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Mathematics
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Operations Research and Optimization: Mathematical Methods and Applications
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Operations Research and Optimization: Mathematical Methods and Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: 31 March 2025 | Viewed by 9170

Special Issue Editors

Prof. Dr. David Canca

E-Mail Website
Guest Editor
Department of Industrial Engineering and Management Science, Universidad de Sevilla, 41092 Seville, Spain
Interests: transportation; logistics; production planning and scheduling; network optimization; heuristics and metaheuristics
Prof. Dr. Gabriel Villa

E-Mail Website
Guest Editor
Department of Industrial Engineering and Management Science, University of Seville, 41092 Seville, Spain
Interests: data envelopment analysis; network optimization; multiobjective optimization; metaheuristic optimization; OR in sports

Special Issue Information

Dear Colleagues,

Operations research is an applied science focused on formulating and solving quantitative decision problems in a wide variety of areas, such as operations management, transportation and logistics, telecommunications, energy generation and distribution, financing, healthcare, and public services management, among others. This Special Issue aims to serve as a platform to disseminate recent research in this field, both theoretical and applied, in the most distinct operations research application areas. Submissions including new theoretical results, models and algorithms, and new applications are welcome. Potential topics include but are not limited to:

  • Integer linear programming and combinatorial optimization problems;
  • Exact integer and combinatorial solving methods and techniques: branch-and-bound, brunch-and-cut, decomposition-based methods, reformulations, linearizations;
  • Approximated solving methods: heuristics, meta-heuristics, metaheuristics, and model-based metaheuristics for integer and combinatorial optimization problems; hybridized approaches;
  • Real-world OR applications in industry and services: operations management, supply chain management, logistics and transportation, production planning, scheduling, energy, telecommunications, location, and healthcare.

Prof. Dr. David Canca
Prof. Dr. Gabriel Villa
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 100 words) can be sent to the Editorial Office for announcement on this website.

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

  • integer programming and combinatorial optimization
  • exact optimization methods
  • approximated optimization methods
  • OR applications

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Published Papers (6 papers)

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Research

16 pages, 1467 KiB  
Article
An Iterated Local Search Heuristic for the Multi-Trip Vehicle Routing Problem with Multiple Time Windows
by Yinghui Wu, Haoran Du and Huixin Song
Mathematics 2024, 12(11), 1712; https://doi.org/10.3390/math12111712 - 30 May 2024
Cited by 1 | Viewed by 790
Abstract
This paper studies the multi-trip vehicle routing problem with multiple time windows, which extends the multi-trip vehicle routing problem by deciding not only the sequence of customers that each vehicle serves but also the service time window of each customer. It also requires [...] Read more.
This paper studies the multi-trip vehicle routing problem with multiple time windows, which extends the multi-trip vehicle routing problem by deciding not only the sequence of customers that each vehicle serves but also the service time window of each customer. It also requires that the delivery service time is within the selected time windows and that the total demand of the customers served by the vehicle on each trip does not exceed the maximum carrying capacity. For solving the studied problem, we develop a mixed integer linear programming model with the objective of minimizing the total travel distance of vehicles and design a tailored iterative local search heuristic. Within the framework of the iterative local search, an improved Solomon greedy insertion algorithm suitable for multiple time windows and multi-trip scenarios is designed to generate the initial solution, and local search operators such as Or-opt and Relocate, as well as Random Exchange perturbation operations, are also developed. The experiment results demonstrate the effectiveness of the proposed model and algorithm and confirm that by providing customers with multiple time windows option, carriers can flexibly plan vehicle routes and select appropriate service time windows, thereby reducing the number of vehicles used and the total distance travelled and improve delivery success. Full article
(This article belongs to the Special Issue Operations Research and Optimization: Mathematical Methods and Applications)
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20 pages, 341 KiB  
Article
Tropical Modeling of Battery Swapping and Charging Station
by Nikolai Krivulin and Akhil Garg
Mathematics 2024, 12(5), 644; https://doi.org/10.3390/math12050644 - 22 Feb 2024
Cited by 1 | Viewed by 967
Abstract
We propose and investigate a queueing model of a battery swapping and charging station (BSCS) for electric vehicles (EVs). A new approach to the analysis of the queueing model is developed, which combines the representation of the model as a stochastic dynamic system [...] Read more.
We propose and investigate a queueing model of a battery swapping and charging station (BSCS) for electric vehicles (EVs). A new approach to the analysis of the queueing model is developed, which combines the representation of the model as a stochastic dynamic system with the use of the methods and results of tropical algebra, which deals with the theory and applications of algebraic systems with idempotent operations. We describe the dynamics of the queueing model by a system of recurrence equations that involve random variables (RVs) to represent the interarrival time of incoming EVs. A performance measure for the model is defined as the mean operation cycle time of the station. Furthermore, the system of equations is represented in terms of the tropical algebra in vector form as an implicit linear state dynamic equation. The performance measure takes on the meaning of the mean growth rate of the state vector (the Lyapunov exponent) of the dynamic system. By applying a solution technique of vector equations in tropical algebra, the implicit equation is transformed into an explicit one with a state transition matrix with random entries. The evaluation of the Lyapunov exponent reduces to finding the limit of the expected value of norms of tropical matrix products. This limit is then obtained using results from the tropical spectral theory of deterministic and random matrices. With this approach, we derive a new exact formula for the mean cycle time of the BSCS, which is given in terms of the expected value of the RVs involved. We present the results of the Monte Carlo simulation of the BSCS’s operation, which show a good agreement with the exact solution. The application of the obtained solution to evaluate the performance of one BSCS and to find the optimal distribution of battery packs between stations in a network of BSCSs is discussed. The solution may be of interest in the case when the details of the underlying probability distributions are difficult to determine and, thus, serves to complement and supplement other modeling techniques with the need to fix a distribution. Full article
(This article belongs to the Special Issue Operations Research and Optimization: Mathematical Methods and Applications)
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12 pages, 396 KiB  
Article
Performance of a Synchronisation Station with Abandonment
by Dieter Fiems
Mathematics 2024, 12(5), 628; https://doi.org/10.3390/math12050628 - 21 Feb 2024
Viewed by 615
Abstract
The paper presents a Markovian queueing model for assessing the performance of synchronisation between stations in a production system. The system at hand consists of K distinct buffers, each buffer storing an item that is needed for the next production stage. Departures are [...] Read more.
The paper presents a Markovian queueing model for assessing the performance of synchronisation between stations in a production system. The system at hand consists of K distinct buffers, each buffer storing an item that is needed for the next production stage. Departures are immediate when all items are present. Due to the presence of multiple buffers, there is no reasonably fast way to calculate the stationary distribution of the Markov chain. Therefore, we focused on the series expansion of the stationary distribution in terms of the arrival rate. We provide a fast algorithm for calculating these terms. Comparing our results with stochastic simulation, we show that the expansion approach converges to the simulated values for a wide range of arrival rates. Full article
(This article belongs to the Special Issue Operations Research and Optimization: Mathematical Methods and Applications)
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18 pages, 1221 KiB  
Article
A Truthful Reverse Auction Mechanism for Federated Learning Utility Maximization Resource Allocation in Edge–Cloud Collaboration
by Linjie Liu, Jixian Zhang, Zhemin Wang and Jia Xu
Mathematics 2023, 11(24), 4968; https://doi.org/10.3390/math11244968 - 15 Dec 2023
Viewed by 1229
Abstract
Federated learning is a promising technique in cloud computing and edge computing environments, and designing a reasonable resource allocation scheme for federated learning is particularly important. In this paper, we propose an auction mechanism for federated learning resource allocation in the edge–cloud collaborative [...] Read more.
Federated learning is a promising technique in cloud computing and edge computing environments, and designing a reasonable resource allocation scheme for federated learning is particularly important. In this paper, we propose an auction mechanism for federated learning resource allocation in the edge–cloud collaborative environment, which can motivate data owners to participate in federated learning and effectively utilize the resources and computing power of edge servers, thereby reducing the pressure on cloud services. Specifically, we formulate the federated learning platform data value maximization problem as an integer programming model with multiple constraints, develop a resource allocation algorithm based on the monotone submodular value function, devise a payment algorithm based on critical price theory and demonstrate that the mechanism satisfies truthfulness and individual rationality. Full article
(This article belongs to the Special Issue Operations Research and Optimization: Mathematical Methods and Applications)
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36 pages, 13632 KiB  
Article
A Multilayer Network Approach for the Bimodal Bus–Pedestrian Line Planning Problem
by David Canca, Belén Navarro-Carmona, Gabriel Villa and Alejandro Zarzo
Mathematics 2023, 11(19), 4185; https://doi.org/10.3390/math11194185 - 6 Oct 2023
Viewed by 1139
Abstract
In this paper, we formulate and solve the urban line planning problem considering a multilayer representation of a bimodal transportation network. Classical formulations are usually constructed over a planar network, which implies the need to introduce several strong non-linearities in terms of frequencies [...] Read more.
In this paper, we formulate and solve the urban line planning problem considering a multilayer representation of a bimodal transportation network. Classical formulations are usually constructed over a planar network, which implies the need to introduce several strong non-linearities in terms of frequencies when modeling transfer times. In the proposed network representation, each candidate line is stored in a specific layer and the passengers’ movements for each origin–destination pair are modelled considering a strategy subgraph, contributing to a sparse model formulation that guarantees feasibility and simplifies the assignment process. The methodology is first tested using the Mandl network, obtaining results that are comparable in terms of quality with the best metaheuristic approaches proposed in the scientific literature. With the aim of testing its applicability to large scenarios, the proposed approach is then used to design the main urban transit network of Seville, a large scenario with 141 nodes and 454 links, considering artificial unfavorable demand data. The reasonable computation time required to exactly solve the problem to optimality confirms the possibility of using the multilayer approach to deal with multimodal network design strategic problems. Full article
(This article belongs to the Special Issue Operations Research and Optimization: Mathematical Methods and Applications)
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16 pages, 1360 KiB  
Article
A Combinatorial Optimization Approach for Air Cargo Palletization and Aircraft Loading
by Xiangling Zhao, Yun Dong and Lei Zuo
Mathematics 2023, 11(13), 2798; https://doi.org/10.3390/math11132798 - 21 Jun 2023
Cited by 1 | Viewed by 3519
Abstract
The current air cargo loading plan handles the Air Cargo Palletization Problem (ACPP) and the Aircraft Weight and Balance Problem (WBP) separately, which has an impact on the optimization of the payload and the aircraft’s center of gravity (CG). Thanks to improvements in [...] Read more.
The current air cargo loading plan handles the Air Cargo Palletization Problem (ACPP) and the Aircraft Weight and Balance Problem (WBP) separately, which has an impact on the optimization of the payload and the aircraft’s center of gravity (CG). Thanks to improvements in computer processing power, the joint combinatorial optimization of ACPP and WBP is now feasible. Three integer linear programming models are proposed: a Bi-objective Optimization Model (BOM), a Combinatorial Optimization Model (COM), and an Improved Combinatorial Optimization Model (IOM). The objectives of the models are the maximum loading capacity and the lowest CG deviation from a specified target CG. The models also consider a wide range of restrictions in the actual packing and stowage procedures, such as volume, weight, loading position, aircraft balance, and other aspects of aircraft and unit load devices. Four scenarios with various conditional metrics for three models are solved for the B777F aircraft using Gurobi. The results of the computations demonstrate that the BOM has the fastest solution speed, but the CG deviation is the largest, and in several cases the CG deviation results are unacceptable. The COM has the longest solution time, which is difficult to tolerate in practice. Despite taking a little longer to solve computationally than the BOM, the IOM offers the best optimization solution. Full article
(This article belongs to the Special Issue Operations Research and Optimization: Mathematical Methods and Applications)
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