Capacitated Vehicle Routing Problem (CVRP) with Preference

The Capacitated Vehicle Routing Problem with Preference (CVRP with Preference) modifies the standard CVRP by considering individual customer preferences or priorities. This variant optimizes routes not only based on the capacity and distance but also integrates preference metrics which may dictate the sequence or selection of customer visits. This adaptation is particularly relevant in service industries where customer satisfaction is paramount, enabling companies to tailor their logistical operations to better meet specific customer needs and build competitive advantage.

At each step, the agent chooses a customer to visit depending on the current location and the remaining capacity. When the agent visits a customer, the remaining capacity is updated. If the remaining capacity is not enough to visit any customer, the agent must go back to the depot. Each agent has it's preferred area. The reward is 0 unless the agent visits all the cities. In that case, the reward is (-)length of the path: maximizing the reward is equivalent to minimizing the path length.

Observations

• location of the depot.
• locations and demand of each customer.
• current location of the vehicle.
• the remaining customer of the vehicle.
• the preference matrix of vehicles.

Constrains

• the tour starts and ends at the depot.
• each customer must be visited exactly once.
• the vehicle cannot visit customers exceed the remaining capacity.
• the vehicle can return to the depot to refill the capacity.

Finish Condition

• the vehicle has visited all customers and returned to the depot.

Reward

• (minus) the negative length of the path with preference punishment.