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Nodes and bookings (orders)

The Vehicle Routing Problem (VRP) revolves around efficiently delivering goods or services to a set of customers. Two fundamental concepts underpin the VRP: nodes and orders.

Nodes:

In the context of the VRP, a node represents a location. This can be a customer's location, a warehouse or depot (where vehicles start and end their routes), or any other point that requires a visit. Nodes are typically represented as points on a map or in a network, with associated coordinates or addresses. The depot is often designated as a special node, serving as the origin and destination for all vehicle routes.  

Orders:

An order represents a request for delivery or service. Each order is associated with a specific node (the customer location) and specifies the quantity of goods to be delivered or the service to be performed. Orders can also have other attributes, such as time windows, priority levels, or specific product requirements. In essence, orders define what needs to be delivered and where.  

The Relationship Between Nodes and Orders:

Nodes and orders are inextricably linked. Each order is tied to at least two nodes, indicating the delivery location and pickup location. The collection of all orders defines the set of nodes that must be visited by the vehicles. The VRP's objective is to determine the optimal routes for vehicles to visit all the nodes associated with the orders, satisfying the demand of each order while minimizing costs (e.g., travel distance, time, or number of vehicles).  

Here's a breakdown of how they relate:

  • Orders define node visits: Each order necessitates a visit to its corresponding node.
  • Nodes are locations for orders: Nodes represent the geographical locations where orders need to be fulfilled.
  • The set of orders determines the set of customer nodes: The number and location of customer nodes are directly derived from the orders.
  • The depot node is the origin and destination for all routes: While orders are associated with customer nodes, all routes start and end at the depot node.

In the SWAT model, each order (booking) consists of at least two nodes (one for drop-off and another for pick-up). Additionally, all vehicles and any extra waypoints are also internally represented as nodes.