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Mathematical Modelling and Optimization for Sustainable Operations Management
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Mathematical Modelling and Optimization for Sustainable Operations Management

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

Deadline for manuscript submissions: 15 December 2024 | Viewed by 9755

Special Issue Editor

Prof. Dr. Elias Olivares-Benitez

E-Mail Website
Guest Editor
Faculty of Engineering, Universidad Panamericana, Guadalajara 45010, Mexico
Interests: operations research; logistics and supply chain management; text and data analytics; metaheuristics; manufacturing and materials; technological competitive intelligence
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues, 

The Special Issue of Mathematics, entitled "Mathematical Modelling and Optimization for Sustainable Operations Management", focuses on the application of mathematical models and optimization techniques to enhance sustainable operations management. Sustainability has been linked with development by the World Commission on Environment and Development (WCED), which defines it as "development that meets the needs of the present without compromising the ability of future generations to meet their own needs''. The United Nations has proposed 17 sustainable development goals (SDGs). As such, sustainable operations management is of increasingly greater interest and importance for practice and research world, in which some modeling and optimization problems have been paid special attention. These include dynamic scheduling and planning, supply chain collaboration, location and allocation problems, inventory problems, vehicle routing problems, etc. There is rising interest from mathematical modelers on the topic of incorporating aspects of sustainability into their models. 

In this Special Issue, we are interested in the modeling and optimization to sustainable operations management in a broad sense. The aim of this Special Issue is to bring together high-quality contributions in multiple application fields tackling real-world optimization problems where mathematical programming-based methods are used. A particular interest of this Issue is to attract relevant state-of-the-art contributions that analyze and provide insights and knowledge regarding applied methodologies in this field, especially for sustainable operations management. This includes the applications of mathematical modelling and optimization techniques to any aspect associated with the UN sustainable development goals. This includes, but is not limited to, the following topics: 

  • Mathematical methods for sustainable supply chain collaboration;
  • Mathematical programming-based sustainable inventory management;
  • Mathematical optimization for closed loop supply chains;
  • Optimization and modes for waste reduction, recycling, and reuse in supply chains;
  • Stochastic programming and optimization for green logistics and transportation;
  • Mathematical and statistical analysis of efficiency for sustainable operations management practices;
  • Game theory in sustainable operations management;
  • Multicriteria evaluation and optimization for green manufacturing;
  • Optimization in dynamic planning and scheduling for sustainable operations management;
  • Models for 4.0 technologies applied to UN sustainable development goals.

Prof. Dr. Elias Olivares-Benitez
Guest Editor

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

  • mathematical programming
  • multicriteria optimization
  • dynamic programming and optimization
  • stochastic programming and optimization
  • game theory
  • sustainable operations research
  • green logistics and transportation

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Published Papers (6 papers)

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Research

20 pages, 593 KiB  
Article
An Inventory Service-Level Optimization Problem for a Multi-Warehouse Supply Chain Network with Stochastic Demands
by Roberto León, Pablo A. Miranda-Gonzalez, Francisco J. Tapia-Ubeda and Elias Olivares-Benitez
Mathematics 2024, 12(16), 2544; https://doi.org/10.3390/math12162544 - 17 Aug 2024
Viewed by 909
Abstract
This research aims to develop a mathematical model and a solution approach for jointly optimizing a global inventory service level and order sizes for a single-commodity supply chain network with multiple warehouses or distribution centers. The latter face stochastic demands, such as most [...] Read more.
This research aims to develop a mathematical model and a solution approach for jointly optimizing a global inventory service level and order sizes for a single-commodity supply chain network with multiple warehouses or distribution centers. The latter face stochastic demands, such as most real-world supply chains do nowadays, yielding significant model complexity. The studied problem is of high relevance for inventory management, inventory location, and supply chain network design-related literature, as well as for logistics and supply chain managers. The proposed optimization model minimizes the total costs associated with cycle inventory, safety stock, and stock-out-related events, considering a global inventory service level and differentiated order sizes for a fixed and known set of warehouses. Subsequently, the model is solved by employing the Newton–Raphson algorithm, which is developed and implemented assuming stochastic demands with a normal approximation. The algorithm reached optimality conditions and the convergence criterion in a few iterations, within less than a second, for a variety of real-world sized instances involving up to 200 warehouses. The model solutions are contrasted with those obtained with a previous widely employed approximation, where safety stock costs were further approximated and order sizes were optimized without considering stock-out-related costs. This comparison denotes valuable benefits without significant additional computational efforts. Thus, the proposed approach is suitable for managers of real-world supply chains, since they would be able to attain system performance improvements by simultaneously optimizing the global inventory service level and order sizes, thereby providing a better system cost equilibrium. Full article
(This article belongs to the Special Issue Mathematical Modelling and Optimization for Sustainable Operations Management)
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25 pages, 1709 KiB  
Article
Modeling and Solution Algorithm for Green Lock Scheduling Problem on Inland Waterways
by Ziyun Wu, Bin Ji and Samson S. Yu
Mathematics 2024, 12(8), 1192; https://doi.org/10.3390/math12081192 - 16 Apr 2024
Cited by 1 | Viewed by 962
Abstract
Inland navigation serves as a vital component of transportation, boasting benefits such as ample capacity and minimal energy consumption. However, it also poses challenges related to achieving navigation efficiency and environmental friendliness. Locks, which are essential for inland waterways, often cause ship passage [...] Read more.
Inland navigation serves as a vital component of transportation, boasting benefits such as ample capacity and minimal energy consumption. However, it also poses challenges related to achieving navigation efficiency and environmental friendliness. Locks, which are essential for inland waterways, often cause ship passage bottlenecks. This paper focuses on a green lock scheduling problem (GLSP), aiming to minimize fuel emissions and maximize navigation efficiency. Considering the realistic constraints, a mixed-integer linear programming model and a large neighborhood search solution algorithm are proposed. From a job shop scheduling perspective, the problem is decomposed into three main components: ship-lockage assignment, ship placement subproblem, and lockage scheduling subproblem coupled with ship speed optimization. A large neighborhood search algorithm based on a decomposition framework (LNSDF) is proposed to tackle the GLSP. In this, the complex lockage scheduling problem is addressed efficiently by mapping it to a network planning problem and applying the critical path method. Numerical experiments substantiate the effectiveness of our proposed model and a heuristic approach was used in solving the GLSPs. In the sensitivity analysis, under three different objective weight assignments, the resulting solutions achieved average effective ship fuel savings of 4.51%, 8.86%, and 2.46%, respectively. This indicates that our green lock scheduling problem considering ship speed optimization can enhance ship passage efficiency while reducing carbon emissions. Full article
(This article belongs to the Special Issue Mathematical Modelling and Optimization for Sustainable Operations Management)
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21 pages, 3046 KiB  
Article
Optimal Shipping Route under the Designation of the Mediterranean Sulfur Emission Control Area: Mathematical Models and Applications
by Haoqing Wang, Yuan Liu, Ying Yang, Ran Yan and Shuaian Wang
Mathematics 2023, 11(24), 4897; https://doi.org/10.3390/math11244897 - 7 Dec 2023
Viewed by 1386
Abstract
In order to tackle sulfur oxides (SOx) emissions from maritime activities, both local governmental bodies and the International Maritime Organization (IMO) have implemented a range of regulations with the establishment of sulfur emission control areas (SECAs) being one crucial measure. [...] Read more.
In order to tackle sulfur oxides (SOx) emissions from maritime activities, both local governmental bodies and the International Maritime Organization (IMO) have implemented a range of regulations with the establishment of sulfur emission control areas (SECAs) being one crucial measure. Recently, the IMO made the significant decision to designate the Mediterranean as an SECA, aiming to promote environmental conservation as well as sustainable development in the maritime industry and mitigate the adverse health effects caused by air pollutants emitted from ships in Mediterranean regions. While this policy signifies significant progress in the reduction of sulfur emissions, it simultaneously presents intricate challenges for maritime enterprises. Notably, under the Mediterranean SECA designation, shipping companies may opt to bypass this region and choose routes through the Cape of Good Hope as a means of minimizing the overall costs, resulting in a potential increase in global carbon emissions. To support shipping companies in formulating optimal strategies within the framework of this new policy, the research introduces advanced techniques to make the optimal decisions concerning route selection, sailing speeds, and the appropriate number of ships for both SECAs and non-SECAs. Furthermore, we elucidate how these optimal decisions can be dynamically adapted in response to the dynamic fluctuations in fuel prices and the weekly operational expenditures incurred by maritime fleets. In the experimental results, taking into account factors like route distance and fuel costs, shipping companies select routes through the Mediterranean region in both eastward and westward directions. The total cost amounts to $6,558,766.78, utilizing eight vessels. Regarding ship speeds, vessels sail at reduced speeds in SECAs compared to non-SECAs. Furthermore, longer voyage distances require deploying a greater number of ships to maintain a weekly service frequency. This research exhibits robust timeliness and practicality, which is in line with practice. It not only timely supplements and enhances the extant body of knowledge concerning SECAs but also serves as a valuable point of reference and emulation for shipping companies seeking to optimize their operations within the framework of the new policy landscape. Furthermore, it offers pertinent insights for the IMO in formulating policies related to SECAs. Full article
(This article belongs to the Special Issue Mathematical Modelling and Optimization for Sustainable Operations Management)
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20 pages, 430 KiB  
Article
Optimal Sailing Speeds and Time Windows in Inland Water Transportation Operations Management: Mathematical Models and Applications
by Haoqing Wang, Yuan Liu, Yong Jin and Shuaian Wang
Mathematics 2023, 11(23), 4747; https://doi.org/10.3390/math11234747 - 24 Nov 2023
Cited by 1 | Viewed by 1859
Abstract
Inland waterway transportation plays a pivotal role in advancing economic development and nurturing sustainable progress. It serves as a vital conduit linking communities, industries, and markets, thereby facilitating the seamless flow of essential commodities and fostering regional integration. However, in today’s era, marked [...] Read more.
Inland waterway transportation plays a pivotal role in advancing economic development and nurturing sustainable progress. It serves as a vital conduit linking communities, industries, and markets, thereby facilitating the seamless flow of essential commodities and fostering regional integration. However, in today’s era, marked by a resolute commitment to environmental responsibility and sustainability, inland shipping confronts formidable challenges, particularly pertaining to emission pollution and the escalating costs of fuel. These challenges represent significant impediments to the pursuit of environmentally conscious and sustainable growth by shipping companies. This research endeavor is geared towards the creation of a mathematical model that takes into account various factors, including the types of waterways, temporal constraints, and punctual arrival at the port of discharge. The primary objective is to empower shipping companies to make informed decisions about optimal sailing speeds and the most opportune time windows for entering one-way waterway segments. This, in turn, leads to reductions in fuel costs and waiting times for shipping companies, all while achieving cost minimization and mitigating emissions issues in inland waterway transportation. Ultimately, this research advances the cause of green and sustainable development in the inland waterway shipping sector. Specifically, this study focuses on routes that involve the dynamic transition between one-way and two-way segments. To accomplish this, an integer programming (IP) model is proposed to meticulously analyze the ideal sailing speed for each segment of the route and determine the optimal windows for accessing single-direction channels, thus representing a multistage decision-making process. Meanwhile, the model’s reliability is substantiated through a rigorous comparative assessment against three benchmark strategies (EAS, LAS, and MAS). In our experiments, the optimization model yielded a total cost for the entire inland waterway amounting to $80,626.20. This figure stands below the total costs of $87,118.14 under the EAS strategy and $83,494.70 under the MAS strategy (the LAS strategy failed to meet the port of discharge deadline), thereby conclusively validating its ability to guide vessels to their port of discharge within prescribed schedules, all while reducing overall operational costs and promoting sustainable and environmentally responsible practices. Full article
(This article belongs to the Special Issue Mathematical Modelling and Optimization for Sustainable Operations Management)
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22 pages, 374 KiB  
Article
Paradox of Book and Claim for Carbon Emission Reduction in Maritime Operations Management: Mathematical Models and Numerical Experiments
by Shuaian Wang, Yuan Liu, Haoqing Wang and Yuquan Du
Mathematics 2023, 11(21), 4410; https://doi.org/10.3390/math11214410 - 24 Oct 2023
Cited by 1 | Viewed by 1673
Abstract
In recent years, the maritime industry’s carbon emissions have garnered increasing attention, leading to the proposal of various policy measures aimed at mitigating emissions and fostering a green and sustainable maritime sector. Among these measures, the book and claim mechanism, which allows shippers [...] Read more.
In recent years, the maritime industry’s carbon emissions have garnered increasing attention, leading to the proposal of various policy measures aimed at mitigating emissions and fostering a green and sustainable maritime sector. Among these measures, the book and claim mechanism, which allows shippers to access low or zero-emission bunkering by purchasing such fuels without physically participating in the refueling process, has emerged as a crucial catalyst for fuel conversion within the maritime industry. While book and claim has gained widespread recognition and facilitated the sale of clean fuels by some bunker suppliers, there has been limited research focused on evaluating its practical efficacy. Thus, we construct two distinct Mixed-Integer Linear Programming (MILP) models—one with the inclusion of the book and claim mechanism and one without—and conduct an analytical comparison of optimal decisions made by bunker suppliers and shippers under different model scenarios. Through numerical experiments, we have uncovered a noteworthy insight: with book and claim, bunker suppliers may set higher prices to maximize total profits due to various price sensitivities among shippers towards clean fuels, thus promoting low-price-sensitive shippers to purchase clean fuels while making it challenging for high-price-sensitive shippers to do so. Consequently, when compared to a scenario without book and claim, the total quantity of clean fuels purchased by shippers in the presence of book and claim may decrease, giving rise to a paradox where the implementation of book and claim inadvertently increases societal carbon emissions. This underscores the imperative for policymakers to conduct comprehensive market research, understand different shippers’ price sensitivities towards clean fuels, and make scientifically sound decisions when considering the implementation of the book and claim mechanism. Full article
(This article belongs to the Special Issue Mathematical Modelling and Optimization for Sustainable Operations Management)
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14 pages, 286 KiB  
Article
Optimal Selection of Multi-Fuel Engines for Ships Considering Fuel Price Uncertainty
by Yiwei Wu, Hongyu Zhang, Fei Li, Shuaian Wang and Lu Zhen
Mathematics 2023, 11(17), 3621; https://doi.org/10.3390/math11173621 - 22 Aug 2023
Cited by 3 | Viewed by 1859
Abstract
Maritime transport serves as the backbone of international trade, accounting for more than 90% of global trade. Although maritime transport is cheaper and safer than other modes of transport, it often means long sailing distances, which often results in substantial fuel consumption and [...] Read more.
Maritime transport serves as the backbone of international trade, accounting for more than 90% of global trade. Although maritime transport is cheaper and safer than other modes of transport, it often means long sailing distances, which often results in substantial fuel consumption and emissions. Liner shipping, a vital component of maritime transport, plays an important role in achieving sustainable maritime operations, necessitating the implementation of green liner shipping practices. Therefore, this study formulates a nonlinear integer programming model for a multi-fuel engine selection optimization problem to optimally determine ship order choice in terms of the fuel engine type, fleet deployment, fuel selection, and speed optimization, with the aim of minimizing the total weekly cost containing the weekly investment cost for ship orders and the weekly fuel cost. Given the complexity of solving nonlinear models, several linearization techniques are applied to transform the nonlinear model into a linear model that can be directly solved by Gurobi. To evaluate the performance of the linear model, 20 sets of numerical instances with, at most, seven routes are conducted. The results show that among 20 numerical instances, 16 sets of numerical instances are solved to optimality within two hours. The average gap value of the remaining four sets of numerical instances that cannot be solved to optimality within two hours is 0.51%. Additionally, sensitivity analyses are performed to examine crucial parameters, such as the weekly investment cost for ordering ships, the ship ordering budget, and the potential application of new fuel engine types, thereby exploring managerial insights. In conclusion, our findings indicate that equipping ships with low-sulfur fuel oil engines proves to be the most economical advantageous option in the selected scenarios. Furthermore, ordering ships with low-sulfur fuel, oil + methanol + liquefied natural gas engines, is beneficial when the weekly investment cost for such engines does not exceed $13,000, under the current parameter value setting. Full article
(This article belongs to the Special Issue Mathematical Modelling and Optimization for Sustainable Operations Management)
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