Preface to the Special Issue on “Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling, 2nd Edition”

In the last decade, the Fourth Industrial Revolution (Industry 4.0) brought to the fore flexible supply chains and flexible design projects. More recently, the COVID-19 pandemic, the economic problems that accompanied it, and the resulting supply issues have further increased the role of logistics and supply chains. Therefore, planning and scheduling procedures that can respond flexibly to changing circumstances have become more valuable in both logistics and projects.

There are already several competing criteria in project and logistics process planning and scheduling that need to be reconciled. Additionally, the pandemic has shown that even more emphasis needs to be placed on taking potential risks into account. Flexibility and resilience are emphasized in all decision-making processes, including the scheduling of logistics processes, activities, and projects.

The aim of this Special Issue was to gather novel, original publications that offer new methods and approaches in the field of planning and scheduling in logistics and project planning that are able to respond to the challenges of a dynamic environment.

The present Special Issue of the MDPI journal Mathematics, titled “Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling, 2nd Edition”, contains a total of eight articles that cover a wide range of topics related to the theory, models, and applications of project planning, project scheduling, and operation research problems in logistics. These topics include, among others, scheduling problems, research allocation problems in project planning, routing and warehousing problems in logistics, and risk aggregation problems in risk assessments.

In Contribution 1, Wang et al. develop a resilient supply chain optimization model that considers both proactive and reactive defense strategies to address disruptions caused by events like the COVID-19 pandemic. The model aims to maximize the expected profit by determining optimal raw material inventory, temporary distribution center locations, and product design changes in response to supply disruptions and distribution center failures. The study contributes to logistics and operations research by providing a comprehensive approach to improving supply chain resilience, demonstrating how combining strategies like inventory mitigation, temporary facility locations, and product redesign can significantly reduce losses during major disruptions.

In Contribution 2, Zhang et al. present a multi-objective Q-learning-based brain storm optimization (MQBSO) algorithm to solve an integrated distributed flow shop and distribution scheduling problem. The proposed MQBSO outperforms other metaheuristics in obtaining promising solutions, as demonstrated through extensive numerical experiments and statistical tests. The study contributes to operations research, particularly scheduling problems, by addressing a novel integrated production and distribution problem in a distributed manufacturing environment and introducing an effective solution method that combines reinforcement learning with metaheuristics.

In Contribution 3, Xu et al. propose a novel shared bicycle demand prediction method based on station clustering and a deep learning model called GCN-GRU-AM. This approach outperforms other models in predicting bicycle demand across different regions and time periods. The study contributes to logistics and transportation research by improving resource allocation and bicycle management in shared bicycle systems, while also advancing machine learning applications through the development of a hybrid deep learning model that effectively captures spatial–temporal patterns in bicycle usage data.

In Contribution 4, Nirenjan et al. analyze a complex queueing system with multiple control policies, including two-phase bulk service, active Bernoulli feedback, server breakdowns, and vacations. The authors derive a probability-generating function for queue size and various performance measures using supplementary variable techniques. The model has practical applications in optimizing power efficiency in LTE-A networks using the Discontinuous Reception (DRX) mechanism, contributing to the research fields of telecommunications and operations.

In Contribution 5, Leon et al. propose a two-step methodology combining heuristic algorithms and simulation techniques to optimize task sequencing for Automated Guided Vehicles (AGVs) in manufacturing environments. The developed heuristic algorithms, particularly MLRF/LPTF, consistently outperform the NEH-based approach in minimizing makespan, with improvements ranging from 16.82% to 19.49% on average across various instances. The study contributes to the field of operations and logistics research by addressing the complex challenge of AGV task sequencing with resource sharing and dynamic queues, offering a scalable solution that can handle large instances and potentially be extended to stochastic settings.

In Contribution 6, Mihalcz and Kosztyán describe how incorporating additional factors beyond the traditional three used in FMEA (Severity, Occurrence, and Detection) can lead to a more comprehensive risk assessment in supply chains. Specifically, their study demonstrates that adding Cost and Control as factors and using a fuzzy logic approach results in a more accurate identification of significant risks. The proposed framework, TREF (Total Risk Evaluation Framework), offers supply chain managers a practical tool to evaluate their processes, regardless of the mathematical foundations or the variety of variables utilized in risk assessment.

In Contribution 7, Ni et al. investigate a two-machine group scheduling problem with sequence-independent setup times and round-trip transportation times, derived from steel manufacturing requirements. The authors develop a mixed-integer programming model to minimize makespan and propose a two-stage heuristic algorithm for an NP-hard case of a single transporter, which achieves solutions within 1.38% of lower bounds for large problem instances. The study contributes to the fields of both scheduling and transportation by incorporating round-trip transportation times and limited transportation capacity constraints into the group scheduling problem, advancing our understanding of coordinated scheduling decisions with restricted material flows in multi-stage manufacturing settings.

Finally, in Contribution 8, Souse et al. propose a novel approach to the fuzzy multi-item newsvendor problem for inventory management applications. The main contributions of their study include a new credibility estimation to explore impactful demand scenarios, a simulation procedure for comparing different fuzzy MINP approaches, and a modified genetic algorithm to enhance solution generation and evaluation. The proposed hybrid algorithm significantly outperformed previous fuzzy approaches, improving profit by up to 55% in low-budget scenarios, and slightly outperformed classical approaches in complex cases.

Collectively, these eight studies enhance our theoretical understanding and provide practical methodologies that may be immediately implemented and modified across various sectors. This collection successfully addresses the complex issues encountered by contemporary logistics and scheduling systems by integrating heuristic approaches, stochastic optimization, and real-world supply chain scenarios.

This volume will serve as a vital reference for researchers, practitioners, and decision-makers aiming to create and operate efficient, robust, and flexible logistics and scheduling systems.

As Guest Editors of this Special Issue, we are grateful to all authors who contributed their articles. We would also like to express our gratitude to all reviewers for their valuable comments on improving the submitted papers. The goal of this Special Issue was to attract quality and novel papers in the field of “Mathematical Methods and Operation Research in Logistics, Project Planning, and Scheduling”. We hope that the international scientific community finds the included research papers impactful, and that these contributions will motivate further operations research on solving complex problems in various disciplines and application fields.