Mathematical Methods and Operation Research in Planning, Scheduling and Supply Chain Operations Management

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 30 November 2025 | Viewed by 5074

Special Issue Editors


E-Mail Website1 Website2
Guest Editor
Engineering Department, Universidad Nacional del Sur INMABB-CONICET, Bahia Blanca 8000, Argentina
Interests: industrial engineering; optimization; scheduling; operations research
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Guest Editor
Faculty of Mathematics, Otto-von-Guericke-University, P.O. Box 4120, D-39016 Magdeburg, Germany
Interests: scheduling; development of exact and approximate algorithms; stability investigations; discrete optimization; scheduling with interval processing times; complex investigations for scheduling problems; train scheduling; graph theory; logistics; supply chains; packing; simulation; applications
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent times, there have been vertiginous changes made to industrial systems, giving rise to profound transformations in the way decision-making processes are approached in operation environments. These modifications are associated with the growing level of digitization of processes and operations, which increases and improves the decision-making capacity due to a higher level of information being available. Likewise, this digitization allows for the integration into the same management system of tools capable of processing data and solving situations in an autonomous way and in an optimal manner. Therefore, these transformations allow for the integration of different operational research tools that are needed at each operations management level.

On the other hand, the growing demands to reduce the environmental impact of industrial operations have generated a specific need for the design of tools that allow the optimization of processes in order to ensure sustainability. In this Special Issue, a sustainable approach aligned with the UN SDG agenda is considered, and it is expected to encourage the development of OR methods and tools capable of addressing these needs.

For this Special Issue, we encourage authors to make contributions that highlight the most advanced and innovative ideas addressing operations planning problems. Operations planning can address short-term problems, as well as tactical or strategic decisions. Contributions that manage to add theoretical contributions to the existing body of knowledge are welcome, as are works on applications and study cases where the application of operations research is innovative. 

Potential topics of OR applications include, but are not limited to:

  • Intelligent manufacturing systems;
  • Intelligent operations management;
  • Data-driven production planning;
  • OR methods applied to green manufacturing;
  • Machine learning approaches in manufacturing systems operations;
  • Operations management;
  • Sustainable management;
  • Cyber-physical production systems;
  • Analytics models and inventory control;
  • Production networks;
  • Assembly line and production planning;
  • Scheduling problems;
  • Decision making in supply chain management;
  • Digital twin implementations in production environments;
  • Closed-loop supply chains.

Dr. Daniel A. Rossit
Prof. Dr. Frank Werner
Guest Editors

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Keywords

  • operations research
  • production planning
  • supply chain, optimization
  • operations Management
  • decision making

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Published Papers (5 papers)

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Research

19 pages, 3165 KiB  
Article
Improving Scheduling Efficiency: A Mathematical Approach to Multi-Operation Optimization in MSMEs
by Reyner Pérez-Campdesuñer, Alexander Sánchez-Rodríguez, Margarita De Miguel-Guzmán, Gelmar García-Vidal and Rodobaldo Martínez-Vivar
Mathematics 2025, 13(9), 1444; https://doi.org/10.3390/math13091444 - 28 Apr 2025
Viewed by 154
Abstract
Optimizing the use of resources is a key aspect of organizational management. Various methods have been developed and applied to optimize different variables, including sequencing methods that aim to minimize work time. This paper presents an integrated approach for optimizing the sequencing of [...] Read more.
Optimizing the use of resources is a key aspect of organizational management. Various methods have been developed and applied to optimize different variables, including sequencing methods that aim to minimize work time. This paper presents an integrated approach for optimizing the sequencing of operations, considering indicators such as usage time, completion time, waiting time, delivery delay, and flow time. A multi-criteria optimization method with weighted aggregation was used, employing either an exhaustive search or a heuristic algorithm with nested loops, in which multiple possible combinations of operational sequences were evaluated, considering several key indicators and their respective weights. The application of the methodology in a press validated its effectiveness, providing managers with key information to prioritize the indicators according to their needs, whether optimizing resource usage or minimizing waiting times and delays. The application resulted in a 95.3% improvement in the level of utilization; a 79.3% reduction in the average completion time; a 90.5% reduction in machine waiting time; and a 90.9% decrease in product delivery delay. The results show that prioritizing the objective function leads to a balanced optimization of all indicators, improving operational efficiency and reducing flow time. This study contributes to the body of knowledge on production scheduling by offering a novel multi-criteria optimization approach in manufacturing settings. The validated methodology can be adapted to a variety of industries and offers flexibility to align with the specific interests of each organization. Full article
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23 pages, 493 KiB  
Article
Flow Shop Scheduling with Shortening Jobs for Makespan Minimization
by Zheng-Wei Sun, Dan-Yang Lv, Cai-Min Wei and Ji-Bo Wang
Mathematics 2025, 13(3), 363; https://doi.org/10.3390/math13030363 - 23 Jan 2025
Cited by 3 | Viewed by 526
Abstract
This paper deals with a two-machine flow shop problem with shortening jobs. A shortening job means that the job’s processing time is a decreasing function of its starting time. The aim is to find a sequence that minimizes the makespan of all the [...] Read more.
This paper deals with a two-machine flow shop problem with shortening jobs. A shortening job means that the job’s processing time is a decreasing function of its starting time. The aim is to find a sequence that minimizes the makespan of all the jobs. several dominance properties, some lower bounds, and an initial upper bound are derived, which are applied to propose a branch-and-bound algorithm to solve the problem. We also propose some heuristics and mathematical programming. Computational experiments are conducted to evaluate the performance of the proposed algorithms. Full article
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22 pages, 828 KiB  
Article
Deep Q-Networks for Minimizing Total Tardiness on a Single Machine
by Kuan Wei Huang and Bertrand M. T. Lin
Mathematics 2025, 13(1), 62; https://doi.org/10.3390/math13010062 - 27 Dec 2024
Cited by 1 | Viewed by 699
Abstract
This paper considers the single-machine scheduling problem of total tardiness minimization. Due to its computational intractability, exact approaches such as dynamic programming algorithms and branch-and-bound algorithms struggle to produce optimal solutions for large-scale instances in a reasonable time. The advent of Deep Q-Networks [...] Read more.
This paper considers the single-machine scheduling problem of total tardiness minimization. Due to its computational intractability, exact approaches such as dynamic programming algorithms and branch-and-bound algorithms struggle to produce optimal solutions for large-scale instances in a reasonable time. The advent of Deep Q-Networks (DQNs) within the reinforcement learning paradigm could be a viable approach to transcending these limitations, offering a robust and adaptive approach. This study introduces a novel approach utilizing DQNs to model the complexities of job scheduling for minimizing tardiness through an informed selection utilizing look-ahead mechanisms of actions within a defined state space. The framework incorporates seven distinct reward-shaping strategies, among which the Minimum Estimated Future Tardiness strategy notably enhances the DQN model’s performance. Specifically, it achieves an average improvement of 14.33% over Earliest Due Date (EDD), 11.90% over Shortest Processing Time (SPT), 17.65% over Least Slack First (LSF), and 8.86% over Apparent Tardiness Cost (ATC). Conversely, the Number of Delayed Jobs strategy secures an average improvement of 11.56% over EDD, 9.10% over SPT, 15.01% over LSF, and 5.99% over ATC, all while requiring minimal computational resources. The results of a computational study demonstrate DQN’s impressive performance compared to traditional heuristics. This underscores the capacity of advanced machine learning techniques to improve industrial scheduling processes, potentially leading to decent operational efficiency. Full article
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37 pages, 5410 KiB  
Article
Emergency Supply Alternatives for a Storage Facility of a Repairable Multi-Component System
by Yonit Barron and Chananel Benshimol
Mathematics 2024, 12(17), 2730; https://doi.org/10.3390/math12172730 - 31 Aug 2024
Viewed by 1198
Abstract
This paper studies a continuous-review stochastic replenishment model for a multi-component system with regular and emergency orders. The system consists of N parallel and independent components, each of which has a finite life span. In addition, there is a warehouse with a limited [...] Read more.
This paper studies a continuous-review stochastic replenishment model for a multi-component system with regular and emergency orders. The system consists of N parallel and independent components, each of which has a finite life span. In addition, there is a warehouse with a limited stock of new components. Each broken component is replaced by a new component from the stock. When no component is available, an emergency supply is ordered. The stock is managed according to an ((s,S),(0,Qe)) policy, which is a combination of an (s,S) policy for the regular order and a (0,Qe) policy for the emergency order. The regular order is delivered after an exponentially distributed lead time, whereas the emergency order is delivered immediately. We study three sub-policies for emergency orders, which differ from each other in size and in relation to the regular order. Applying the results from queueing theory and phase-type properties, we derive the optimal thresholds for each sub-policy and then compare the economic benefit of each one. Full article
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16 pages, 323 KiB  
Article
Developing New Bounds for the Performance Guarantee of the Jump Neighborhood for Scheduling Jobs on Uniformly Related Machines
by Felipe T. Muñoz, Guillermo Latorre-Núñez and Mario Ramos-Maldonado
Mathematics 2024, 12(1), 6; https://doi.org/10.3390/math12010006 - 19 Dec 2023
Cited by 1 | Viewed by 1088
Abstract
This study investigates the worst-case performance guarantee of locally optimal solutions to minimize the total weighted completion time on uniformly related parallel machines. The investigated neighborhood structure is Jump, also called insertion or move. This research focused on establishing the local optimality condition [...] Read more.
This study investigates the worst-case performance guarantee of locally optimal solutions to minimize the total weighted completion time on uniformly related parallel machines. The investigated neighborhood structure is Jump, also called insertion or move. This research focused on establishing the local optimality condition expressed as an inequality and mapping that maps a schedule into an inner product space so that the norm of the mapping is closely related to the total weighted completion time of the schedule. We determine two new upper bounds for the performance guarantee, which take the form of an expression based on parameters that describe the family of instances: the speed of the fastest machine, the speed of the slowest machine, and the number of machines. These new bounds outperform the parametric upper bound previously established in the existing literature and enable a better understanding of the performance of the solutions obtained for the Jump neighborhood in this scheduling problem, according to parameters that describe the family of instances. Full article
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