Dynamic pricing for vehicle ferries: Using packing and simulation to optimize revenues

We propose an heuristic approach to the vehicle ferry revenue management problem, where the aim is to maximize the revenue obtained from the sale of vehicle tickets by varying the prices charged to different vehicle types, each occupying a different amount of deck space. Customers arrive and purchase tickets according to their vehicle type and their willingness-to-pay, which typically increases over time because customers purchasing tickets closer to departure tend to accept higher prices. The optimization problem can be solved using dynamic programming but the possible states in the selling season are the set of all feasible vehicle mixes that fit onto the ferry. This makes the problem intractable as the number of vehicle types and ferry size increases. We propose a state space reduction, which uses a vehicle ferry loading simulator to map each vehicle mix to a remaining-space state. This reduces the state space of the dynamic program. Our approach allows the value function to be approximated rapidly and accurately with a relatively coarse discretization of states. We present simulations of the selling season using this reduced state space to validate the method. The vehicle ferry loading simulator was developed in collaboration with a vehicle ferry company and addresses real-world constraints such as manoeuvrability, elevator access, strategic parking gaps, vehicle height constraints and ease of implementation of the packing solutions.