۱- Introduction

۲- Related literature

۳- Case study

۴- Dynamic pricing

۵- Load optimizer

۶- Numerical experiments

۷- Discussion

References

Abstract

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.

Introduction

Vehicle ferries are used to transport passengers and their vehicles and, for many island populations, they can be the sole means of transporting goods, as well as providing a service to commuters and tourists. The global ferry market in 2012 was valued at over $15 billion, carrying more than 2 billion passengers and 350 million vehicles. Space on the vehicle deck is typically the binding constraint and managing prices to ensure efficient use of the available space is an important problem. In this article we describe an heuristic pricing algorithm that takes into account the efficiency of the packing, and practical considerations such as vehicle manoeuvrability when setting prices for different vehicle types, ranging from large freight vehicles to motorcycles. Customer arrivals into the booking system are stochastic and a customer will purchase a ticket with a probability dependent on the price, their vehicle type and the time left until departure. This assumption allows us to use price as a lever of demand to push towards more efficient and profitable vehicle mixes, where a vehicle mix is defined as the number of vehicles of each type. While this article is focused on vehicle ferries, a similar problem is encountered in other industries, e.g., sale of advertising time on radio or television channels, setting costs for bespoke manufacturing, and other freight transportation applications. We use dynamic programming to set prices, where the state of the dynamic program gives an indication of the space remaining on the ferry. To obtain an exact solution, the states of the dynamic program should correspond to the mix of vehicles that have already purchased tickets for the ferry and in other work we describe how to obtain exact solutions using a combination of mixed integer linear programming and dynamic pricing (see MartinezSykora, Currie, So, Bayliss, & Bennell, 2017).