Multi-objective Mathematical Model Research Articles

Prediction of CO2 emissions to achieve net-zero objectives in the iron and steel sectors of North America

ABSTRACT Predictive models are widely used to create effective plans for reducing CO2 emissions in manufacturing. The Iron and Steel (I&S) industries play a crucial role in meeting international commitments to achieve Net-zero emissions by 2050. The objective of this study is to forecast carbon dioxide emissions from the I&S industries in North America through the utilization of a Multi-Objective Mathematical model. The proposed data-driven approach is integrated with various machine learning algorithms capable of accurately predicting future values with a small dataset. Additionally, sensitivity analyses under different scenarios are conducted to evaluate the impact of implementing proposed solutions by the research community. Results show a significant improvement in accuracy through the employment of the Whale Optimization Algorithm (WOA). Forecasts reveal a sustained increment of 0.7 MtCO2 every year spanning between 2022 and 2050. This study provides valuable information for stakeholders and policymakers as it allows a more precise evaluation to integrate new technologies to abate forthcoming CO2 emissions.

Multi-objective location-distribution optimization in blood supply chain: an application in Turkiye.

Blood donors are crucial in maintaining the blood supply chain. This study aims to improve the location and distribution of blood donation centers by focusing on two main objectives: minimizing costs and maximizing quality. Minimizing costs includes setting up and transporting blood efficiently while maximizing quality to ensure that blood products are delivered to hospitals promptly and in the right quantities. A multi-objective mathematical model is proposed to address the placement of both fixed and mobile blood donation centers. The first objective focuses on minimizing the costs of setting up centers and transporting blood. The second objective aims to maximize quality by ensuring timely deliveries and meeting hospitals' blood demand. The model utilizes real-world traffic and blood donation data from urban settings to simulate its effectiveness and applicability in practice. The model uses the constraint method to optimize both objectives simultaneously. The model was tested in various scenarios, optimizing cost and quality separately. The algorithm determined the ideal locations for blood donation centers to meet demand by exploring different options. It also accounted for factors that reduce quality, such as delayed deliveries and product returns, and showed that these issues could be minimized. This study highlights the need to balance cost and quality when determining the locations of blood donation centers. Using the constraint method, the model successfully optimized both objectives, offering valuable insights for improving the efficiency and effectiveness of blood donation operations.

A Decision Support Framework for Resilient and Sustainable Service Design

AbstractResilient and sustainable service design is essential for ensuring the longevity and effectiveness of service systems. However, existing literature often neglects key aspects such as articulating resilience attributes and integrating sustainability dimensions. This study proposes a decision support model for a “resilient-sustainable service design” that merges service design principles with resilient system attributes and organizational sustainability goals. The framework incorporates a multi-objective mathematical programming model and a multi-phased Quality Function Deployment (QFD) approach to derive Pareto optimal solutions using the Brute Force algorithm. Applied in the m-health service sector in Bangladesh, the study reveals significant challenges, including limited awareness of services and logistical inefficiencies. To address these issues, flexible strategies such as demand planning and service innovation are implemented. The findings have direct implications for the improvement of service delivery processes and underscore the importance of considering both resilience and sustainability. While focusing on Bangladesh’s m-health sector, the insights gained have broader relevance globally. The integration of resilience and sustainability principles into service design is crucial for addressing complex challenges across sectors and regions. Future research could involve longitudinal studies to capture evolving resilience strategies and explore resilient-sustainable service systems from a broader perspective. This entails examining various factors such as technological advancements and socio-economic dynamics shaping resilient and sustainable service ecosystems.

Algorithm for solving multi-objective hybrid flow shop scheduling problem

Aiming at the multi-objective unrelated parallel machine hybrid flow shop scheduling problem, a multi-objective mathematical model is established with the goal of minimizing the maximum completion time, total machine energy consumption and machine processing cost. An improved multi-objective evolution algorithm based on decomposition (IMOEAD) is proposed. The uniform design table is used to generate the initial weight vector to improve the population diversity. Normal distribution crossover and adaptive Gaussian mutation are used to improve the global and local search capabilities of the algorithm. Individuals are selected in the neighborhood of the weight vector to generate new solutions. The non-dominated rank and crowding distance are used to update the external archive. The inverse generation distance, generation distance and number of non-dominated solutions are used as performance indicators. Through a large number of case simulations, the algorithm is compared with the non-dominated sorting genetic algorithm II and the multi-objective evolution algorithm based on decomposition. The results verify the effectiveness of the algorithm.

Developing a Robust Multi-Skill, Multi-Mode Resource-Constrained Project Scheduling Model with Partial Preemption, Resource Leveling, and Time Windows

Real-world projects encounter numerous issues, challenges, and assumptions that lead to changes in scheduling. This exposure has prompted researchers to develop new scheduling models, such as those addressing constrained resources, multi-skill resources, and activity pre-emption. Constrained resources arise from competition among projects for limited access to renewable resources. This research presents a scheduling model with constrained multi-skill and multi-mode resources, where activity durations vary under different scenarios and allow for partial pre-emption due to resource shortages. The main innovation is the pre-emption of activities when resources are unavailable, with defined minimum and maximum delivery time windows. For this purpose, a multi-objective mathematical programming model is developed that considers Bertsimas and Sim’s robust model in uncertain conditions. The model aims to minimize resource consumption, idleness, and project duration. The proposed model was solved using a multi-objective genetic algorithm and finally, its validation was completed and confirmed. Analysis shows that limited renewable resources can lead to increased activity pre-emption and extended project timelines. Additionally, higher demand raises resource consumption, reducing availability and prolonging project duration. Increasing the upper time window extends project time while decreasing the lower bound pressures resources, leading to higher consumption and resource scarcity.

An investigation of mixed-model assembly line balancing problem with uncertain assembly time in remanufacturing

In recent decades, remanufacturing has emerged as an effective way to address resource crises and environmental pollution issues. Unlike traditional manufacturing, remanufacturing production is filled with various variable factors, especially in the assembly phase. Due to changes in part types, quality conditions, and assembly methods, the assembly time becomes highly uncertain. Assembly line balancing is a key challenge to achieve the stable operation of remanufacturing system. This study proposes an evaluation method for remanufacturing assembly time and establishes a multi-objective mathematical model for balancing remanufacturing mixed-model assembly (RMMA) line. The evaluation method utilizes the Fuzzy Graphical Evaluation Review Technique (FGERT) network to predict expected assembly time for each operation. The balancing model aims to optimize remanufacturing takt time and comprehensive balance rate (CBR). To effectively solve this model, an adaptive double-layer genetic algorithm (ADGA) is designed, where layer I ensures production efficiency and layer II optimizes assembly line balance. Finally, an assemble example of high-pressure common rail fuel pumps (HCRFP) is used to validate the effectiveness of the proposed method. The results demonstrate notable improvements compared to traditional single-product assembly (TSPA) line in scenarios with workstation numbers 4, 5, 6, and 7. Specifically, the production takt time is reduced by 4.19% to 9.56%, and CBR is enhanced by approximately 50%. Further comparison with three other classic algorithms confirms the superiority of ADGA. Additionally, it is observed that remanufacturability (proportion of remanufactured parts) has a significant impact on assembly performance. As remanufacturability increases, both takt time and CBR increase, reaching their maximum values when remanufacturability is around 0.5.

BIG DATA, BUSINESS PROCESSES, AND MATHEMATICAL ALGORITHMS FOR MULTI-OBJECTIVE MANAGERIAL DECISION OPTIMIZATION

The use of Big Data and the engineering of business processes are becoming increasingly important for managing the business of companies and large international corporate groups. For more successful outcomes, even for complex interventions such as those of the PNRR (National Recovery and Resilience Plan), the use of mathematical models to assist management decisions represents a significant lever to optimize time, costs, and planned overall performance. This analytical approach strengthens traditional qualitative techniques like SWOT analysis and finds useful application in the optimal definition of any form of PPP (Public-Private Partnership), such as the recent “Partnership for Innovation” (PPI) included in the new procurement code. The scientific work developed from the systematic analysis of processes proposes a particular multi-objective mathematical model that uses a system of vectors in an m-dimensional reference space.

A multi-objective mathematical programming model for location-routing of COVID-19 healthcare waste in Tunisia

A multi-objective mathematical programming model for location-routing of COVID-19 healthcare waste in Tunisia

Flower pollination algorithm with ring topology for multi-solution spaces to solve the disassembly line balancing problem

Abstract The Disassembly Line Balancing Problem (DLBP) is of significant importance in the product recycling process. However, existing DLBP research have primarily proposed improved optimization algorithms for single solution space. To provide decision makers with more efficient disassembly solutions, this paper chooses three classical layouts (straight, U-shaped, and parallel) to broaden the solution space and expands an incomplete DLBP with multi-solution spaces (DLBP-MS). By employing the strategy of incomplete disassembly, only the essential components are retained. In DLBP-MS, the disassembly information from used products is processed and imported into the three types of disassembly spaces to be solved and compared to find suitable disassembly solutions. And a multi-objective mathematical model is developed, this includes factors such as workstation count, free time, disassembly smoothness index, carbon emission, and disassembly revenue. The part constraints are established based on directed graphs, and the encoding and decoding methods for multi-solution spaces disassembly sequences in the random incomplete case are designed respectively. A ring topology based flower pollination algorithm (RTFPA) is introduced to effectively address the DLBP-MS. The solution set obtained during the iterative process is divided into subsets based on the congestion level and the overall diversity is preserved by internal optimization of these subsets. After that, the RTFPA is applied to the DLBP-MS of waste cell phones and computers. The improvement of the algorithm's optimization ability under different solution spaces is verified by comparing the results with those obtained from four other algorithms.

Multiphysical field and multiobjective mathematical modeling of grain-oilseed storage: Current status and future trends.

Storage is an important process involved in the postharvest treatment of grain-oilseed and is necessary for maintaining high quality and ensuring the long-term supply of these commodities in the food industry. Proper storage practices help prevent spoilage, maintain nutritional value, and preserve marketable quality. It is of great interest for storage to investigate flow, heat and mass transfer processes, and quality change for optimizing the operation parameters and ensuring the quality of grain-oilseed. This review discusses the mathematical models developed and applied to describe the physical field, biological field, and quality change during the storage of grain-oilseed. The advantages, drawbacks, and industrial relevance of the existing mathematical models were also critically evaluated, and an organic system was constructed by correlating them. Finally, the future research trends of the mathematical models toward the development of multifield coupling models based on biological fields to control quality were presented to provide a reference for further directions on the application of numerical simulations in this area. Meanwhile, artificial intelligence (AI) can greatly enhance our understanding of the coupling relationships within grain-oilseed storage. AI's strengths in both qualitative and quantitative analysis, as well as its effectiveness, make it an invaluable tool for this purpose.

Multi-objective Mathematical Model for Optimal Wind Turbine Placement in Wind Farm under Uncertainty

The main objective of this research is to introduce three energy risk management models grounded in optimization techniques for the strategic placement of wind turbines, considering wake effects and uncertainties in wind speed and direction. For this purpose, wind speed and direction data are gathered, and Monte Carlo simulation is employed to model the uncertainties. Subsequently, the risk management models undergo optimization using Non-Dominated Sorting Genetic Algorithm II (NSGA-II), Pareto envelope-based selection algorithm II (PESA-II), and Multi-Objective Particle Swarm Optimization (MOPSO) algorithms. Findings reveal that the wind farm's maximum power output reaches approximately 5.8 megawatts across all three algorithms and optimal turbine placements. A risk assessment was conducted using a tenth percentile criterion, revealing a significant production risk within the study area, with production falling below 1.8 megawatts in 90% of cases. Regarding the performance evaluation of the algorithms across all three models, superior performance in terms of solution proximity to the ideal solution is exhibited by PESA-II, while enhanced diversity and solution spread compared to the other algorithms are demonstrated by NSGA-II.

Advancements in Multi-Objective Mathematical Programming Models and Solution Approaches for Sustainable Waste Management Practices in Vehicle Routing Problem: A Systematic Literature Review

In recent years, the integration of sustainable principles into the Vehicle Routing Problem (VRP) for efficient waste management has gained significant attention. This paper provides an overview of advancements in multi-objective mathematical programming (MP) models and the optimization techniques for sustainable waste management practices within the VRP framework. Sustainable waste management practices in the context of the VRP involve optimizing routes and schedules aim to reduce the environmental impact of waste collection. It investigates the integration of multi-objectives with sustainability criteria, including social, economic, and environmental considerations. Furthermore, it surveys various optimization methodologies applied in waste management to enhance efficiency and sustainability practices. The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement was employed as a formal systematic review guideline for data gathering. Data was obtained from studies conducted between 2017 and 2023. The analysis included a total of 18 papers from online sources and databases. Based on the literature review, it has been observed that the majority of the research focused on employing Mixed-Integer Linear Programming (MILP) models to tackle the optimization problem for waste management. The literature survey demonstrated significant contributions in computational performance, cost-effectiveness, operational efficiency, and utilization of real-world data by improving the solution approaches, aiming to prioritize economic, social, and environmentally friendly solutions. The paper aims to serve as a convenient reference for researchers and practitioners seeking information on using the MP model and solution approaches to optimize VRP for waste management.

Exam scheduling under pandemic conditions: A mathematical model and decision support system

The scheduling of university exams is a complex task that involves various constraints such as administrative limits, pedagogical needs, student volume, and different courses. The emergence of Covid-19 and future pandemics has added new constraints related to infection prevention and contact tracing. To address these challenges, this study proposes a multi-objective mathematical model that considers university resources, reduced classroom occupancy, and minimized student interaction. The model aims to minimize violations of pandemic-related constraints and categorize exams by difficulty. To facilitate scheduling for entire faculties or universities, a Genetic Algorithm based web-based decision support system is developed. With these tools, the study successfully created an optimal schedule for eight departments simultaneously.

An innovative integrated framework for multi-level production planning and control systems in construction

The construction industry is plagued by chronic inefficiencies, such as low productivity, significant waste, cost overruns, and schedule delays. One of the most critical contributors to these issues is fragmented and ineffective planning and control methods. This research aims to address these challenges by developing an innovative integrated multi-level framework for production planning and control that harmonizes various planning methods and control metrics across different schedule levels. Employing the Design Science Research (DSR) methodology, this study systematically develops and evaluates an innovative framework that integrates internal and external project characteristics, utilizing the concept of "functionality" as a primary key for coherent integration. Furthermore, a multi-objective mathematical model is incorporated to clarify the framework's components and optimize the number of suggested planning methods and control metrics at each scheduling level, aiming to balance the functional requirements of project teams with the practicality of implementation.The application of the framework to a renovation case study demonstrates its practicality and strategic value, effectively addressing real-world project management challenges. Moreover, industry and academic evaluations highlight its potential to significantly improve construction project management practices.

The planning of the distribution of relief items and road network repair through multiple heterogeneous crews and prioritizing damaged roads under a flexible and uncertain environment

This study introduces an integrated and flexible program to coordinate two critical operations in the response phase of disaster management, namely the distribution of relief items and the repair of damaged roads under different types of road damage. In this regard, considerations such as the classification of critical areas according to the severity of the incident, location-allocation, scheduling, and routing of heterogeneous multiple crews, prioritization of road repair, sequence of operations, and the simultaneity of various activities are considered. Therefore, a new multi-period and multi-objective mathematical model is presented, where the first objective minimizes the total operation cost, the second objective minimizes the total operation time, and the third objective maximizes the prioritization of repairing damaged roads. Also, owing to the uncertain essence of a disaster, containing the types of demand and service time in each operation, a robust optimization approach is used to tackle this concern. The proposed model is ultimately checked for validation in a real case study. The acquired computational outcomes and presented managerial insights show the efficiency and effectiveness of the proposed model.

Optimization of renewable energy project portfolio selection using hybrid AIS-AFS algorithm in an international case study

In the coming decade, as restrictions on fossil fuel usage become more stringent, investment in renewable energy projects presents an increasingly appealing opportunity. Evaluating investment attractiveness involves considering both profitability and investment risk. This study proposes a multi-objective mathematical model for identifying the optimal Renewable Energy Project Portfolio (REPP), aiming to maximize net present value while minimizing investment risk. The key innovation of this model is its incorporation of project lifetime and workforce employment considerations to discern the best REPP. To optimize the objective functions of this mathematical model, a hybrid meta-heuristic algorithm combining Artificial Immune System (AIS) and Artificial Fish Swarm (AFS) algorithms is introduced. Genuine data from a varied spectrum of renewable energy projects spanning 20 countries has been meticulously collected. The proposed model is optimized using this dataset, considering portfolio sizes of 3, 5, 10, and 15. The numerical results indicate that, at a specific investment risk threshold, the proposed hybrid algorithm outperforms both AIS and AFS in terms of profitability. Furthermore, the assessment of the geographical distribution of selected projects reveals a deliberate effort to avoid concentration in any specific region, demonstrating a commitment to identifying optimal investment opportunities globally. This research advances the understanding of renewable energy project portfolio optimization, providing valuable insights for investors, policymakers, and sustainable development practitioners.

Multi-objective sustainable flexible job shop scheduling problem: Balancing economic, ecological, and social criteria

Industry 5.0 makes it imperative to reevaluate the manner of using resources in manufacturing systems to ensure sustainability. In this context, scheduling problems are encountering new environmental and human-related challenges, and the concept of sustainable scheduling has gained importance, aiming to balance economic, environmental, and human factors. In this paper, we propose two multi-objective mathematical models to simultaneously address these three factors as objective functions. In the first model, we consider the operator safety while using the Occupational Repetitive Action (OCRA) index to assess ergonomic risks related to task execution. The second model includes workers’ preferences in terms of machines, shifts and task variety. The objective is to improve the general well-being of workers by proposing a schedule that respects as much as possible their preferences. Both models integrate the travel time of workers and products between machines. To solve these NP-hard scheduling problems, we use the Non-dominated Sorting Genetic Algorithms II and III (NSGA-II and NSGA-III), enhanced with a Q-learning strategy for parameter selection and a variable neighborhood search based on reinforcement learning. The obtained results provide a comprehensive analysis of the interactions between these criteria, demonstrating the capability of such approach to achieve a favorable balance between multiple objectives while addressing the new challenges of production scheduling in Industry 5.0 context.

An integrated scenario-based multi-period multi-objective mathematical model for a sustainable biomass supply chain network considering social factors and disruption risk under uncertainty

An integrated scenario-based multi-period multi-objective mathematical model for a sustainable biomass supply chain network considering social factors and disruption risk under uncertainty

NSGA-III algorithm for optimizing robot collaborative task allocation in the internet of things environment

To improve the performance of intelligent products and reasonably distribute the load of the loading robot, a multi-objective, and multi-objective (Traveling-salesman-problem, TSP) mathematical model was established. A genetic algorithm based on speed invariant and the elite algorithm is proposed to solve the multi-TSP assignment problem. To ensure the integration of the population, a population resettlement strategy with elite lakes was proposed to improve the probability of population transfer to the best Pareto solution. The experiment verified that this strategy can approach the optimal solution more closely during the population convergence process, and compared it with traditional Multi TSP algorithms and single function multi-objective Multi TSP algorithms. By comparing the total distance and maximum deviation of multiple robot systems, it is proven that this algorithm can effectively balance the path length of each robot in task allocation. From the research results, it can be seen that in genetic algorithms, resetting the population after reaching precocity can maintain the optimization characteristics of the population and have a high probability of obtaining Pareto solutions. At the same time, storing elite individuals from previous convergent populations for optimization can better obtain Pareto solutions.

A matheuristic applied to clustering rural properties and allocating plants for biogas generation

Establishing partnerships among agro-industrial properties and selecting ideal locations for biogas plants are crucial challenges in large-scale biogas production and can influence both operational efficiency and waste management. In this context, this research proposes a new matheuristic that addresses the problems of defining a group of properties and an optimal number of groups and identifies the best allocation to the biogas plant. The group properties were defined by hierarchical and K-means cluster algorithms. The best location for the biogas plant was determined by the proposed multiobjective mathematical model. The best cluster number was decided by two strategies: (1) one that selected the closest non-dominated solutions to the ideal solution (M1) and (2) one that favored the most environmentally friendly solution (M2). The matheuristic was tested using three real databases, which yielded strategic clusters with an average daily biogas production of 544.93 m³/day (M1 and M2) for DataBase 1, 1635,156.00 m³/day (M1) and 403,497.50 m³/day (M2) for DataBase 2, and 318,662.50 m³/day (M1) and 20,479.58 m³/day (M2) for DataBase 3. This research provides an opportunity to add value to agro-industrial properties by achieving energy security and developing new business networks.