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This 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.

Two 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.

Therefore, 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.

This 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.

This study aims to apply for the first time in literature a new multi-objective sensor selection and placement optimization methodology based on the multi-objective Lichtenberg algorithm and test the sensors' configuration found in a delamination identification case study.

This work aims to study the damage identification in an aircraft wing using the Lichtenberg and multi-objective Lichtenberg algorithms. The former is used to identify damages, while the last is associated with feature selection techniques to perform the first sensor placement optimization (SPO) methodology with variable sensor number. It is applied aiming for the largest amount of information about using the most used modal metrics in the literature and the smallest sensor number at the same time.

The proposed method was not only able to find a sensor configuration for each sensor number and modal metric but also found one that had full accuracy in identifying delamination location and severity considering triaxial modal displacements and minimal sensor number for all wing sections.

This study demonstrates for the first time in the literature how the most used modal metrics vary with the sensor number for an aircraft wing using a new multi-objective sensor selection and placement optimization methodology based on the multi-objective Lichtenberg algorithm.

The vehicle routing problem (VRP) has been widely investigated during last decades to reduce logistics costs and improve service level. In addition, many researchers have realized the importance of green logistic system design in decreasing environmental pollution and achieving sustainable development.

In this paper, a bi-objective mathematical model is developed for the capacitated electric VRP with time windows and partial recharge. The first objective deals with minimizing the route to reduce the costs related to vehicles, while the second objective minimizes the delay of arrival vehicles to depots based on the soft time window. A hybrid metaheuristic algorithm including non-dominated sorting genetic algorithm (NSGA-II) and teaching-learning-based optimization (TLBO), called NSGA-II-TLBO, is proposed for solving this problem. The Taguchi method is used to adjust the parameters of algorithms. Several numerical instances in different sizes are solved and the performance of the proposed algorithm is compared to NSGA-II and multi-objective simulated annealing (MOSA) as two well-known algorithms based on the five indexes including time, mean ideal distance (MID), diversity, spacing and the Rate of Achievement to two objectives Simultaneously (RAS).

The results demonstrate that the hybrid algorithm outperforms terms of spacing and RAS indexes with p-value <0.04. However, MOSA and NSGA-II algorithms have better performance in terms of central processing unit (CPU) time index. In addition, there is no meaningful difference between the algorithms in terms of MID and diversity indexes. Finally, the impacts of changing the parameters of the model on the results are investigated by performing sensitivity analysis.

In this research, an environment-friendly transportation system is addressed by presenting a bi-objective mathematical model for the routing problem of an electric capacitated vehicle considering the time windows with the possibility of recharging.

The purpose of this paper is to review studies on mathematical optimization of the sustainable gasoline supply chain to help decision-makers understand the current situation, the exact dimensions of the problem and the models provided in the literature. So, a more realistic mathematical optimization model can be achieved by fully covering all dimensions of the supply chain of this product.

To evaluate and comprehend the mathematical optimization of the sustainable gasoline supply chain research area, a systematic literature review is undertaken that covers material collection, descriptive analysis, content analysis and material evaluation steps. Finally, based on this process, 69 related articles were carefully investigated.

The results of the systematic literature review show the main areas of the published papers on mathematical optimization of sustainable gasoline supply chain problems and the gaps for future research in this field presented based on them.

This approach is subject to limitations because the protocol of the systematic review of the research literature only included searching for the considered combination of keywords in the Scopus and ProQuest databases. Furthermore, the protocol used in this paper restricts documents to English.

The results have significant implications for both academicians and practitioners in this field. It can be useful for academics to comprehend the gaps and future trends in this field. Also, for practitioners, it can be useful to identify and understand the parts of the mathematical optimization model, which can help them model this problem effectively and efficiently.

No systematic literature review has been done in this field by considering gasoline to the best of the authors’ knowledge and delivers new facts for the future development of this field.

Aluminium alloys can be used as lightweight and high-strength materials in combination with the technology of laser beam welding, an efficient joining method, in the manufacturing of automotive parts. The purposes of this paper are to conduct laser welding experiments with Al2024 in the lap joint configuration, model the laser welding process parameters of Al2024 alloys and use propounded models to optimize the process parameters.

Laser welding of Al2024 alloy has been conducted in the lap joint configuration. Then, the influences of explanatory variables (laser peak power, scanning speed and frequency) on outcome variables (weld width [WW], throat length [TL] and breaking load [BL]) have been investigated with Poisson regression analysis of the data set derived from experimentation. Thereafter, a multi-objective genetic algorithm (MOGA) has been used using MATLAB to find the optimum solutions. The effects of various input process parameters on the responses have also been analysed using response surface plots.

The promulgated statistical models, derived with Poisson regression analysis, are evinced to be well-fit ones using the analysis of deviance approach. Pareto fronts have been used to demonstrate the optimization results, and the maximized load-bearing capacity is computed to be 1,263 N, whereas the compromised WW and TL are 714 µm and 760 µm, respectively.

This work of conducting laser welding of lap joint of Al2024 alloy incorporating the Taguchi method and optimizing the input process parameters with the promulgated statistical models proffers a neoteric perspective that can be useful to the manufacturing industry.

Supply chains (SCs) have been growingly virtualized in response to the market challenges and opportunities that are presented by new and cost-effective internet-based technologies today. This paper designed a virtual closed-loop supply chain (VCLSC) network based on multiperiod, multiproduct and by using the Internet of Things (IoT). The purpose of the paper is the optimization of the VCLSC network.

The proposed model considers the maximization of profit. For this purpose, costs related to virtualization such as security, energy consumption, recall and IoT facilities along with the usual costs of the SC are considered in the model. Due to real-world demand fluctuations, in this model, demand is considered fuzzy. Finally, the problem is solved using the Grey Wolf algorithm and Firefly algorithm. A numerical example and sensitivity analysis on the main parameters of the model are used to describe the importance and applicability of the developed model.

The findings showed that the Firefly algorithm performed better and identified more profit for the SC in each period. Also, the results of the sensitivity analysis using the IoT in a VCLSC showed that the profit of the virtual supply chain (VSC) is higher compared to not using IoT due to tracking defective parts and identifying reversible products. In proposed model, chain members can help improve chain operations by tracking raw materials and products, delivering products faster and with higher quality to customers, bringing a new level of SC efficiency to industries. As a result, VSCs can be controlled, programmed and optimized remotely over the Internet based on virtual objects rather than direct observation.

There are limited researches on designing and optimizing the VCLSC network. This study is one of the first studies that optimize the VSC networks considering minimization of virtual costs and maximization of profits. In most researches, the theory of VSC and its advantages have been described, while in this research, mathematical optimization and modeling of the VSC have been done, and it has been tried to apply SC virtualization using the IoT. Considering virtual costs in VSC optimization is another originality of this research. Also, considering the uncertainty in the SC brings the issue closer to the real world. In this study, virtualization costs including security, recall and energy consumption in SC optimization are considered.

1. Investigates the role of IoT for virtual supply chain profit optimization and mathematical optimization of virtual closed-loop supply chain (VCLSC) based on multiperiod, multiproduct with emphasis on using the IoT under uncertainty.

2. Considering the most important costs of virtualization of supply chain include: cost of IoT information security, cost of IoT energy consumption, cost of recall the production department, cost of IoT facilities.

3. Selection of the optimal suppliers in each period and determination of the price of each returned product in virtual supply chain.

4. Solving and validating the proposed model with two meta-heuristic algorithms (the Grey Wolf algorithm and Firefly algorithm).

Investigates the role of IoT for virtual supply chain profit optimization and mathematical optimization of virtual closed-loop supply chain (VCLSC) based on multiperiod, multiproduct with emphasis on using the IoT under uncertainty.

Considering the most important costs of virtualization of supply chain include: cost of IoT information security, cost of IoT energy consumption, cost of recall the production department, cost of IoT facilities.

Selection of the optimal suppliers in each period and determination of the price of each returned product in virtual supply chain.

Solving and validating the proposed model with two meta-heuristic algorithms (the Grey Wolf algorithm and Firefly algorithm).

The purpose of this study is to propose a new mathematical model that integrates strategic decision-making with tactical-operational decision-making in order to optimize production and scheduling decisions.

This study presents a multi-objective optimization framework to make production planning, scheduling and maintenance decisions. An epsilon-constraint method is used to solve small instances of the model, while new hybrid optimization algorithms, including multi-objective particle swarm optimization (MOPSO), non-dominated sorting genetic algorithm, multi-objective harmony search and improved multi-objective harmony search (IMOHS) are developed to address the high complexity of large-scale problems.

The computational results demonstrate that the metaheuristic algorithms are effective in obtaining economic solutions within a reasonable computational time. In particular, the results show that the IMOHS algorithm is able to provide optimal Pareto solutions for the proposed model compared to the other three algorithms.

This study presents a new mathematical model that simultaneously determines green production planning and scheduling decisions by minimizing the sum of the total cost, makespan, lateness and energy consumption criteria. Integrating production and scheduling of a shop floor is critical for achieving optimal operational performance in production planning. To the best of the authors' knowledge, the integration of production planning and maintenance has not been adequately addressed.

To solve the problem that the traditional methods miss key information in the process of bearing fault identification, this paper aims to apply the phase-space reconstruction (PSR) theory and intelligent diagnosis techniques to extend the one-dimensional vibration signal to the high-dimensional phase space to reveal the system information implied in the univariate time series of the vibration signal.

In this paper, a new method based on the PSR technique and convolutional neural network (CNN) is proposed. First, the delay time and the embedding dimension are determined by the C-C method and the false nearest neighbors method, respectively. Through the coordinate delay reconstruction method, the two-dimensional signal is constructed, and this information is saved in a set of gray images. Then, a simple and efficient convolutional network is proposed. Finally, the phase diagrams of different states are used as samples and input into a two-dimensional CNN for learning modeling to construct a PSR-CNN fault diagnosis model.

The proposed PSR-CNN model is tested on two data sets and compared with support vector machine (SVM), k-nearest neighbor (KNN) and Markov transition field methods, and the comparison results showed that the method proposed in this paper has higher accuracy and better generalization performance.

The method proposed in this paper provides a reliable solution in the field of rolling bearing fault diagnosis.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-04-2023-0113/

This paper deals with the combined management and design of a sustainable pharmaceutical supply chain network with considering recycling.

This paper first utilizes the analytical hierarchy process to select and rank green manufacturers. Second, the authors proposed a multi-objective nonlinear mathematical model to design a sustainable pharmaceutical supply chain network. The proposed model has been linearized and solved using the LP-metric method using GAMS software.

A real case study has been conducted in Iran. The results show that environmental and social issues can be improved while minimizing total costs.

Given the criticality and importance of drugs in human health and the importance of recycling in today's world, proper management and design of a sustainable drug supply chain are necessary. This study pays special attention to environmental issues by utilizing multi-criteria decision approaches and customer satisfaction.

Two-level support with Level 1 consisting of a set of beams and Level 2 consisting of a tree-like structure is an efficient support structure for extrusion-based additive manufacturing (EBAM). However, the literature for finding a slim two-level support is rare. The purpose of this paper is to design a lightweight two-level support structure for EBAM.

To efficiently solve the problem, the lightweight design problem is split into two subproblems: finding a slim Level 1 support and a slim Level 2 support. To solve these two subproblems, this paper develops three efficient metaheuristic algorithms, i.e. genetic algorithm (GA), genetic programming (GP) and particle swarm optimization (PSO). They are problem-independent and are powerful in global search. For the first subproblem, considering the path direction is a critical factor influencing the layout of Level 1 support, this paper solves it by splitting the overhang region into a set of subregions, and determining the path direction (vertical or horizontal) in each subregion using GA. For the second subproblem, a hybrid of two metaheuristic algorithms is proposed: the GP manipulates the topologies of the tree support, while the PSO optimizes the position of nodes and the diameter of tree branches. In particular, each chromosome is encoded as a single virtual tree for GP to make it easy to manipulate Crossover and Mutation. Furthermore, a local strategy of geometric search is designed to help the hybrid algorithm reach a better result.

Simulation results show that the proposed method is preferred over the existing method: it saves the materials of the two-level support up to 26.34%, the materials of the Level 1 support up to 6.62% and the materials of the Level 2 support up to 37.93%. The proposed local strategy of geometric search can further improve the hybrid algorithm, saving up to 17.88% of Level 2 support materials.

The proposed approach for sliming Level 1 support requires the overhanging region to be a rectilinear polygon and the path direction in a subregion to be vertical or horizontal. This limitation limits the further material savings of the Level 1 support. In future research, the proposed approach can be extended to handle an arbitrary overhang region, each with several choices of path directions.

The details of how to integrate the proposed algorithm into the open-source program CuraEngine 4.13.0 is presented. This is helpful for the designers and manufacturers to practice on their own 3D printers.

The path planning of the overhang is a critical factor influencing the distribution of supporting points and will thus influence the shape of the support structure. Different from existing approaches that use single path directions, the proposed method optimizes the volume of the support structure by planning hybrid paths of the overhangs.