A Multi-stage Optimisation Approach to Design Relocation Strategies in One-way Car-sharing Systems with Stackable Cars

TL;DR

A multi-stage decision support system for vehicle relocation that decomposes the general relocation problem into three independent decision stages to allow scalable solutions and finds that stackable vehicles can achieve a relocation performance close to that of autonomous cars, even with a small workforce of relocators.

Abstract

One of the main operational challenges faced by the operators of one-way car-sharing systems is to ensure vehicle availability across the regions of the service areas with uneven patterns of rental requests. Fleet balancing strategies are required to maximise the demand served while minimising the relocation costs. However, the design of optimal relocation policies is a complex problem, and global optimisation solutions are often limited to very small network sizes for computational reasons. In this work, we propose a multi-stage decision support system for vehicle relocation that decomposes the general relocation problem into three independent decision stages to allow scalable solutions. Furthermore, we adopt a rolling horizon control strategy to cope with demand uncertainty. Our approach is highly modular and flexible, and we leverage it to design user-based, operator-based and robotic relocation schemes. Besides, we formulate the relocation problem considering both conventional cars and a new class of compact stackable vehicles that can be driven in a road train. We compare the proposed relocation schemes with two recognised benchmarks using a large data set of taxi trips in New York. Our results show that our approach is scalable and outperforms the benchmark schemes in terms of quality of service, vehicle utilisation and relocation efficiency. Furthermore, we find that stackable vehicles can achieve a relocation performance close to that of autonomous cars, even with a small workforce of relocators.

Figures (7)

• Figure 1: The ESPRIT train of vehicles.
• Figure 2: Functional architecture of the multi-stage decision support system for vehicle relocation we propose in this study. The blocks in the diagram represent the main components of the systems with the input and output variables. Variable $v^k_i$ and $b_{i}^{k}$ denotes the available vehicles and the vehicle inventory imbalance, respectively, of station $i$ at the decision point $k$, while $x_{ij}^{k}$ is the relocation flow from station $i$ to station $j$ during the $k$-th decision interval. The formal definition of these variables is provided in Section \ref{['sec:relocation']}.
• Figure 3: Illustrative timeline of the relocation decision process with $n_C=10$, $n_R=25$ and $n_O=75$ time slots. Circles represent the time points when relocation decisions are taken
• Figure 4: Examples of the virtual inventory level of a (a) feeder station and a (b) receiver station. Orange circles denote vehicle arrivals, while green circles denote customers' trip requests. Initial inventory level $v^k_i=2$. Both cases include four vehicle arrivals and four customers' trip requests in total, but different time orders.
• Figure 5: Example of relocation decisions for operator $o_u$ at decision interval $k$ in the case $y^k_{uijl}=1$.