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Mathematics
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Recent Advances in Planning and Scheduling for Supply Chain Optimization
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Recent Advances in Planning and Scheduling for Supply Chain Optimization

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D2: Operations Research and Fuzzy Decision Making".

Deadline for manuscript submissions: 30 June 2026 | Viewed by 7052

Special Issue Editors

Prof. Dr. Danyu Bai

E-Mail Website
Guest Editor
School of Maritime Economics and Management, Dalian Maritime University, Dalian 116026, China
Interests: production scheduling; combination optimization; evolutionary computation
Special Issues, Collections and Topics in MDPI journals
Dr. Dehua Xu

E-Mail Website
Guest Editor
School of International Economics and Business, Nanjing University of Finance & Economics, Nanjing 210023, China
Interests: machine scheduling; approximation algorithm; process optimization
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The intellectualization and greenization of supply chains are driving transformative innovations in optimization theories and operation techniques, enabling enterprises to achieve cost reduction and efficiency enhancement. Recent advancements in smart technologies (e.g., big data, cloud computing, and AI) have intensified academic and industrial focus on the optimization of planning and scheduling—the decision-making cores of supply chain management. Numerous successful applications have been presented in supply chain domains, including order processing, product manufacture, equipment assembly, warehousing and transportation, etc.

This Special Issue aims to collect up-to-date and high-quality studies incorporating novel methods on planning and scheduling in the area of supply chain optimization, as well as to promote developments and applications of operations research theory and methods in relevant fields. In this Special Issue, original research articles and reviews are welcome. Research areas may include (but are not limited to) the following:

  • Scheduling in advanced manufacturing;
  • Logistics scheduling and optimization;
  • AI-based planning and scheduling;
  • Routing optimization in distribution;
  • Data-driven production scheduling;
  • Optimization for facility location.

We look forward to receiving your contributions.

Prof. Dr. Danyu Bai
Dr. Dehua Xu
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • planning and scheduling
  • production scheduling
  • logistics optimization
  • facility location
  • combination optimization
  • evolutionary computation
  • machine learning

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Published Papers (7 papers)

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Research

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27 pages, 3243 KB  
Article
Multiple Waste Crane Scheduling Based on Cooperative Optimization of Discrete Ivy Algorithm and Simulated Annealing
by Liang Wu, Donghao Huang, Jiaxiang Luo, Cuihong Luo, Gang Yi and Tao Liang
Mathematics 2026, 14(6), 980; https://doi.org/10.3390/math14060980 - 13 Mar 2026
Viewed by 313
Abstract
Efficient scheduling of co-rail waste cranes is critical for ensuring continuous incinerator operation and reducing energy costs in waste-to-energy plants. Existing scheduling methods fail to address the unique characteristics of waste crane operations like task heterogeneity and dynamic spatial interference. To address this, [...] Read more.
Efficient scheduling of co-rail waste cranes is critical for ensuring continuous incinerator operation and reducing energy costs in waste-to-energy plants. Existing scheduling methods fail to address the unique characteristics of waste crane operations like task heterogeneity and dynamic spatial interference. To address this, a mixed-integer linear programming model is established to minimize the total crane traveling distance and task delays. A two-stage Discrete Ivy-Simulated Annealing (DIVY-SA) algorithm is proposed: the Ivy algorithm (IVYA) is discretized to generate high-quality task sequences, which are then refined by Simulated Annealing (SA) via a fine-grained local search. A heuristic task assignment scheme and a discrete-event simulation module are designed to evaluate task sequences accurately. Experiments using real-world operational data from a waste incineration plant cover task scales of 25 to 200, representing scheduling horizons of 15 min to 2 h. The algorithm’s runtime (15.04–652.81 s) demonstrates computational feasibility for near-real-time scheduling via a rolling horizon strategy. Results show that DIVY-SA outperforms representative metaheuristic algorithms and reduces the average total traveling distance by 22.19% compared with manual scheduling. This work provides technical support for the intelligent upgrading of waste incineration plants, effectively cutting energy consumption and improving operational efficiency. Full article
(This article belongs to the Special Issue Recent Advances in Planning and Scheduling for Supply Chain Optimization)
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33 pages, 10743 KB  
Article
Bi-Level Optimization for Multi-UAV Collaborative Coverage Path Planning in Irregular Areas
by Hua Gong, Ziyang Fu, Ke Xu, Wenjuan Sun, Wanning Xu and Mingming Du
Mathematics 2026, 14(3), 416; https://doi.org/10.3390/math14030416 - 25 Jan 2026
Viewed by 535
Abstract
Multiple Unmanned Aerial Vehicle (UAV) collaborative coverage path planning is widely applied in fields such as regional surveillance. However, optimizing the trade-off between deployment costs and task execution efficiency remains challenging. To balance resource costs and execution efficiency with an uncertain number of [...] Read more.
Multiple Unmanned Aerial Vehicle (UAV) collaborative coverage path planning is widely applied in fields such as regional surveillance. However, optimizing the trade-off between deployment costs and task execution efficiency remains challenging. To balance resource costs and execution efficiency with an uncertain number of UAVs, this paper analyzes the characteristics of irregular mission areas and formulates a bi-level optimization model for multi-UAV collaborative CPP. The model aims to minimize both the number of UAVs and the total path length. First, in the upper level, an improved Best Fit Decreasing algorithm based on binary search is designed. Straight-line scanning paths are generated by determining the minimum span direction of the irregular regions. Task allocation follows a longest-path-first, minimum-residual-range rule to rapidly determine the minimum number of UAVs required for complete coverage. Considering UAV’s turning radius constraints, Dubins curves are employed to plan transition paths between scanning regions, ensuring path feasibility. Second, the lower level transforms the problem into a Multiple Traveling Salesman Problem that considers path continuity, range constraints, and non-overlapping path allocation. This problem is solved using an Improved Biased Random Key Genetic Algorithm. The algorithm employs a variable-length master–slave chromosome encoding structure to adapt to the task allocation of each UAV. By integrating biased crossover operators with 2-opt interval mutation operators, the algorithm accelerates convergence and improves solution quality. Finally, comparative experiments on mission regions of varying scales demonstrate that, compared with single-level optimization and other intelligent algorithms, the proposed method reduces the required number of UAVs and shortens the total path length, while ensuring complete coverage of irregular regions. This method provides an efficient and practical solution for multi-UAV collaborative CPP in complex environments. Full article
(This article belongs to the Special Issue Recent Advances in Planning and Scheduling for Supply Chain Optimization)
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26 pages, 2510 KB  
Article
A Three-Machine Flowshop Scheduling Problem with Linear Fatigue Effect
by Weiping Xu, Zehou Sun, Xiaotian Ai, Baoyun Zhao, Jingyi Lu, Hanyu Zhou, Xinqi Mao, Xiaoling Wen, Chin-Chia Wu and Shufeng Liu
Mathematics 2025, 13(22), 3670; https://doi.org/10.3390/math13223670 - 16 Nov 2025
Viewed by 787
Abstract
Highly customized requirements in smart manufacturing result in the unavoidable manual execution of complex operational procedures. Physical and mental fatigue from long work periods for assembly-line operators induces production issues, such as defective work-in-processes or equipment failure. An effective production schedule should account [...] Read more.
Highly customized requirements in smart manufacturing result in the unavoidable manual execution of complex operational procedures. Physical and mental fatigue from long work periods for assembly-line operators induces production issues, such as defective work-in-processes or equipment failure. An effective production schedule should account for worker fatigue. This study investigates a three-machine flowshop scheduling problem with the objective of makespan minimization, in which a linear fatigue effect function provides an approximate mathematical representation of fatigue and recovery processes in workers. A mixed integer programming (MIP) model is developed to optimize the integration of automated and human-operated production in manufacturing systems. Given its NP-hardness, an improved tabu search (ITS) algorithm is designed to obtain high-quality solutions, incorporating multiple initial solutions, a well-designed encoding-decoding strategy, and a tabu-based adaptive search mechanism to enhance efficiency. Numerical simulations indicate the veracity of the MIP model and the effectiveness of the ITS algorithm. Full article
(This article belongs to the Special Issue Recent Advances in Planning and Scheduling for Supply Chain Optimization)
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32 pages, 2409 KB  
Article
Rolling Horizon Optimization of Allocation-Location in Agricultural Emergency Supply Chains
by Qinxi Shi, Yiping Jiang and Jie Chu
Mathematics 2025, 13(18), 2967; https://doi.org/10.3390/math13182967 - 13 Sep 2025
Viewed by 1978
Abstract
Ensuring the smooth production and distribution of agricultural products is a crucial pathway to achieving a balance between supply and demand. However, the information within the agricultural product supply chain is characterized by its dynamic and asymmetric nature, compounded by frequent outbreaks of [...] Read more.
Ensuring the smooth production and distribution of agricultural products is a crucial pathway to achieving a balance between supply and demand. However, the information within the agricultural product supply chain is characterized by its dynamic and asymmetric nature, compounded by frequent outbreaks of infectious diseases that lead to supply interruptions and allocation difficulties. These factors collectively undermine the operational efficiency and resilience of the agricultural product supply chain. This study develops an integrated allocation-location optimization model for emergency agricultural product supply chains based on a rolling horizon approach. The model accounts for both supply shortage and sufficient scenarios, with objectives to maximize the comprehensive material satisfaction rate, minimize the activation cost of distribution centers, and minimize allocation time. The proposed model is solved using the Benders decomposition algorithm. Finally, a case study based on the Shanghai pandemic outbreak is conducted for numerical simulation. The results demonstrate the effectiveness of the model: the comprehensive material satisfaction rate increases progressively over the rolling periods, rising from approximately 84% in period 1 to 100% by period 3. Furthermore, fairness analysis confirms that the model also effectively ensures equitable distribution of supplies. Full article
(This article belongs to the Special Issue Recent Advances in Planning and Scheduling for Supply Chain Optimization)
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22 pages, 764 KB  
Article
An Integrated Entropy–MAIRCA Approach for Multi-Dimensional Strategic Classification of Agricultural Development in East Africa
by Chia-Nan Wang, Duy-Oanh Tran Thi, Nhat-Luong Nhieu and Ming-Hsien Hsueh
Mathematics 2025, 13(15), 2465; https://doi.org/10.3390/math13152465 - 31 Jul 2025
Cited by 3 | Viewed by 1278
Abstract
Agricultural development is vital for East Africa’s economic growth, yet the region faces significant disparities and systemic barriers. A critical problem exists due to the lack of an integrated quantitative framework to systematically comparing agricultural capacities and facilitate optimal resource allocation, as existing [...] Read more.
Agricultural development is vital for East Africa’s economic growth, yet the region faces significant disparities and systemic barriers. A critical problem exists due to the lack of an integrated quantitative framework to systematically comparing agricultural capacities and facilitate optimal resource allocation, as existing studies often overlook combined internal and external factors. This study proposes a comprehensive multi-criteria decision-making (MCDM) model to assess, categorize, and strategically profile the agricultural development capacity of 18 East African countries. The method employed is an integrated Entropy-MAIRCA model, which objectively weighs six criteria (the food production index, arable land, production fluctuation, food export/import ratios, and the political stability index) and ranks countries by their distance from an ideal development state. The experiment applied this framework to 18 East African nations using official data. The results revealed significant differences, forming four distinct strategic groups: frontier, emerging, trade-dependent, and high risk. The food export index (C4) and production volatility (C3) were identified as the most influential criteria. This model’s contribution is providing a science-based, transparent decision support tool for designing sustainable agricultural policies, aiding investment planning, and promoting regional cooperation, while emphasizing the crucial role of institutional factors. Full article
(This article belongs to the Special Issue Recent Advances in Planning and Scheduling for Supply Chain Optimization)
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20 pages, 2268 KB  
Article
Improved Fuel Consumption Estimation for Sailing Speed Optimization: Eliminating Log Transformation Bias
by Qi Hong, Xuecheng Tian, Yong Jin, Zhiyuan Liu and Shuaian Wang
Mathematics 2025, 13(12), 1987; https://doi.org/10.3390/math13121987 - 16 Jun 2025
Cited by 2 | Viewed by 992
Abstract
Sailing Speed Optimization (SSO) is a crucial problem in shipping operations management, aiming to reduce both operating costs and carbon dioxide emissions. The ship’s sailing speed directly impacts fuel consumption, where fuel consumption is generally assumed to follow a power function with respect [...] Read more.
Sailing Speed Optimization (SSO) is a crucial problem in shipping operations management, aiming to reduce both operating costs and carbon dioxide emissions. The ship’s sailing speed directly impacts fuel consumption, where fuel consumption is generally assumed to follow a power function with respect to sailing speed. Previous studies have used transformation-based fitting methods, such as logarithmic transformations, to investigate the relationship between sailing speed and fuel consumption using historical data. However, these methods introduce estimation bias and heteroskedasticity, violating the core assumptions of Ordinary Least Squares (OLS) used for general linear regression. To address these issues, we propose two novel fitting methods that directly optimize the original nonlinear model without relying on transformations. By analyzing the characteristics of the objective function, we derive parameter constraints and integrate them into a discrete optimization framework, resulting in improved fitting accuracy. Our methods are validated through extensive case studies, demonstrating their effectiveness in enhancing the reliability of SSO decisions. These methods offer a practical approach to optimizing fuel consumption in real-world maritime operations. Full article
(This article belongs to the Special Issue Recent Advances in Planning and Scheduling for Supply Chain Optimization)
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Review

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29 pages, 4240 KB  
Review
Considering the Impact of Adverse Weather: Integrated Scheduling Optimization of Berths and Quay Cranes
by Jianing Zhao, Hongxing Zheng and Mingyu Lv
Mathematics 2026, 14(3), 475; https://doi.org/10.3390/math14030475 - 29 Jan 2026
Viewed by 361
Abstract
To promptly address the disruptions caused by various sudden weather events to the normal operations of the quay apron, this study focuses on the optimization of integrated berth and quay crane (QC) scheduling under the impact of adverse weather. It emphasizes two key [...] Read more.
To promptly address the disruptions caused by various sudden weather events to the normal operations of the quay apron, this study focuses on the optimization of integrated berth and quay crane (QC) scheduling under the impact of adverse weather. It emphasizes two key influences of adverse weather: port closures and the uncertainty in vessel handling times induced by weather conditions. A decision mechanism is designed, and strategies such as vessel dispatch, cargo omission, and backhaul are incorporated. Meanwhile, constraints including the prohibition of QC crossover and the spatio-temporal limitations on vessel berthing are taken into account. With the optimization objective of minimizing the total scheduling cost, a mixed-integer programming (MIP) model is constructed. A variable neighborhood search (VNS) algorithm is developed for solving the model, which proposes multi-layer encoding and a corresponding hybrid initialization strategy. Finally, comparative experiments are conducted to verify the effectiveness of the model and the rationality of the algorithm. Sensitivity analysis is also performed on the duration of port closures and QC handling efficiency. The research results can provide decision support for ports in formulating response strategies against adverse weather. Full article
(This article belongs to the Special Issue Recent Advances in Planning and Scheduling for Supply Chain Optimization)
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