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Mathematics
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New Advance in Operations Research and Analytics
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New Advance in Operations Research and Analytics

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

Deadline for manuscript submissions: 30 June 2024 | Viewed by 6016

Special Issue Editors

Dr. Ehsan Ahmadi

E-Mail Website
Guest Editor
School of Business, Mercer University, Atlanta, GA 30341, USA
Interests: operations research; data mining; machine learning; supply chain management; inventory management; metaheuristics
Dr. Reza Maihami

E-Mail Website
Guest Editor
Department of Management & Marketing, East Tennessee State University, Johnson City, TN 37614, USA
Interests: operations research; supply chain management; inventory management; revenue management; game theory; machine learning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Operations research (OR) and analytics are two important scientific processes that are used to study, analyze, and translate data of complex problems into useful insights to make better decisions. They enable organizations to tackle complex issues by identifying the problem, examining all available alternatives, predicting outcomes carefully, and estimating the risk. As a result, this improves daily operations, enhances communication and information sharing, reduces waste, increases productivity and efficiency, and provides higher customer satisfaction.

This Special Issue brings together state-of-the-art OR methods with their integration with analytics techniques such as machine learning to provide a collection of high-quality papers. We invite contributions for covering a wide range of topics, including (but not limited to): deterministic and stochastic mathematical models, linear programming, mixed integer linear programming, robust optimization, integrating mathematical models with supervised, unsupervised, and reinforcement machine learning methods, among others. We welcome papers that apply these methods to emerging real-world problems in the healthcare, finance, marketing, supply chain, and economy.

Dr. Ehsan Ahmadi
Dr. Reza Maihami
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

  • operations research
  • machine learning
  • metaheuristics
  • mathematical optimization models
  • linear programming
  • mixed integer linear programming
  • robust optimization

Published Papers (5 papers)

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Research

8 pages, 259 KiB  
Article
Two-Person Stochastic Duel with Energy Fuel Constraint Ammo
by Song-Kyoo (Amang) Kim
Mathematics 2023, 11(17), 3625; https://doi.org/10.3390/math11173625 - 22 Aug 2023
Viewed by 737
Abstract
This paper deals with a novel variation of the versatile stochastic duel game that incorporates an energy fuel constraint into a two-player duel game. The energy fuel not only measures the vitality of players but also determines the power of the shooting projectile. [...] Read more.
This paper deals with a novel variation of the versatile stochastic duel game that incorporates an energy fuel constraint into a two-player duel game. The energy fuel not only measures the vitality of players but also determines the power of the shooting projectile. The game requires players to carefully balance their energy usage, while trying to outmaneuver their opponent. This unique theoretical framework for the stochastic game model provides a valuable method for understanding strategic behavior in competitive environments, particularly in decision-making scenarios with fluctuating processes. The proposed game provides players with the challenge of optimizing their energy fuel usage, while managing the risk of losing the game. This novel model has potential for implementation across diverse fields, as it allows for a versatile conception of energy fuel. These energy fuels may encompass conventional forms, such as natural gas, petroleum, and electrical power, and even financial budgets, human capital, and temporal resources. The unique rules and constraints of the game in this research are expected to contribute insights into the decision-making strategies and behaviors of players in a wide range of practical applications. This research primarily focuses on deriving compact closed-form solutions, utilizing transformation and flexible analysis techniques adapted to varying the concept of the energy fuel level. By presenting a comprehensive description of our novel analytical approach and its application to the proposed model, this study aims to elucidate the fundamental principles underlying the energy fuel constraint stochastic duel game model. Full article
(This article belongs to the Special Issue New Advance in Operations Research and Analytics)
14 pages, 301 KiB  
Article
Approximate Subdifferential of the Difference of Two Vector Convex Mappings
by Abdelghali Ammar, Mohamed Laghdir, Ahmed Ed-dahdah and Mohamed Hanine
Mathematics 2023, 11(12), 2718; https://doi.org/10.3390/math11122718 - 15 Jun 2023
Viewed by 648
Abstract
This paper deals with the strong approximate subdifferential formula for the difference of two vector convex mappings in terms of the star difference. This formula is obtained via a scalarization process by using the approximate subdifferential of the difference of two real convex [...] Read more.
This paper deals with the strong approximate subdifferential formula for the difference of two vector convex mappings in terms of the star difference. This formula is obtained via a scalarization process by using the approximate subdifferential of the difference of two real convex functions established by Martinez-Legaz and Seeger, and the concept of regular subdifferentiability. This formula allows us to establish approximate optimality conditions characterizing the approximate strong efficient solution for a general DC problem and for a multiobjective fractional programming problem. Full article
(This article belongs to the Special Issue New Advance in Operations Research and Analytics)
26 pages, 3365 KiB  
Article
A Data-Driven Decision-Making Model for Configuring Surgical Trays Based on the Likelihood of Instrument Usages
by Ehsan Ahmadi, Dale T. Masel and Seth Hostetler
Mathematics 2023, 11(9), 2219; https://doi.org/10.3390/math11092219 - 08 May 2023
Viewed by 1507
Abstract
In order to perform a surgical procedure, substantial numbers of sterile instruments should be readily available to surgeons through the containers referred to as surgical trays and peel packs. After the procedure, all instruments in the opened containers, regardless of whether they have [...] Read more.
In order to perform a surgical procedure, substantial numbers of sterile instruments should be readily available to surgeons through the containers referred to as surgical trays and peel packs. After the procedure, all instruments in the opened containers, regardless of whether they have been used or not, must go through the labor-intensive re-sterilization process. Empirical studies have shown that the utilization rate of instruments within trays is very low due to not having optimized tray configurations. Additionally, surgical trays often include instruments that are not likely to be used but are included “just in case”, which imposes an additional cost on hospitals through unnecessary instrument re-sterilization. This study is the first analytical attempt to address the issue of configuring surgical trays based on the likelihood of instrument usage through formulating and solving a probabilistic tray optimization problem (PTOP). The PTOP model can serve as a decision support for surgeons by providing them with the tray’s probability of being used for optimally configured trays and its associated reprocessing costs. The PTOP is constructed upon an integer non-linear programming model. A decomposition-based heuristic and metaheuristic method coupled with two novel local search algorithms are developed to solve the PTOP. The application of this model can be illustrated through a case study. We discuss how hospitals could benefit from our model in reducing the costs associated with opening trays unnecessarily before a procedure. Additionally, we conducted a risk analysis to estimate the level of confidence for the recommended solution. Full article
(This article belongs to the Special Issue New Advance in Operations Research and Analytics)
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22 pages, 858 KiB  
Article
Application of an Intensive Longitudinal Functional Model with Multiple Time Scales in Objectively Measured Children’s Physical Activity
by Mostafa Zahed, Trent Lalonde and Maryam Skafyan
Mathematics 2023, 11(8), 1973; https://doi.org/10.3390/math11081973 - 21 Apr 2023
Viewed by 1233
Abstract
This study proposes an intensive longitudinal functional model with multiple time-varying scales and subject-specific random intercepts through mixed model equivalence that includes multiple functional predictors, one or more scalar covariates, and one or more scalar covariates. An estimation framework is proposed for estimating [...] Read more.
This study proposes an intensive longitudinal functional model with multiple time-varying scales and subject-specific random intercepts through mixed model equivalence that includes multiple functional predictors, one or more scalar covariates, and one or more scalar covariates. An estimation framework is proposed for estimating a time-varying coefficient function that is modeled as a linear combination of time-invariant functions with time-varying coefficients. The model takes advantage of the information structure of the penalty, while the estimation procedure utilizes the equivalence between penalized least squares estimation and linear mixed models. A number of simulations are conducted in order to empirically evaluate the process. In the simulation, it was observed that mean square errors for functional coefficients decreased with increasing sample size and level of association. Additionally, sample size had a greater impact on a smaller level of association, and level of association also had a greater impact on a smaller sample size. These results provide empirical evidence that ILFMM estimates of functional coefficients are close to the true functional estimate (basically unchanged). In addition, the results indicated that the AIC could be used to guide the choice of ridge weights. Moreover, when ridge weight ratios were sufficiently large, there was minimal impact on estimation performance. Studying two time scales is important in a wide range of fields, including physics, chemistry, biology, engineering, economics, and more. It allows researchers to gain a better understanding of complex systems and processes that operate over different time frames. Consequently, studying physical activities with two time scales is critical for advancing our understanding of human performance and health and for developing effective strategies to optimize physical activity and exercise programs. Therefore, the proposed model was applied to analyze the physical activity data from the Active Schools Institute of the University of Northern Colorado to determine what kind of time-structure patterns of activities could adequately describe the relationship between daily total magnitude and kids’ daily and weekly physical activity. Full article
(This article belongs to the Special Issue New Advance in Operations Research and Analytics)
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19 pages, 1176 KiB  
Article
Impact of Government Environmental Regulations on Remanufacturing Supply Chain with Multi-Subject Responsibility for Recycling and Disposal
by Xiao Jiang, Qiang Hu, Tingyuan Lou, Wenjin Zuo and Jicai Li
Mathematics 2023, 11(8), 1780; https://doi.org/10.3390/math11081780 - 08 Apr 2023
Cited by 1 | Viewed by 1089
Abstract
With the emergence of a large number of waste electronic products and the enhancement of social awareness of environmental protection, the recycling of waste electronic products has become one of the pressing issues of social concern. Government environmental regulation is an important policy [...] Read more.
With the emergence of a large number of waste electronic products and the enhancement of social awareness of environmental protection, the recycling of waste electronic products has become one of the pressing issues of social concern. Government environmental regulation is an important policy to promote the development of the remanufacturing industry. In this paper, we study the government levies recycling and disposal fees on original products for environmental governance and establish two game models based on the perspective of maximizing social welfare with no government regulation and a tripartite liability system. The optimal decisions on wholesale, retail prices and quantity of original and remanufactured products, as well as the recycling and disposal fee are analyzed under both models. Based on the numerical results, the impact of the main parameter (such as the responsibility sharing ratio) on the decisions and profits of the parties is discussed. The results show that (1) the wholesale and retail prices of remanufactured products are not affected by government regulation; (2) the tripartite liability system can increase the output of remanufactured products and reduce the output of original products while cutting the profits of remanufacturing supply chain members, and increasing social welfare; (3) government’s optimal recycling and disposal fee is not related to the sharing ratio. The study can provide practitioners with suggestions for ways to develop environmental regulation. Full article
(This article belongs to the Special Issue New Advance in Operations Research and Analytics)
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