A vehicle routing problem requires that a fleet of vehicles make deliveries to customers within specified time windows.

Each customer j must take delivery between ej and dj, and vehicle i requires time pijk to travel from customer j to customer k.

The objective is to minimize the number of vehicles.

Describe a Benders-based solution method in which the master problem assigns customers to vehicles and the sub problem routes each vehicle.

The sub problem for each vehicle is a traveling salesman problem with time windows. The sub problem can be written with variable indices and the circuit constraint , although it would be desirable to design a metaconstraint specifically for traveling salesman problems with time windows.