objects

Create the Model-class

In this example the Warehouse Location Model (WLP) is created. The WLPs objective is to minimize the opening and production costs of the warehouses while serving all customers.

Model Generator Class

WarehouseLocationModel.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;


namespace WLP
{
    using OPTANO.Modeling.Optimization;
    using OPTANO.Modeling.Optimization.Operators;
    using OPTANO.Modeling.Optimization.Enums;

   /// <summary>
    /// A warehouse location model
    /// </summary>
    public class WarehouseLocationModel
    {
       
        /// <summary>
        /// Initializes a new instance of the 
        /// <see cref="WarehouseLocationModel"/> class and initializes all fields. 
        /// </summary>
        /// <param name="nodes">
        /// The network nodes of the model
        /// </param>
        /// <param name="edges">
        /// The edges of the model
        /// </param>
        public WarehouseLocationModel(List<INode> nodes, List<IEdge> edges)
        {
            this.Nodes = nodes;
            this.Edges = edges;
         
            this.Model = new Model();
               
            // Supply amount variable
            this.x = new VariableCollection<IEdge>(
                this.Model,
                this.Edges,
                "x", // the name of the variable collection
                edge => $"Supply flowing from {edge.FromNode} to {edge.ToNode}",
                edge => 0, 
                edge => edge.Capacity,
                edge => VariableType.Continuous);

            // Depot activation variable
            this.y = new VariableCollection<INode>(
               this.Model, 
               this.Nodes, 
               "y",
               node => $"{node.Name} status:",
               node => 0, // Warehouse is not used
               node => 1, // Warehouse is used
               node => VariableType.Binary); 
                
            // Create Constraints

            // if any edge is unbounded, take the highest of all demands as Big M
            // var bigM = nodes.Where(node => node.Demand > 0).Max(node => node.Demand);


            // fulfill all demands
            foreach (var node in this.Nodes)
            {
                if (node.Demand > 0)
                {
                    // Add Constraint to model
                    this.Model.AddConstraint(
                        // sum of transported goods to customers
                        Expression.Sum(this.Edges.Where(edge => edge.ToNode == node).Select(edge => this.x[edge]))
                        == node.Demand,
                        $"Fulfill the demand of node, {node}");
                }
            }

            // open facility if edge used
            foreach (var node in this.Nodes)
            {
                if (node.CreationCost > 0)
                {
                    // Add Constraint to model
                    this.Model.AddConstraint(
                        // edge activation for outgoing warehouse edges
                        Expression.Sum(this.Edges.Where(edge => edge.FromNode == node) .Select(edge => this.x[edge]))
                        <= this.y[node] * Math.Abs(node.Demand), // take the absolute value
                        $"Force facility {node} to open if outgoing edge is used");
                }
            }

            // Add the objective
            // Sum of all flows times the flow-unit-cost
            // + all warehouse opening decisions and their respective costs.
            // \sum_{edge \in Edges} \{ x_{edge} * costPerFlowUnit_{edge} 
            // + y_{node} * creationCost_{node} \}
            this.Model.AddObjective(
                new Objective(Expression.Sum(this.Edges.Select(edge => x[edge] * edge.CostPerFlowUnit)) +
                              Expression.Sum(this.Nodes.Select(node => y[node] * node.CreationCost)),
                "sum of all cost",
                ObjectiveSense.Minimize) // minimize
            );
        }

        /// <summary>
        /// Gets the Model instance
        /// </summary>
        public Model Model { get; private set; }

        /// <summary>
        /// Gets the edges of this network
        /// </summary>
        public List<IEdge> Edges { get; }

        /// <summary>
        /// Gets the nodes of this network
        /// </summary>
        public List<INode> Nodes { get; }

        /// <summary>
        /// Gets the Collection of all flow variables
        /// </summary>
        public VariableCollection<IEdge> x { get; }

        /// <summary>
        /// Gets the Collection of all design variables
        /// </summary>
        public VariableCollection<INode> y { get; }
    }
}

Next Step

• Retrieving the Solution