The Vehicle Routing Problem with Time Windows (VRPTW) is the extension of the Capacitated Vehicle Routing Problem (CVRP) where the service at each customer must start within an associated time interval, called a time window. Time windows may be hard or soft. In case of hard time windows, a vehicle that arrives too early at a customer must wait until the customer is ready to begin service. In general, waiting before the start of a time window incurs no cost. In the case of soft time windows, every time window can be violated barring a penalty cost. The time windows may be one-sided, e.g., stated as the latest time for delivery. Time windows arise naturally in problems faced by business organizations which work on flexible time schedules. Specific problems with hard time windows include security patrol service, bank deliveries, postal deliveries, industrial refuse collection, grocery delivery, school bus routing, and urban newspaper distribution. Among the soft time window problems, dial-a-ride problems constitute an important example.
The Vehicle Routing Problem with Time Windows (VRPTW) is the extension of the Capacitated Vehicle Routing Problem (CVRP) where the service at each customer must start within an associated time interval, called a time window. Time windows may be hard or soft. In case of hard time windows, a vehicle that arrives too early at a customer must wait until the customer is ready to begin service. In general, waiting before the start of a time window incurs no cost. In the case of soft time windows, every time window can be violated barring a penalty cost. The time windows may be one-sided, e.g., stated as the latest time for delivery. Time windows arise naturally in problems faced by business organizations which work on flexible time schedules. Specific problems with hard time windows include security patrol service, bank deliveries, postal deliveries, industrial refuse collection, grocery delivery, school bus routing, and urban newspaper distribution. Among the soft time window problems, dial-a-ride problems constitute an important example.