Multi-objective Mathematical Model Research Articles

Fuzzy correlation entropy-based NSGA-II for energy-efficient hybrid flow-shop scheduling problem

Green scheduling of manufacturing industry with energy saving as the core has been paid more and more attention in academia and industry. As a classic scheduling problem, hybrid flow-shop scheduling problem (HFSP) has been receiving increasing research attention. However, most studies only focus on time-related metrics while neglecting energy consumption. In this article, we studied energy-efficient HFSP and assumed that machines can operate at different speeds. This is an assumption that has been rarely explored but can make the problem more relevant to real-world production. Moreover, the energy-efficient HFSP at a variable machine speed (EHFSP-VMS) was formulated as a multiobjective mathematical optimization model aiming to optimize make-span and total energy consumption simultaneously. As a landmark achievement in the field of multiobjective optimization, non-dominated sorting genetic algorithm-II (NSGA-II) is adopted and improved as the solver, which is called fuzzy correlation entropy (FCE)-based NSGA-II (FCENSGA-II). Firstly, FCE, a fusion of fuzzy mathematics and information theory, is used to describe the difference and the FCE-based crowding distance is proposed for the first time. Its time complexity is lower than the original crowding distance. In addition, a machine learning strategy, namely opposition-based learning (OBL), is used to learn from opposite regions of the search space and increase the exploratory ability of the algorithm and the diversity of solutions. Finally, a critical path knowledge-based energy saving strategy (ESC) is adopted to discover non-dominant solutions by reducing the speed of machines on non-critical paths. A large number of experiments are conducted to test the performance of FCENSGA-II. The results show that in all test instances, the average, best and worst values of the solution obtained by FCENSGA-II are better than the compared state-of-the-art algorithms, and even the worst values obtained by FCENSGA-II in 75% of test instances are better than the best values of compared algorithms, which strongly confirms that FCENSGA-II outperforms the compared state-of-the-art algorithms for solving EHFSP-VMS.

Multi-Objective Optimization for Controlling the Dynamics of the Diabetic Population

To limit the adverse effects of diabetes, a personalized and long-term management strategy that includes appropriate medication, exercise and diet has become of paramount importance and necessity. Compartment-based mathematical control models for diabetes usually result in objective functions whose terms are conflicting, preventing the use of single-objective-based models for obtaining appropriate personalized strategies. Taking into account the conflicting aspects when controlling the diabetic population dynamics, this paper introduces a multi-objective approach consisting of four steps: (a) modeling the problem of controlling the diabetic population dynamics using a multi-objective mathematical model, (b) discretizing the model using the trapezoidal rule and the Euler–Cauchy method, (c) using swarm-intelligence-based optimizers to solve the model and (d) structuring the set of controls using soft clustering methods, known for their flexibility. In contrast to single-objective approaches, experimental results show that the multi-objective approach obtains appropriate personalized controls, where the control associated with the compartment of diabetics without complications is totally different from that associated with the compartment of diabetics with complications. Moreover, these controls enable a significant reduction in the number of diabetics with and without complications, and the multi-objective strategy saves up to 4% of the resources needed for the control of diabetes without complications and up to 18% of resources for the control of diabetes with complications.

Solving distributed low carbon scheduling problem for large complex equipment manufacturing using an improved hybrid artificial bee colony algorithm

Multi-agent collaborative manufacturing, high energy consumption and pollution, and frequent operation outsourcing are the three main characteristics of large complex equipment manufacturing enterprises. Therefore, the production scheduling problem of large complex equipment to be studied is a distributed flexible job shop scheduling problem involving operation outsourcing (Oos-DFJSP). Besides, the influences of each machine on carbon emission and job scheduling at different processing speeds are also involved in this research. Thus the Oos-DFJSP of large complex equipment consists of the following four sub-problems: determining the sequence of operations, assigning jobs to manufactories, assigning operations to machines and determining the processing speed of each machine. In the Oos-DFJSP, if a job is assigned to a manufactory of a group manufacturing enterprise, and the manufactory cannot complete some operations of the workpiece, then these operations will be assigned to other manufactories with related processing capabilities. Aiming at solving the problem, a multi-objective mathematical model including costs, makespan and carbon emission was established, in which energy consumption, power generation of waste heat and treatment capacity of pollutants were considered in the calculation of carbon emission. Then, a multi-objective improved hybrid genetic artificial bee colony algorithm was developed to address the above model. Finally, 45 groups of random comparison experiments were presented. Results indicate that the developed algorithm performs better than other multi-objective algorithms involved in the comparison experiments not only on quality of non-dominated solutions but also on Inverse Generational Distance and Error Ratio. That is, the proposed mathematical model and algorithm were proved to be an excellent method for solving the multi-objective Oos-DFJSP.

Countries Classification According to Covid-19 Data, Based on Aged-65 and Older, Using Multi-Objective Mathematical Goal Programming Model

Countries Classification According to Covid-19 Data, Based on Aged-65 and Older, Using Multi-Objective Mathematical Goal Programming Model

An integrated multi-objective mathematical model for sugarcane harvesting considering cumulative degree-days

Sugarcane is one of the main commodities in the world economy. An important step in the sugarcane supply chain is the harvest stage, requiring the support of mathematical modeling and optimization tools. Integrating the process of choosing the areas for harvesting according to the sugarcane maturation with the formation of the harvesting fronts and associating them with machine relocation costs is challenging. This paper contributes with a novel integer mathematical model that considers these concerns using three conflicting objectives. The first is that the sugarcane should be harvested as close as possible to its maturity, considering the sugarcane should be harvested as close as possible to its maturity by considering a combined measure of temperature and time since planting. The second aims to minimize the number of harvest fronts. The third objective is to minimize the costs involved with the relocation of the harvesters that cut the cane. Different strategies for obtaining Pareto-optimal solutions were proposed using exact methods, including MIP start and a decomposition technique. In the worst case, solutions with tolerable integrality gaps were obtained (inferior to 3%) in less than 1.5 h. Computational tests in real case studies were conducted in the sugarcane industry in two countries, indicating strong trade-offs in the determined solutions. In the Brazilian case, harvesting as close to maturation as possible, for example, causes an increase of 158% in the number of harvest fronts and 47% in the transportation costs, considering the minimum values for these objectives. Other trade-offs were seen and discussed when one of the other objectives was prioritized. These different compromise solutions help the decision-makers choose the most appropriate harvesting schedule according to their preferences.

Location selection of field hospitals amid COVID-19 considering effectiveness and fairness: A case study of Florida

The world has experienced an unprecedented global health crisis since 2020, the COVID-19 pandemic, which inflicted massive burdens on countries' healthcare systems. During the peaks of the pandemic, the shortages of intensive care unit (ICU) beds illustrated a critical vulnerability in the fight. Many individuals suffering the effects of COVID-19 had difficulty accessing ICU beds due to insufficient capacity. Unfortunately, it has been observed that many hospitals do not have enough ICU beds, and the ones with ICU capacity might not be accessible to all population strata. To remedy this going forward, field hospitals could be established to provide additional capacity in helping emergency health situations such as pandemics; however, location selection is a crucial decision ultimately for this purpose. As such, we consider finding new field hospital locations to serve the demand within certain travel-time thresholds, while accounting for the presence of vulnerable populations. A multi-objective mathematical model is proposed in this paper that maximizes the minimum accessibility and minimizes the travel time by integrating the Enhanced 2-Step Floating Catchment Area (E2SFCA) method and travel-time-constrained capacitated p-median model. This is performed to decide on the locations of field hospitals, while a sensitivity analysis addresses hospital capacity, demand level, and the number of field hospital locations. Four counties in Florida are selected to implement the proposed approach. Findings can be used to identify the ideal location(s) of capacity expansions concerning the fair distribution of field hospitals in terms of accessibility with a specific focus on vulnerable strata of the population.

Organic waste derived bioethanol supply chain network: Multiobjective snapshot model with a real-Korea case study

Bioethanol, a promising biofuel gasoline additive, was recently produced by a new technology using acetic acid derived from organic waste. This study develops a multiobjective mathematical model with two competing minimization objectives: economy and environmental impact. The formulation is based on a mixed integer linear programming approach. The configuration of the organic-waste (OW)-based bioethanol supply chain network is optimized in terms of the number and locations of bioethanol refineries. The flows of acetic acid and bioethanol between the geographical nodes must meet the bioethanol regional demand. The model is validated in three real-scenario case studies with different OW utilization rates (30%, 50%, and 70%) in South Korea in the near future (2030). The multiobjective problem is solved using the ε-constraint method and the selected Pareto solutions balance the trade-off between the economic and environmental objectives. At the “best-choice” solution points, increasing the OW utilization rate from 30% to 70% decreased the total annual cost from 904.2 to 707.3 million $/yr and the total greenhouse emissions from 1087.2 to −15.7 CO2 equiv./yr.

A Multi-Objective Mathematical Model for Vehicle Location-Routing Problem with Flexible Fuzzy Constraints

A Multi-Objective Mathematical Model for Vehicle Location-Routing Problem with Flexible Fuzzy Constraints

A novel optimization approach for rural development based on sustainable agriculture planning, considering the energy and water consumption nexus

In today's world, there are many changes and transformations in different sectors of the economy, and today's world economy has become more dependent on each other. The economy of many developing countries is highly dependent on agriculture. In addition, in developed countries, the agricultural sector is of special importance, so they are currently turning to the production of more organic and healthy products. One of the reasons that caused the agricultural sector to receive more attention in the economy is the existential importance of this sector in providing the raw materials of a part of the industry and the food industry needed in that country. Accordingly, in this research, the optimal cultivation pattern is determined using a linear multi-objective mathematical model, including economic, social, and environmental objectives. Moreover, the uncertainty in the input parameters of the proposed model is considered, and a robust optimization approach is applied to deal with this uncertainty. After collecting the research data for the crop year 2021-2022, the proposed robust counterpart formulation is optimized using GAMS software. The numerical results show that increasing the level of conservatism in the robust model cause to decrease in the profit of agriculture as well as increasing the total consumed water. Moreover, the results of the current research can help the decision-makers of the agricultural sector in achieving the goal of obtaining the highest profit.

An intelligent modeling framework to optimize the spatial layout of ocean moored buoy observing networks

This research is motivated by the practical requirements in the sustainable deployment of ocean moored buoy observing networks. Ocean moored buoys play an important role in the global marine environment monitoring. Ocean buoy station layout planning is a typical multiple-objective spatial optimization problem that aims to reduce the spatial correlation of buoy stations and improve their spatial monitoring efficiency. In this paper, we develop a multi-objective mathematical model for allocating ocean buoy stations (MOLMofOBS) based on Tobler’s first law of geography. A spatial neighborhood model based on a Voronoi diagram is built to represent the spatial proximity of distributed buoy stations and delimit the effective monitoring region of every station. Then, a heuristic method based on a multiple-objective particles swarm optimization (MOPSO) algorithm is developed to calculate the MOLMofOBS via a dynamic inertia weight strategy. Meanwhile, a series of experiments is conducted to verify the efficiency of the proposed model and algorithms in solving single- and multiple-buoy station location problems. Finally, an interactive portal is developed in the Cyberinfrastructure environment to provide decision-making services for online real-time planning of the ocean buoy station locations. The work reported in this paper will provide spatial decision-making support for the sustainable development of ocean buoy observing networks.

Presenting a Fuzzy Multiobjective Mathematical Model of the Reverse Logistics Supply Chain Network in the Automotive Industry to Reduce Time and Energy

The current research aims to design a fuzzy multiobjective model of the reverse logistics supply chain network in the automotive industry, taking into account the energy and time reduction approach. The automobile industry is one of the industries with a high demand worldwide. To continue the competition, the manufacturers of the leading car equipment should strive for better product quality by continuously improving their production processes, directing the production of greenhouse gases with low carbon levels, and increasing sustainability. In this regard, reverse supply chain networks and closed-loop chains have unique features that are very useful in the industry under review. The goal is to transform this model into a supply chain of a secure link in the automotive industry. Deterministic methods, genetic algorithm, particle swarm algorithm, and several scenarios with different aspects have been used to solve the model. The results show that the effectiveness of the three ways in terms of solution time is higher in the deterministic solution method. Proper use of the proposed process can help managers effectively manage the flow of recycled products concerning environmental considerations, and this process provides a sustainable competitive advantage for companies.

Berth and quay crane allocation and scheduling problem with renewable energy uncertainty: A robust exact decomposition

Container terminals are moving towards using renewable energy sources to manage their operations and cope with the traditional ones impacting the environment. However, renewable energy sources are limited, more costly, uncertain, and supplied in a non-continuous way. To improve operations’ sustainability, terminals are called to alternate between traditional and renewable energy sources. In this context, this paper proposes a multi-objective mathematical model to solve the berth and quay crane allocation and scheduling problem (BACASP), considering energy uncertainty and operations’ sustainability. The model considers two conflicting objectives: maximising renewable energy usage and minimising operational and energy costs. A robust version of the model is proposed to handle the uncertainty of renewable energy availability, whose objective is to optimize the worst-case scenario. Since many uncertain scenarios are involved, a simple commercial solver could not solve the model, even for small instances. Thus, we propose an exact decomposition algorithm that alleviates the model complexity, based on novel reinforcement procedures including novel set partitioning and valid inequalities, lower bounds, a warm-up scenario picking formula, speed up upper bounds, and a max–min MIP cutting procedure. A series of experiments show how the proposed approach helped tighten the model bounds, improve algorithm convergence, and alleviate computational time. We also conduct an economic analysis to assess the value of integration of energy parameters within BACASP. An additional investigation is made to show how Pareto optimal curves are sensitive to the price and availability of renewable energy uncertain scenarios.

Designing blood supply chain networks with disruption considerations by a new interval-valued fuzzy mathematical model: M/M/C queueing approach

The healthcare system of countries encounters several challenges during their performance, but the most significant one is to provide sufficient and safe required blood products for the individuals in need in the areas affected by disasters and to manage all of the aspects in those critical conditions. This paper presents a new multi-objective mathematical model to design an efficient blood supply chain in disasters considering temporary facilities along with fixed ones when it would be necessary and investigate potential disruptions both in blood facilities and links. Given the uncertainties caused by the arrival flows and to minimize the waiting time in blood banks (BBs), employing the queue theory leads the model to be efficient. Likewise, as the operations related to disaster responses deal with uncertainties, this paper presents a new extended interval-valued fuzzy (IVF) solution method based on weighted multi-choice goal programming (weighted MCGP) approach capable of helping decision-makers to set various weights for every goal and to find appropriate solutions. The optimization model is then solved by two metaheuristics, including genetic algorithm (GA) and red deer algorithm (RDA). Finally, the application of the proposed model is examined through a case study and numerical examples, and some managerial insights are provided based on the analysis of results.

Designing a sustainable fish closed-loop supply chain network under uncertainty.

There is increasing attention to the sustainable development of supply chain (SC) and reverse logistics (RL) in the contemporary competitive economy, notably in the food sector, by scholars and stakeholders. This study investigates a sustainable closed-loop supply chain (CLSC) for fish due to its high value in the family food basket, its perishability, and the importance of waste product recycling. A multi-objective mathematical model is developed under uncertainty and sustainability criteria to optimize production rates with the aim of better distribution among different demand markets, total costs, social issues, and negative environmental effects (e.g., CO2 emissions and unused/waste products). A combination of exact, meta-heuristic, and hybrid meta-heuristic algorithms are used to solve the suggested model. Then, the optimal solutions are found using the Taguchi method by evaluating the best initial replies. The solutions are evaluated based on various performance metrics. The analysis of variance (ANOVA) and the "filtering/displaced ideal solution" methods determine the best solution approach. Moreover, a case study with a trout CLSC in Northern Iran is examined. In addition, the Lingo software utilizes the ε-constraint method to evaluate and check the performance of the algorithms under different levels of uncertainty. Finally, sensitivity analyses are carried out to confirm the efficacy of the proposed algorithms. The findings demonstrate the proposed network's outstanding consistency with the algorithms used and its application and efficiency.

Enhance and balance AVT and PCE of the semi-transparent perovskite solar cells for BIPV via grating-based photonic crystals

Semi-transparent perovskite solar cells attract significant attention in building-integrated photovoltaics, especially for solar window application. However, thinning the perovskite photoactive layer, setting up nanostructures in the perovskite layer, and improving the functional layer transparent can neither effectively balance the power conversion efficiency (PCE) and average visible transmittance (AVT), nor can it effectively resolve the issue of colorful transmitted light. Here, based on the light polarization-selective absorption characteristics of photonic crystals, a semi-transparent perovskite solar cell with the grating-based photonic crystals is presented. It can apply the original layer structure of high efficiency perovskite solar cells without any transparent replacement, including the retention of opaque electrodes. Through the developed multiphysics and multi-objective mathematical model, the semi-transparent FAPbI3 solar cells can be optimized with PCE of 10% and AVT of 60.3%. When PCE increases to 12%, 15%, and 17%, the corresponding AVTs are 52.6%, 41.1%, and 33.4%, respectively. The performance far exceeds the benchmark of PCE (10%) and AVT (25%) for solar window application. Also, the transmitted light remains white regardless of the values of AVT and PCE. Furthermore, the semi-transparent perovskite solar cells with the grating-based photonic crystals can exhibit stable high-performance when the dimension tolerance varies from 1% to 20%, which reduces the requirement of processing technology. In the end, a design and optimization guideline for the semi-transparent perovskite solar cells is proposed through the analyses on the effect of a broad incident angle. These findings provide effective design strategies for the semi-transparent perovskite solar cells in the context of building-integrated photovoltaics.

Forecast energy demand, CO2 emissions and energy resource impacts for the transportation sector

Managing energy demand and reducing greenhouse gas emissions are among the most significant challenges ahead for many countries. Accurate prediction of energy demand and CO2 emissions is an important method to tackle the challenge. In addition, as a major source of energy consumption and CO2 emissions, the transportation sector is at the center of the problem. This study employs a hybrid approach integrating a multi-objective mathematical model with data-driven machine learning algorithms to predict energy demand and CO2 emissions in the transportation sector with improved accuracy. Sensitivity analyses are conducted to evaluate the impact of individual and joint consumptions of different energy resources on CO2 emissions. Case studies are conducted with countrywide statistics in Canada where the prediction indicates that energy demand and CO2 emissions will increase by 34.72% and 50.02% from 2019 to 2048 in the Canadian transportation sector. Results also indicated the varied impacts of different energy resources such that a 5% increase in energy demand in oil, gas, electricity, and renewable energy will result in + 4.8%, +0.315%, +0.28%, and −0.51% changes in CO2 emissions respectively. The proposed framework with integrated prediction model and the sensitivity analyses can help identify critical factors impacting CO2 emissions in the transportation sector and provide quantitative references for energy demand management and CO2 emissions reduction.

Small tradeoffs between social equity and conservation outcomes in a freshwater payment for ecosystem services scheme.

Conservation programs around the world aim to balance social equity, economic efficiency, and conservation outcomes. Tradeoffs among these three objectives necessarily exist but have been quantified in only a handful of systems. Here, we use a multi-objective mathematical optimization model in a large, water-limited river basin to quantify these tradeoffs in a freshwater payment for ecosystem services (PES) program aimed at establishing environmental flows (e-flows). Across a range of budgetary and future climate scenarios, we find that tradeoffs between social equity and conservation outcomes are small. We also show that payment schemes in which incentives are allocated to a single water use sector are much less cost-effective than schemes in which incentives are allocated among multiple sectors. Thus, allocating payments equally among agricultural, municipal, and industrial sectors can be both more equitable and more cost-effective. Overall, our results illustrate how some carefully designed conservation programs may be able to achieve a triple bottom line of social equity, economic efficiency, and conservation effectiveness.

Selecting an Optimal Scenario for Addressing Supplier Selection Problem by Considering Sustainable Scheduling: A Hybrid Approach

The iron and steel industry is a pillar industry of the national economy in many countries and is also a source of high energy consumption and pollution gas emissions. In addition to the economic aspect, there have been increasing concerns over how to minimise the negative environmental impact and enhance the awareness of social responsibility for iron and steel enterprises. Therefore, this study proposes an intelligent scheduling system for addressing the supplier selection problem by considering sustainable scheduling (SS) (ISS-AFLCSS) to achieve maximised benefits of logistics costs, carbon emission and fatigued driving for the Chengsteel Company. In the ISS-AFLCSS, first, a multiobjective mathematical optimisation model is formulated. Second, this study proposed a hybrid approach using an improved genetic algorithm (GA) to optimise multiple objectives of scenarios and adopting the technique for order preference by similarity to an ideal solution (TOPSIS) method with the analytic hierarchy process (AHP) to precisely optimise and select a best-ideal scenario. The results confirm that the proposed ISS-AFLCSS can provide accurate guidance in practicing SS for managers of enterprises.

A hybrid decision-making method using robust programming and interval-valued fuzzy sets for sustainable-resilient supply chain network design considering circular economy and technology levels

This study introduces a new three-stage optimization approach with a circular economy perspective for sustainable-resilient supply chain network design for perishable products. The proposed model specifies the number of facilities and the number of products flowing within the supply chain in case of disruption. The three contributions of the mathematical model are considering product lifetime, monitoring financial resources, and selecting technology levels. It incorporates suppliers’ green image and circular economy rating in the supply chain network structure. Epistemic uncertainty is considered in the optimization model to deal with the unknown capacity, cost, and demand. The study includes three main stages. In the first stage, to determine suppliers' green image and circular economy rating, a new interval-valued fuzzy (IVF)-compromise decision-making method is presented based on possibilistic mean and standard deviation evaluations. In the second stage a new multi-objective mathematical model is proposed to reduce total costs, reduce environmental impacts, and increase social sustainability. To deal with uncertainties in the mathematical model, a new IVF-robust solution approach is introduced. In the third stage, the solution is incorporated with the AUGMECON2 method to produce separate Pareto-optimal solutions, offering a hybrid of trade-offs between cost, emissions, and social responsibility. A case study in the food, dairy, and drink industry is presented to show how the suggested approach might be applied. Finally, several sensitivity analyses and comprehensive comparisons of the proposed approach with the literature were performed.

Investigating the green inventory control problem considering liquidity risk: Application in the dairy industry

In recent years, increasing concern regarding environmental issues has attracted the attention of researchers and managers to incorporate the greenness concept into business activities. Furthermore, one of the critical problems that plays an important role in the productivity of each company is the inventory management problem considering financial issues. Liquidity risk and inventory value must be closely monitored. Hence, this research studies the green inventory control problem considering liquidity to help managers to make best decisions in competitive environment. To achieve this objective, a multi-objective mathematical model is proposed that maximizes profit, minimizes risk, and maximizes greenness. Also, the proposed model is solved by a recent efficient method named multi-choice meta-goal programming by considering a real-world case study in the dairy industry. In addition, the impact of sales in different sales channels with different accounts receivable days and material substitution are examined. The obtained results show that increasing the raw milk allocated totally increases the quick ratio and contribution margin. Moreover, the usage of environmentally friendly materials have an extreme effect on customers to be loyal customers. Thus, the company's efficiency and profitability have increased due to considering hidden expenses. Finally, managerial insights and theoretical implications are presented.