Multi-objective Mathematical Model Research Articles

A multi-objective fuzzy mathematical model for circular economy with leasing as a strategy

PurposeThis paper aims at developing a multi-objective mathematical model of circular economy that integrates key concept of leasing as a strategy in addition to reuse, refurbishing, primary recycling, secondary recycling and disposal.Design/methodology/approachThis paper proposes multi-objective fuzzy mixed integer linear programming mathematical model considering multi-product, multi-echelon and multi-capacitated concepts of the circular economy. The three objectives of the proposed model, namely, economic, environmental and social are solved simultaneously using constraint approach to obtain balanced trade-off between the objective functions. The model is validated by solving a case study from the literature. The proposed model is made pragmatic for industrial application by considering multi-external suppliers multi-customer zones, multi-disassembly centers, multi-collection centers and multi-refurbishing centers and accounting for purchasing, processing, transportation, set-up costs and capacity constraints at the same time.FindingsThe results show that the leasing of the products improves the economic function in addition to the known environmental improvements. The proposed model also shows that the circular economy can generate the jobs for the unskilled people at different locations.Research limitations/implicationsThe proposed model can be further improved by considering the non-linearity due to economy of scale at various centers and in transportation. The model can be further extended to make it multi-period model.Practical implicationsThe proposed model of circular economy can be used by the organizations as a policy tool to decide the optimum number of collection centers, disassembly centers, refurbishing centers, recycling centers and disposal centers and their optimum locations and allocations. The organizations can also trade-off among economic, environmental and social benefits of their proposed decisions in circular economy.Originality/valueThe originality of the proposed mathematical model is consideration of leasing as a strategy to have better control over the supply chain for circularity; considering the training of unskilled people for backward supply chain jobs and accounting for primary recycling and secondary recycling separately for economical computation.

Integrating IoT and blockchain for intelligent inventory management in supply chains: A multi-objective optimization approach for the insurance industry

This research aims to develop and optimize an intelligent supply chain framework tailored for the insurance industry by integrating an innovative inventory management policy supported by the Internet of Things (IoT) and blockchain technologies. Through an extensive literature review, key assumptions are established, needs are identified, and objectives are formulated. A multi-objective mathematical planning model is proposed to minimize cost and time within the supply chain, with optimization conducted under deterministic and fuzzy conditions. The model utilizes augmented epsilon constraint and weighted sum methods to address its multi-objectiveness. Noteworthy is the integration of advanced technologies such as Wireless Sensor Networks (WSN), Radio-Frequency Identification (RFID), blockchain, and online sales, distinguishing it from traditional approaches. Initial validation and testing in smaller dimensions demonstrate the model’s adaptability to precise methods, while larger dimensions necessitate the use of meta-heuristic algorithms for efficient problem resolution. Additionally, a comprehensive sensitivity analysis in the insurance industry on objective function coefficients reveals intricate relationships, offering valuable insights into optimization dynamics across diverse conditions.

A multi-objective model for selecting response strategies of primary and secondary project risks under interval-valued fuzzy uncertainty

Risks are uncertain events that can affect criteria such as project cost, quality, and completion time and ultimately lead to project failure. That is why the project risk management process, which is one of the most fundamental parts of project management, must be done properly. In this paper, a new multi-objective fuzzy model is proposed to respond appropriately to the primary and secondary project risks. The contributions, such as risk interdependency, considering the project with multi-mode activities, resource considerations, as well as attention to interval-valued fuzzy uncertainties are regarded simultaneously for the first time. The purpose of the proposed multi-objective mathematical model is to minimize cost, quality reduction, and project completion time. Then, a new two-stage uncertain solution approach is introduced in this paper. In this solution approach, using the equivalent method in the first step and then using the extended multi-choice goal programming method in the second step, for both the lower and upper limits of the membership functions for interval-valued fuzzy numbers, the computational processes are performed. To show the application and effectiveness of the proposed model, a case study adapted from the literature is given. Finally, sensitivity analysis is conducted to analyze the behavior of the developed mixed-integer programming model. The analysis of obtained results indicates that the utilization of the proposed model leads to better and more appropriate solutions.

Resilience of sustainability for a smart production system to produce biodiesel from waste animal fat

The smart production system is implemented for more effective labor, less waste, and a reduction of energy consumption. Biofuels are significant substitutes for conventional fuels and decreases air pollution and carbon monoxide, can be made through a smart production system with automated machines. Biodiesel can be produced using an assortment of sources that can be both edible and inedible, but animal fat is a sensible alternative among inedible sources because of its affordable price and ease of availability. The model studies the smart biodiesel production system with energy utilization and less carbon emissions to produce pure biodiesel. The multi-objective mathematical model minimizes the total biodiesel supply chain cost followed by minimizing the total biodiesel supply chain environmental impact and enhancing its social impact. The smart production system with a variable production rate produces the biodiesel with less impurities, but still impurities in the biodiesel, that can be detected by a two-stage autonomated inspection system. The impure biodiesel is remanufactured in the biorefineries at the end of every natural production cycle. For the best utilization of energy, various energy costs, such as lighting and air handling costs are calculated. The improved augmented ϵ-constraint approach with lexicographic optimization is utilized to solve the model. The four mathematical examples are studied, and the repercussions of mathematical experiments reveal that the animal fat purchasing cost is 44.32% of the total cost, and the percentage of impurities in biodiesel can be decreased through minimum energy consumption. The managerial insights of the model, graphical representation, and sensitivity analysis of key parameters are provided in this research. The conclusions can be useful to investors in a sustainable smart production system and biofuel policymakers.

Dynamic Intelligent Scheduling in Low-Carbon Heterogeneous Distributed Flexible Job Shops with Job Insertions and Transfers.

With the rapid development of economic globalization and green manufacturing, traditional flexible job shop scheduling has evolved into the low-carbon heterogeneous distributed flexible job shop scheduling problem (LHDFJSP). Additionally, modern smart manufacturing processes encounter complex and diverse contingencies, necessitating the ability to address dynamic events in real-world production activities. To date, there are limited studies that comprehensively address the intricate factors associated with the LHDFJSP, including workshop heterogeneity, job insertions and transfers, and considerations of low-carbon objectives. This paper establishes a multi-objective mathematical model with the goal of minimizing the total weighted tardiness and total energy consumption. To effectively solve this problem, diverse composite scheduling rules are formulated, alongside the application of a deep reinforcement learning (DRL) framework, i.e., Rainbow deep-Q network (Rainbow DQN), to learn the optimal scheduling strategy at each decision point in a dynamic environment. To verify the effectiveness of the proposed method, this paper extends the standard dataset to adapt to the LHDFJSP. Evaluation results confirm the generalization and robustness of the presented Rainbow DQN-based method.

Sustainable-resilient seaport-dry port network design considering inter-modal transportation

This paper proposes a multi-objective mathematical model for designing an inter-modal transportation network that includes a seaport and multiple dry-ports in both export-oriented and import-oriented modes under sustainability and resilience criteria. A multi-objective particle swarm optimization algorithm is tailored to solve the large-sized instances. The model and its solution method are validated through several numerical examples in different sizes whose results demonstrate that the development and design of such a seaport-dry port network is a critical component of the government's economic development while its development is a challenging issue requiring proper financing.

Developing a tactical decision-making framework for a sustainable egg supply chain considering switchable parallel machines

ABSTRACT The increasing world population has increased food supply needs in recent years. Despite the numerous studies in the field of food supply chains, there are few articles on optimizing a sustainable egg supply chain. A fuzzy multi-objective mathematical model is presented to optimize a sustainable egg supply chain in a tactical decision structure. Switchable green packaging and labeling machines in parallel production lines, suppliers with different reliability rates and the provision of raw materials with different qualities have been studied in this article. Despite the significant reduction of the total costs while using switchable machines, the majority of the costs are still related to raw materials so that an increase of 2 to 4 times in the amount of input materials can change the values of objective functions by 23% to 60%. By using the unused capacity of the packaging and labeling machines, the total costs can be reduced significantly.

Integrated design of a sustainable waste management system with co-modal transportation network: A robust bi-level decision support system

Efficient waste management practices play a critical role in addressing the acute challenges of environmental protection, public health and resource conservation. A well-designed system guarantees that waste is efficiently collected, treated and disposed while minimizing negative impacts on ecosystems and human well-being. This work presents a robust bi-level decision support system to establish a sustainable waste management system using a co-modal transportation network to treat municipal solid waste timely and efficiently. Consequently, two integrated multi-objective mathematical models are developed to formulate the problem. Configuring the municipal solid waste network in the first level of the suggested decision support system, the transportation network is designed in the second level taking into account non-identical modes. The objectives are to minimize total cost and total emission in both levels, while maximization of total job creation is also addressed in the first level. Robust optimization method and weighted goal programming method are then utilized to accommodate the developed decision support system against uncertainty and multi-objectiveness, respectively. To validate the efficiency of these methods, they are assessed against possibilistic linear programming technique and Lp-metric approach with the help of simple additive weighting (SAW) method, respectively. Eventually, several numerical examples are generated based on the benchmarks given in the literature, which are then tackled using CPLEX solve to appraise the applicability and complexity of the developed methodology. The findings reveal the efficacy of the decision support system in terms of finding solutions in less than 448 s on average. Finally, sensitivity analyses are performed to draw out useful practical implications and decision aids.

Designing a Fuzzy Mathematical Model for a Two-Echelon Allocation-Routing Problem by Applying Route Conditions: A New Interactive Fuzzy Approach

In vehicle routing problems (VRP), the optimal allocation of transportation by considering factors such as route hardness, driver experience and vehicle worn-out has a significant effect on costs reduction and approaching real-world conditions. In this paper, a novel fuzzy mixed integer non-linear mathematical model to address the two-echelon allocation-routing problem under uncertainty is proposed by applying route and fleet conditions. The cost of allocating drivers to diverse vehicles is computed at the first echelon of the problem, considering factors such as vehicle type, vehicle wear-out, and driver experience. Additionally, different routes are defused with varying levels of hardness. The goal of the second echelon of the model is to improve reliability by defining the reliability of routes within each section. To solve the model, the Torabi and Hessini (TH), the Selimi and Ozkarahan (SO) methods, and a newly proposed approach (PIA) were utilized to transform the multi-objective model into a single-objective one. Numerical tests and performance indicators were used to validate the effectiveness of both the multi-objective mathematical model and the proposed solution method. The validation computation results indicate that the proposed solution approach outperforms both the TH and SO approaches.

Presenting a Multi-Objective Mathematical Model to Design a Green Reverse Logistics System Considering Energy Recovery

Presenting a Multi-Objective Mathematical Model to Design a Green Reverse Logistics System Considering Energy Recovery

Development and Optimization of an Offset Spiral Tooth Fertilizer Discharge Device

Due to factors such as a small amount of fertilizer application during rice topdressing and slow machine speed, the ordinary fertilizer discharge device fails to distribute the fertilizer uniformly and accurately as required, making it difficult to meet the needs of precise rice topdressing. This research focuses on the development of an offset spiral tooth fertilizer discharge device suitable for rice topdressing. The study analyzes the amount of fertilizer discharged in one cycle, the fertilizer force, and the motion of the fertilizer particles. In order to enhance the uniformity of the fertilizer discharge device at a low speed and small volume, the discrete element method is employed to conduct experimental research on the key structural parameters that affect the one-cycle amount of discharged fertilizer and the dynamics of the fertilizer discharge device. Through single-factor tests, it was found that the angle, height, number of spiral teeth, and diameter of the fertilizer discharge wheel are closely associated with the fertilizer discharge performance. To further investigate the impact of these four parameters on the fertilizer discharge performance, a regression combination test of the four factors is conducted based on the range optimized by the single-factor tests. A multi-objective mathematical model, considering the key parameters of fertilizer uniformity coefficient, one-cycle amount of fertilizer, and fertilizer discharge torque, is established at three speeds: 20, 55, and 90 rpm. The response surface method is utilized to analyze the influence of the interaction factors on the fertilizer discharge performance. The optimal combination of the key structural parameters was determined as follows: spiral tooth angle of 35.42°, tooth height of 9.02 mm, discharge wheel diameter of 57.43 mm, and tooth amount of 9.37. The bench test results of the device, using the optimal parameter combination and a fertilizer discharge speed of 0–90 rpm, were obtained for four commonly used rice fertilizers. The maximum variation coefficient of fertilizer discharge was found to be 10.42%. The one-cycle amount of fertilizer discharge was measured to be 19.82 ± 0.72 (A Kang), 17.20 ± 0.69 (Ba Tian), 20.34 ± 0.54 (Yaran), and 14.51 ± 0.44 (granular urea). The fertilizer discharge torque remained stable. These results indicate that the achieved optimization meets the precise fertilizer application requirements and can provide technical support for precise topdressing operations.

Using new fuzzy regression aptness and healthcare equity indices in cancer hospitals network design: a fuzzy multi-objective mathematical model

Using new fuzzy regression aptness and healthcare equity indices in cancer hospitals network design: a fuzzy multi-objective mathematical model

A multi-objective optimization model of truck scheduling problem using cross-dock in supply chain management: NSGA-II and NRGA

PurposeThis paper aims to develop a multi-objective problem for scheduling the operations of trucks entering and exiting cross-docks where the number of unloaded or loaded products by trucks is fuzzy logistic. The first objective function minimizes the maximum time to receive the products. The second objective function minimizes the emission cost of trucks. Finally, the third objective function minimizes the number of trucks assigned to the entrance and exit doors.Design/methodology/approachTwo steps are implemented to validate and modify the proposed model. In the first step, two random numerical examples in small dimensions were solved by GAMS software with min-max objective function as well as genetic algorithms (GA) and particle swarm optimization. In the second step, due to the increasing dimensions of the problem and computational complexity, the problem in question is part of the NP-Hard problem, and therefore multi-objective meta-heuristic algorithms are used along with validation and parameter adjustment.FindingsTherefore, non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA) are used to solve 30 random problems in high dimensions. Then, the algorithms were ranked using the TOPSIS method for each problem according to the results obtained from the evaluation criteria. The analysis of the results confirms the applicability of the proposed model and solution methods.Originality/valueThis paper proposes mathematical model of truck scheduling for a real problem, including cross-docks that play an essential role in supply chains, as they could reduce order delivery time, inventory holding costs and shipping costs. To solve the proposed multi-objective mathematical model, as the problem is NP-hard, multi-objective meta-heuristic algorithms are used along with validation and parameter adjustment. Therefore, NSGA-II and NRGA are used to solve 30 random problems in high dimensions.

A Framework for Valuation and Portfolio Optimization of Venture Capital Deals with Contractual Terms

Venture capitalists invest not only in the business aspect of a deal but also in its contractual terms. Therefore, the selection of deals and the combination of contractual terms pose challenging decisions for them. This paper consists of two main sections. The first section introduces a novel framework for the valuation of venture capital (VC) deals, including startups and their contractual terms. By taking into account risk situations, this section presents the valuation of combined contractual terms, including call options, liquidity preference, and participant rights. In the second section, a new multiobjective mathematical model for VC deals and contractual terms portfolio selection is developed using right-tail probability, strategy alignment, and a utility function. To solve the proposed model, three metaheuristic algorithms—Non-Dominated Sorting Genetic Algorithm (NSGA-II), Multi-Objective Binary Harmony Search Algorithm, and Dynamic Tuning Parameter Binary Harmony Search Algorithm (DTPBHS)—are applied. Based on numerical examples, DTPBHS outperforms other algorithms in the “Mean Ideal Distance” index, but NSGA-II demonstrates the best performance in the “Rate of Achievement of two objectives simultaneously” index. Furthermore, we demonstrate that the proposed utility function is more robust than the right-tail probability function under default deals conditions.

Multi-Objective Cutting Parameter Optimization Method for the Energy Consumption and Machining Quality of Computerized Numerical Control Lathes

In order to achieve minimum energy consumption in computerized numerical control (CNC) lathe processing under the premise of ensuring the imposed roughness of the machined surface, a black hole-continuous ant colony optimization algorithm (BH-ACOR) is proposed to optimize the turning parameters. Taking turning specific energy and surface roughness as the optimization objectives, a turning test was designed. Subsequently, a multi-objective mathematical model of the cutting stage was formulated through the application of the least-squares method to fit the test data. The black hole algorithm was introduced to mitigate the shortcomings of the continuous-domain ant colony algorithm, which easily falls into a local optimum, so as to put forward a kind of BH-ACOR that is applicable to multi-objective optimization. The algorithm was applied to the multi-objective mathematical model in the turning stage to determine the optimal cutting parameters. Through simulation and test verification, the validity and practicability of the proposed method are further proved.

Job rotations based on physical and psychological workloads: A proposal for the footwear industry

IntroductionThe aim of this study is to propose a model of job rotations in shoes (sandals and tennis shoes) production cells, aiming at reducing the risk exposure to work-related musculoskeletal disorders considering physical and psychological workloads. MethodsThe physical load was assessed by the Occupational Repetitive Actions method, and the psychological load by the Job Stress Scale. A total of 259 workers in the footwear industry participated in this study. These loads were incorporated into a multi-objective mathematical programming model, where the objective functions aimed to minimize the maximum work-related musculoskeletal disorders and the maximum total work demand, and to maximize the minimum work control and social support to which a worker might be exposed during a daily journey. To the best of our knowledge, this is the first time in the literature that physical and psychological aspects are considered when solving job rotation problems. To tackle the problem, we propose a matheuristic based on an epsilon-constraint framework. This method allows us to generate different solutions with respect to the specific objective functions. To assess the effectiveness of the solutions, we calculated the variance of the scores of the physical and psychological loads in the conditions without and with rotations. ResultsFive rotation solutions were reached for the sandal production cells and twelve for the tennis shoe production cells. There was a reduction in the variation of physical and psychological loads in all solutions for both cells when compared to the no rotation condition. However, for the sandal production cells, the reduction in variation between the physical loads of the conditions with and without rotations was not significant due to the similarity of the exposure indices. ConclusionsThe model reduces the risk of work-related musculoskeletal disorders, promoting variability in muscle recruitment and enrichment of work content, being applicable in other segments.

Differential evolution for cleft lip and/or cleft palate patient treatment scheduling problems: a northern Thailand hospital case study

Cleft lip and/or cleft palate (CL/P) are the common birth defects that result when facial structures developing in an unborn baby do not close completely. To design for treatment schedule, some constraints including hospital eligibility constraints, capacity limitations, treatment age limitations, multi-hospital assignment, and multidisciplinary care team assignment should be determined. However, efficient treatment scheduling is difficult owing to the complicated conditions of specific treatment. This paper presents a multi-objective mathematical model of the CL/P patient treatment scheduling problem in order to minimize the makespan, travel distance, and total least preference assignment score. Since the problem is NP-hard, a solution method is developed based on differential evolution (DE) with particular encoding and decoding schemes for solving the CL/P patient treatment scheduling problem. The performance of DE is evaluated and compared the results with those obtained from the modified particle swarm optimization. The results show that DE is capable of finding high-quality solutions with fast convergence. To apply the proposed approach for a case study, the CL/P patient treatment scheduling program is formulated. The program can be a decision support system in helping the administrators to schedule the patients in order to identify a list of selected treatments, assign each operation of patients to the selected hospital, and intelligently identify the period of the selected treatments.

A Multi-Objective Mathematical Programming Model for Project-Scheduling Optimization Considering Customer Satisfaction in Construction Projects

The aim of this study was to develop a multi-objective mathematical programming model for the trade-off of time, cost, and quality in the project-scheduling problem (PSP) by taking priorities and resource constraints as well as activity preemption into account. First, a small-sized problem instance that was a sub-project of an oil and gas construction project was used for te validation of the proposed model and algorithm. Subsequently, considering the sensitivity, complexity, and importance of oil and gas projects, the proposed model was implemented in a large-sized oil and gas construction project. Considering the NP-hardness of this problem, the NSGA-II metaheuristic algorithm was used to deal with the time, cost, and quality trade-off problem. Finally, a sensitivity analysis was implemented on the three main parameters of time, cost, and quality to investigate the effects of changes on the results. The findings show that the proposed model is more sensitive to cost changes, so an increase in project costs leads to a drastic change in the values of other objective functions.

PANDEMİ KOŞULLARI ALTINDA DERS ÇİZELGEMESİ FORMÜLASYONU

The covid-19 pandemic has significantly affected the education sector and raised the new operational challenges that spring from the necessity of planning courses in a way to ensure community safety. Accordingly, many higher education institutions provide guidelines regarding the measures to be implemented in education operations. As such, timetabling of the courses is required to be carried out in line with these guidelines. To address this need, this study introduces a multi-objective mathematical model for a university course timetabling problem under the pandemic-related considerations. In particular, the proposed mathematical model aims to minimize the total number of online courses and sections while considering the balanced distribution of the courses over time slots and days. We test the effectiveness of the proposed model using real-life data. The results show that the proposed approach is able to create an optimal timetable in a reasonable time that addresses the objectives of the faculty administration and satisfies the pandemic-related requirements. The study contributes to the literature by introducing new pandemic constraints and inspires managers facing pandemic guidelines.

Designing a sustainable vaccine supply chain by considering demand substitution and value-added function during a pandemic outbreak

The severe social, economic, and health detriments caused by pandemics (such as COVID-19) lead governments toward exploring survivability challenges. In this regard, some countries produce national vaccines along with receiving global medical supplies, which necessitates the design of a sustainable vaccine supply chain and the evaluation of value-added gained by each vaccine application. Given each vaccine possesses specific efficacy and expiration time, this study addresses products’ brand-based efficacy and perishability derived from existing literature. Additionally, shortages are inevitable in a chaotic pandemic situation as a consequence of limitations in the procurement, distribution, and storage networks of vaccines. Therefore, we investigate the effect of demand substitution based on vaccine efficacy to reduce the unsatisfied demand and combat the prevalence of infection. Moreover, this study implements mobile vaccination centers as well as permanent centers (for instance hospitals and clinics) to relax the personal and geographical constraints of different segments of society and expedite the vaccination. To optimize the multi-objective mathematical model, the augmented ε-constraint method has been utilized, and a real case study is provided to assess the application of the proposed model. The numerical results and sensitivity analysis show the proper utilization of vaccination centers’ combination in our proposed model, also 60% of shortages are compensated by substitutable products, which leads to expeditious immunization.