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Dr Jianghang Chen and Dr Jianyu Xu from the International Business School Suzhou (IBSS) at Xi¡¯an Jiaotong-ºìÐÓÊÓƵ University (XJTLU), together with Dr Iris ?a?gatay from the University of ºìÐÓÊÓƵ and PhD candidate Ruicheng Liu, have had their latest research published in Transportation Research Part E. The journal is ranked JCR Q1, CAS Tier 1 and ABDC A*, with an ABS 3 rating, enjoying solid academic standing across global logistics and transport research communities.

Owing to one-way travel patterns, bike-sharing services regularly suffer from unbalanced station inventory, with certain hubs running out of bikes and others lacking available docking spaces. Conventional management approaches optimise inventory separately for individual stations and adopt the classic predict-then-optimise (PTO) framework. Such methods overlook riders¡¯ roaming behaviour: users unable to borrow or return bikes at their original stations may walk to nearby docks or abandon trips entirely, resulting in lost orders. In addition, forecasting errors get amplified in subsequent optimisation calculations, leading to inefficient bike reallocation and excessive compensation costs for operators. Against these practical drawbacks, the research team develops a network-wide optimisation framework.

Two Core Innovations

1. Aggregated Customer Roaming Behaviour Model

Different from prior simplistic assumptions that dissatisfied customers drop trips immediately, this study constructs an aggregated behavioural model which distinguishes bike borrowers and returners. Key parameters including roaming willingness, walking distance sensitivity and minimum available bikes at qualifying stops are incorporated to quantify users¡¯ choices of nearby stations or trip abandonment, reflecting real-world travel dynamics and laying a behavioural foundation for network-level scheduling.

2. Original End-to-End Deep Learning Framework

Breaking the split predict-then-optimise structure, the proposed E2E model integrates LSTM and fully connected neural networks. It takes raw operational data such as historical trips, station capacities and geographical layouts as inputs and directly outputs optimal bike relocation volumes across the whole network. The team also devises an integer linear programming (ILP) labelling method to generate high-quality training labels, resolving the labelling difficulty for non-linear, non-convex inventory problems. This labelling approach can be extended to broader inventory management scenarios.

Empirical Results

The team validates the model using real operational data from five districts of New York Citi Bike and Boston Bluebikes, focusing on the peak window from 17:00 to 20:00.

1. Compared with multiple PTO benchmarks and fixed-capacity heuristic policies, the E2E model cuts user dissatisfaction costs by up to nearly 80 and reduces lost orders and compensation payouts significantly.
2. While traditional optimisation algorithms take hundreds of seconds per calculation, the E2E model finishes inference within 1¨C3 seconds, supporting real-time operational adjustment.
3. Network-based optimisation incorporating roaming behaviours effectively eliminates unnecessary vehicle transfers and lowers overall operating expenses.

Practical Recommendations for Operators

Based on comprehensive sensitivity tests, the research offers three actionable

suggestions for bike and e-bike platforms:

1. Guide users via APP notifications or on-site signs to boost returners¡¯ roaming willingness and cut compensation spending.
2. Set dynamic minimum bike thresholds for individual stations according to local passenger flow to balance surplus inventory and stock-out losses.
3. Adopt tiered compensation rules aligned with average trip revenue to avoid profit erosion from improper payout standards.

Author Profiles

Dr Jianghang CHEN is an associate professor of IBSS, XJTLU. Dr CHEN¡¯s researches focus on the mathematical modeling for complex systems such as supply chain, logistics transportation, and manufacturing etc., the development of intelligent decision-support tools, and the application of optimization and simulation techniques.

Jianyu Xu is currently an associate professor in Management, IBSS, Xian-Jiaotong ºìÐÓÊÓƵ University. Jianyu got his Bachelor degree in Statistics from Peking University in 2012. Later, he got his PhD degree jointly in Statistics from Chinese Academy of Sciences and in System Engineering and Engineering Safety from City University of Hong Kong. His research interest is in reinforcement learning, quality and reliability engineering and industrial statistics.

Journal Introduction

Published by Elsevier,?Transportation Research Part E?is a well-regarded international journal covering logistics, supply chain and shared mobility research (JCR Q1, CAS Tier 1, ABDC A*, ABS 3). It maintains strict peer-review standards and publishes high-quality empirical works widely referenced by academia and industry practitioners.

By Linlin Xie

Edited by Thomas Durham