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This paper studies a production planning problem in printed circuit board (PCB) assembly. A PCB assembly line has several non‐identical placement machines, so the placement times by different machines are various to the same type of components. Several mathematical models are formulated in order to obtain a best assignment of components to machines with the objective of minimizing the cycle time to have the best line throughput. Moreover, the data structures of the models are analyzed and compared with other similar models to search a good available algorithm. Finally, a numerical example is provided to illustrate these models and is solved by a computer package.

Discusses the component assignment problem in PCB assembly, where assigning components to appropriate machines, in order to get a minimum assembly time for the assembly line, can be formulated as an integer linear programming model. In order to obtain the optimal solution to the component assignment problem, the branch‐and‐bound method can be applied. However, it is not efficient. Applies the tabu search heuristic to the component assignment problem. The procedure of the tabu search to the problem is presented, and a numerical example is provided. Finally, the performance of the tabu search is analyzed with the example.

The purpose of this paper is to investigate the optimization for a placement machine in printed circuit board (PCB) assembly when family setup strategy is adopted.

A complete mathematical model is developed for the integrated problem to optimize feeder arrangement and component placement sequences so as to minimize the makespan for a set of PCB batches. Owing to the complexity of the problem, a specific genetic algorithm (GA) is proposed.

The established model is able to find the minimal makespan for a set of PCB batches through determining the feeder arrangement and placement sequences. However, exact solutions to the problem are not practical due to the complexity. Experimental tests show that the proposed GA can solve the problem both effectively and efficiently.

When a placement machine is set up for production of a set of PCB batches, the feeder arrangement of the machine together with the component placement sequencing for each PCB type should be solved simultaneously so as to minimize the overall makespan.

The paper investigates the optimization for PCB assembly with family setup strategy, which is adopted by many PCB manufacturers for reducing both setup costs and human errors.

The paper investigates the feeder arrangement and placement sequencing problems when family setup strategy is adopted, which has not been studied in the literature.

The purpose of this paper is to propose an effective and efficient solution method for the component allocation problem (CAP) in printed circuit board (PCB) assembly, in order to achieve high‐throughput rates of the PCB assembly lines.

The investigated CAP is intertwined with the machine optimization problems for each machine in the line because the latter determine the process time of each machine. In order to solve the CAP, a solution method, which integrates a meta‐heuristic (genetic algorithm) and a regression model is proposed.

It is found that the established regression model can estimate the process time of each machine accurately and efficiently. Experimental tests show that the proposed solution method can solve the CAP both effectively and efficiently.

Although different regression models are required for different types of assembly machines, the proposed solution method can be adopted for solving the CAPs for assembly lines of any configuration, including a mixed‐vendor assembly line.

The solution method can ensure a high‐throughput rate of a PCB assembly line, and thus improve the production capacity without further investment on the expensive PCB assembly equipment.

The paper proposes an innovative solution method for the CAP in PCB assembly. The solution method integrates the meta‐heuristic method and the regression method, which has not been studied in the literature.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

Today, coronavirus disease-19 (COVID-19) treatment is an evolving process, and synbiotic administration has been suggested as a new therapeutic strategy. This study aims to investigate the effect of synbiotic supplementation in COVID-19 patients.

In this placebo-controlled trial, 80 patients were randomized to receive oral synbiotic capsule (containing fructooligosaccharide and seven bacterial strains; Lactobacillus (L) casei, L. rhamnosus, Streptococcus thermophilus, Bifidobacterium breve, L. acidophilus, Bifidobacterium longum, L. bulgaricus, each one 109 colony-forming units) or placebo for two months. Inflammatory markers (Interleukin-6 [IL-6], C-reactive protein [CRP], erythrocyte sedimentation rate [ESR]) and white blood cell (WBC) count were evaluated at two timepoints (baseline, two months later). The measured variables were adjusted for confounders and analyzed by SPSS v21.0.

All 80 enrolled patients completed the study. The study adherence was good (approximately 70%). The mean changes for IL-6 were not significant (Δ = −0.6 ± 10.4 pg/mL vs Δ = +11.2 ± 50.3 pg/mL, p > 0.05). There were no significant improvements for CRP, ESR and WBC.

Administration of synbiotics for two months did not improve inflammatory markers in COVID-19 patients.

The purpose of this paper is to realize the integrated optimization of process planning and scheduling in printed circuit board assembly (PCBA).

Logical and numerical contour matrix is used to describe the constituent of component and machine for different PCBA processes on the basis of polychromatic sets (PS) theory, and a PS model of PCBA is built. A hybrid genetic algorithm (GA) is developed to optimize the component allocation, PCB assignment and assembly sequence simultaneously.

Integration of PCBA process planning and scheduling (PCBAPPS) can bridge the gap between design and manufacturing to guarantee the assembly quality and improve the production efficiency. However, PCBAPPS have to search for the optimal result in their own vast solution space. They are complex combinatorial optimization problems. The optimization of PCBAPPS constructs a unified solution space which includes two sub‐solution space stated above. In this paper, dynamic optimization of PCBAPPS is implemented and the solution efficiency is improved.

PS model holds unified standard form on the basis of logical contour and numerical matrix. It is adopted to describe the static structure and dynamic characteristic of PCBA system and combine with GA to solve the integrated optimization problem of PCBAPPS effectively and dynamically.

An 8‐node solid element applicable for thin structures is presented. The element employs eighteen assumed stress modes and the conventional displacement interpolation. The formulation starts with the hybrid stress element proposed by Pian and Tong. The higher order stress modes are first decomposed into the ones which do and do not lead to thin‐element locking. The recently established methodology of admissible matrix formulation allows the decoupling of the above two categories of stress modes in the flexibility matrix without triggering element instability or failure of the patch test. The element stiffness can thus be decomposed into a series of matrices. Locking can be eliminated by adjusting the magnitude of the pertinent matrices. Accuracy and convergence rate of the present element are found to be competent to many of the existing plate and shell models.

In this paper, a hybrid stress 12‐node brick element is presented. Its assumed stress field is derived by first examining the deformation modes of a geometrically regular element and then generalizing to other element configurations using tensorial transformation. The total number of stress modes is 30 which is minimal for securing the element rank. To reduce the computational cost associated with the fully populated flexibility matrix, the admissible matrix formation is employed to induce high sparsity in the matrix. Popular beam bending benchmark problems are examined. The proposed elements deliver encouraging accuracy.