Search results for: product optimization

Authors: Harald Lang, Michael Bader, A. Buchroithner

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Holistic methods covering the development process as a whole – e.g. systems engineering – have established themselves in product design. However, technical product optimization, representing improvements in efficiency and/or minimization of loss, usually applies to single components of a system. A holistic approach is being defined based on a hierarchical point of view of systems engineering. This is subsequently presented using the example of an electromechanical flywheel energy storage system for automotive applications.

Keywords: design, product development, product optimization, systems engineering

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Authors: Misganaw Abebe Baye, Ji-Woo Park, Beom-Soo Kang

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The product quality of multi-point dieless forming (MDF) is identified to be dependent on the process parameters. Moreover, a certain variation of friction and material properties may have a substantially worse influence on the final product quality. This study proposed on how to compensate the MDF product defects by minimizing the sensitivity of noise parameter variations. This can be attained by reliability-based robust optimization (RRO) technique to obtain the optimal process setting of the controllable parameters. Initially two MDF Finite Element (FE) simulations of AA3003-H14 saddle shape showed a substantial amount of dimpling, wrinkling, and shape error. FE analyses are consequently applied on ABAQUS commercial software to obtain the correlation between the control process setting and noise variation with regard to the product defects. The best prediction models are chosen from the family of metamodels to swap the computational expensive FE simulation. Genetic algorithm (GA) is applied to determine the optimal process settings of the control parameters. Monte Carlo Analysis (MCA) is executed to determine how the noise parameter variation affects the final product quality. Finally, the RRO FE simulation and the experimental result show that the amendment of the control parameters in the final forming process leads to a considerably better-quality product.

Keywords: dimpling, multi-point dieless forming, reliability-based robust optimization, shape error, variation, wrinkling

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Authors: Michael Zenker, Henrik Prinzhorn, Christian Böning, Tom Strating

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Large-scale products are often assembled according to the job-site principle, meaning that during the assembly the product is located at a fixed position, while the area requirements are constantly changing. On one hand, the product itself is growing with each assembly step, whereas varying areas for storage, machines or working areas are temporarily required. This is an important factor when arranging products to be assembled within the factory. Currently, it is common to reserve a fixed area for each product to avoid overlaps or collisions with the other assemblies. Intending to be large enough to include the product and all adjacent areas, this reserved area corresponds to the superposition of the maximum extents of all required areas of the product. In this procedure, the reserved area is usually poorly utilized over the course of the entire assembly process; instead a large part of it remains unused. If the available area is a limited resource, a systematic arrangement of the products, which complies with the dynamic area requirements, will lead to an increased area utilization and productivity. This paper presents the results of a study on the arrangement of assembly objects assuming dynamic, competing area requirements. First, the problem situation is extensively explained, and existing research on associated topics is described and evaluated on the possibility of an adaptation. Then, a newly developed mathematical optimization model is introduced. This model allows an optimal arrangement of dynamic areas, considering logical and practical constraints. Finally, in order to quantify the potential of the developed method, some test series results are presented, showing the possible increase in area utilization.

Keywords: dynamic area requirements, facility layout problem, optimization model, product assembly

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Authors: Richardson Ciguene, Bertrand Marron, Nicolas Habert

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Today, more and more consumers are purchasing their products and services online. At the same time, the penetration rate of very small and medium-sized businesses on marketplaces continues to increase, which has the direct impact of intensifying competition between sellers. Thus, only the best-optimized deals are ranked well by algorithms and are visible to consumers. However, it is almost impossible to know all the Brand Content rules and criteria established by marketplaces, which is essential to optimizing their product sheets, especially since these rules change constantly. In this paper, we propose to detail this question of Brand Content optimization by taking into account the case of Amazon in order to capture the scientific dimension behind such a subject. In a second step, we will present the genesis of our research project, DEEPERFECT, which aims to set up original methods and effective tools in order to help sellers present on marketplaces in the optimization of their branded content.

Keywords: e-commerce, scoring, marketplace, Amazon, brand content, product sheets

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Authors: Yuhan Lin, Rohan Kekatpure, Cassidy Yeung

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In Digital Marketing, robust quantification of View-through attribution (VTA) is necessary for evaluating channel effectiveness. VTA occurs when a product purchase is aided by an Ad but without an explicit click (e.g. a TV ad). A lack of a tracking mechanism makes VTA estimation challenging. Most prevalent VTA estimation techniques rely on post-purchase in-product user surveys. User surveys enable the calculation of channel multipliers, which are the ratio of the view-attributed to the click-attributed purchases of each marketing channel. Channel multipliers thus provide a way to estimate the unknown VTA for a channel from its known click attribution. In this work, we use Convex Optimization to compute channel multipliers in a way that enables a mathematical encoding of the expected channel behavior. Large fluctuations in channel attributions often result from overfitting the calculations to user surveys. Casting channel attribution as a Convex Optimization problem allows an introduction of constraints that limit such fluctuations. The result of our study is a distribution of channel multipliers across the entire marketing funnel, with important implications for marketing spend optimization. Our technique can be broadly applied to estimate Ad effectiveness in a privacy-centric world that increasingly limits user tracking.

Keywords: digital marketing, survey analysis, operational research, convex optimization, channel attribution

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Authors: Agarana Michael C., Akinlabi Esther T., Pule Kholopane

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Innovation in manufacturing process technologies and associated product design affects the prospects for manufacturing today and in near future. In this study some theoretical methods, useful as tools in advanced manufacturing, are considered. In particular, some basic Mathematical, Operational Research, Heuristic, and Statistical techniques are discussed. These techniques/methods are very handy in many areas of advanced manufacturing processes, including process planning optimization, modelling and analysis. Generally the production rate requires the application of Mathematical methods. The Emerging Trends Processes in Advanced Manufacturing can be enhanced by using Mathematical Modelling and Optimization techniques.

Keywords: mathematical modelling, optimization, emerging trends, advanced manufacturing

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Authors: Farzaneh Rajabighamchi, Stan van Hoesel, Christof Defryn

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The generalized traveling salesman problem (GTSP) is an extension of the traveling salesman problem (TSP) where the set of nodes is partitioned into clusters, and the salesman must visit exactly one node per cluster. In this research, we apply the definition of the GTSP to an order picker routing problem with multiple locations per product. As such, each product represents a cluster and its corresponding nodes are the locations at which the product can be retrieved. To pick a certain product item from the warehouse, the picker needs to visit one of these locations during its pick tour. As all products are scattered throughout the warehouse, the product clusters not separated geographically. We propose an exact LP model as well as heuristic and meta-heuristic solution algorithms for the order picking problem with multiple product locations.

Keywords: warehouse optimization, order picking problem, generalised travelling salesman problem, heuristic algorithm

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Authors: Kiyohiro Yamazaki

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The purpose of this paper is to examine the hypothesis explaining the mechanism in the case, where the product is deleted or reduced the fundamental function of the product through the product concept changes in the digital camera industry. This paper points out not owning the fundamental technology might cause the change of the product concept. Casio could create new competitive factor so that this paper discusses a possibility of the mechanism of changing the product concept.

Keywords: firm without fundamental technology, product development, product concept, digital camera industry, Casio

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Authors: Mitat Uysal

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A new met heuristic optimization algorithm called as Migrating Birds Optimization is used for curve fitting by rational cubic Bezier Curves. This requires solving a complicated multivariate optimization problem. In this study, the solution of this optimization problem is achieved by Migrating Birds Optimization algorithm that is a powerful met heuristic nature-inspired algorithm well appropriate for optimization. The results of this study show that the proposed method performs very well and being able to fit the data points to cubic Bezier Curves with a high degree of accuracy.

Keywords: algorithms, Bezier curves, heuristic optimization, migrating birds optimization

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Authors: Lateef Bamidele

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Over the years, radiographic examinations are the most used diagnostic tools in the Nigerian health care system, but most diagnostic examinations carried out do not have records of patient doses. Lack of adequate information on patient doses has been a major hindrance in quantifying the radiological risk associated with radiographic examinations. This study aimed at estimating dose–area product (DAP) of patient examined in X-Ray units in selected hospitals in Southern Nigeria. The standard projections selected are chest posterior-anterior (PA), abdomen anterior-posterior (AP), pelvis AP, pelvis lateral (LAT), skull AP/PA, skull LAT, lumbar spine AP, lumbar spine, LAT. Measurement of entrance surface dose (ESD) was carried out using thermoluminescent dosimeter (TLD). Measured ESDs were converted into DAP using the beam area of patients. The results show that the mean DAP ranged from 0.17 to 18.35 Gycm². The results obtained in this study when compared with those of NRPB-HPE were found to be higher. These are an indication of non optimization of operational conditions.

Keywords: dose–area product, radiographic examinations, patient doses, optimization

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Authors: Ahmed Metawea, Rodrigo Soto, Majeida Kharejesh, Gavin Walker, Ahmad B. Albadarin

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In this study, towards a green approach, we have investigated the effect of operating conditions of solvent assessed twin-screw extruder (TSE) for the production of 4, 4-bipyridine (1-dimensional coordinated polymer (1D)) based coordinated polymer using cobalt nitrate as a metal precursor with molar ratio 1:1. Different operating parameters such as solvent percentage, screw speed and feeding rate are considered. The resultant product is characterized using offline characterization methods, namely Powder X-ray diffraction (PXRD), Raman spectroscopy and scanning electron microscope (SEM) in order to investigate the product purity and surface morphology. A lower feeding rate increased the product’s quality as more resident time was provided for the reaction to take place. The most important influencing factor was the amount of liquid added. The addition of water helped in facilitating the reaction inside the TSE by increasing the surface area of the reaction for particles

Keywords: MOFS, multivariate analysis, process optimization, chemometric

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Authors: Naga Velamakuri, Jyothi K. Reddy

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Quality must be designed into a product and not inspected has become the main motto of all the companies globally. Due to the rapidly increasing technology in the past few decades, the nature of demands from the consumers has become more sophisticated. To sustain this global revolution of innovation in production systems, companies have to take steps to accommodate this technology growth. In this process of understanding the customers' expectations, all the firms globally take steps to deliver a perfect output. Most of these techniques also concentrate on the consistent development and optimization of the product to exceed the expectations. Quality Function Deployment(QFD) and Modular Function Deployment(MFD) are such techniques which rely on the voice of the customer and help deliver the needs. In this paper, Quality Function Deployment and Modular Function Deployment techniques which help in converting the quantitative descriptions to qualitative outcomes are discussed. The area of interest would be to understand the scope of each of the techniques and the application range in product development when these are applied together to any problem. The research question would be mainly aimed at comprehending the limitations using modularity in product development.

Keywords: quality function deployment, modular function deployment, house of quality, methodology

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Authors: Parisa Bagheri Tookanlou

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In this paper, we analyze a product line design problem faced by a manufacturing firm where the product line consists of a customized product in addition to a standard product and is offered in a market in which customers are heterogeneous on aesthetic attributes of the product. The customization level of a product is defined by the fraction of aesthetic attributes of the product that the manufacturer chooses to customize. In contrast to the existing literature on product line design that predominantly assumes deterministic demand, we consider the presence of demand uncertainty and frame the product line design problem in a single period (news vendor) setting. We examine the effect of demand uncertainty on product line decisions. Furthermore, we also examine how product line decisions are influenced by channel structure. While we use the centralized channel as a benchmark, we consider the decentralized dual channel where the customized product is sold through an online channel owned by the manufacturer and the standard product is sold through a retailer. We introduce a supply contract between the manufacturer and the retailer for improving channel efficiency and coordinate the distribution channel.

Keywords: product line design, demand uncertainty, customization level, distribution channel

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Authors: Meimei Zheng

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Product personalization could not only bring new profits to companies but also provide the direction of long-term development for companies. However, the characteristics of personalized product cause some new problems. This paper investigates how companies make decisions on the supply of personalized products when facing different customer attitudes to personalized product and service, constraints due to limited capacity and updates of personalized demand information. This study will provide optimal decisions for companies to develop personalized markets, resulting in promoting business transformation and improving business competitiveness.

Keywords: demand forecast updating, limited capacity, personalized products, optimization

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Authors: Kostas Metaxiotis

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Portfolio optimization is one of the most important topics in finance. This paper proposes a mean–variance–skewness (MVS) portfolio optimization model. Traditionally, the portfolio optimization problem is solved by using the mean–variance (MV) framework. In this study, we formulate the proposed model as a three-objective optimization problem, where the portfolio's expected return and skewness are maximized whereas the portfolio risk is minimized. For solving the proposed three-objective portfolio optimization model we apply an adapted version of the non-dominated sorting genetic algorithm (NSGAII). Finally, we use a real dataset from FTSE-100 for validating the proposed model.

Keywords: evolutionary algorithms, portfolio optimization, skewness, stock selection

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Authors: Xiaojing Gao, James Njuguna

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This paper emphasizes the importance of integrating project management and systems engineering for innovative system design and production development. The research highlights the need for a flexible approach that unifies these disciplines, as their isolation often leads to communication challenges and complexity within multidisciplinary teams. The paper aims to elucidate the intricate relationship between project management and systems engineering, recommending the consolidation of engineering disciplines into a single lifecycle for improved support of the design and development process. The research identifies a synergy between these disciplines, focusing on streamlining information communication during product design and development. The insights gained from this process can lead to product design optimization. Additionally, the paper introduces a proposed Project Management-Based Systems Engineering (PMBSE) framework, emphasizing effective communication, efficient processes, and advanced tools to enhance product development outcomes within the product lifecycle.

Keywords: system engineering, product design and development, project management, cross-disciplinary

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Authors: Jin-Ho Han, Kyong-Ho Ri, Ju-Yong Hwang, Song-Guk Kim, Sang-Jin Kim

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This study focuses on the design of a sonochemical reactor that has excellent anticorrosion effect and acoustic pressure distribution by optimization of the reaction vessel. Sonochemical reactors using the Barbell horn transducer have advantages, including high efficiency of energy conversion, large amplitude of the transducer and low damping. Meanwhile, we performed COMSOL optimization simulations to minimize the corrosion of the horn and the inner wall of the reaction vessel by cavitation bubbles during the sonochemical reaction. It was experimentally verified that the immersion depth of the horn obtained by simulation and the geometric parameters of the vessel are suitable for optimization purposes. In this way, a sonochemical reactor with good acoustic pressure distribution and suitable for obtaining a purer reaction product can be designed.

Keywords: sonochemical reactor, COMSOL optimization simulation, immersion type, barbell horn

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Authors: J. Satya Eswari, Ch. Venkateswarlu

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The formulation of a commercial pharmaceutical product involves several composition factors and response characteristics. When the formulation requires to satisfy multiple response characteristics which are conflicting, an optimal solution requires the need for an efficient multiobjective optimization technique. In this work, a regression is combined with a non-dominated sorting differential evolution (NSDE) involving Naïve & Slow and ε constraint techniques to derive different multiobjective optimization strategies, which are then evaluated by means of a trapidil pharmaceutical formulation. The analysis of the results show the effectiveness of the strategy that combines the regression model and NSDE with the integration of both Naïve & Slow and ε constraint techniques for Pareto optimization of trapidil formulation. With this strategy, the optimal formulation at pH=6.8 is obtained with the decision variables of micro crystalline cellulose, hydroxypropyl methylcellulose and compression pressure. The corresponding response characteristics of rate constant and release order are also noted down. The comparison of these results with the experimental data and with those of other multiple regression model based multiobjective evolutionary optimization strategies signify the better performance for optimal trapidil formulation.

Keywords: pharmaceutical formulation, multiple regression model, response surface method, radial basis function network, differential evolution, multiobjective optimization

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Authors: Supattra Pranee

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The objectives of this research were to study the product development process to obtain a community standard product certificate and to set a guideline for the product development process to obtain the community product certificate. Focus group discussion was conducted with many experts in the field, local government officials, and representatives from local producers in Bangkontee district. The findings revealed that there were eight important processes to obtain the community product certificate: 1) prepare document, 2) submit the document, 3) set up an appointment for onsite inspection, 4) onsite inspection and sample collections, 5) evaluate samples, 6) obtain test result, and 7) obtain certificate.

Keywords: perceived values, tourist destination, visiting, product development

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Authors: Serges Mendomo Meye, Li Guowei, Shen Zhenzhong, Gan Lei, Xu Liqun

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Given the limitations of the original whale optimization algorithm (WAO) in local optimum and low convergence accuracy in truss structure optimization problems, based on the fundamental whale algorithm, an improved whale optimization algorithm (SWAO) based on information entropy is proposed. The information entropy itself is an uncertain measure. It is used to control the range of whale searches in path selection. It can overcome the shortcomings of the basic whale optimization algorithm (WAO) and can improve the global convergence speed of the algorithm. Taking truss structure as the optimization research object, the mathematical model of truss structure optimization is established; the cross-sectional area of truss is taken as the design variable; the objective function is the weight of truss structure; and an improved whale optimization algorithm (SWAO) is used for optimization design, which provides a new idea and means for its application in large and complex engineering structure optimization design.

Keywords: information entropy, structural optimization, truss structure, whale algorithm

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Authors: Ramin Javadzadeh

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The particle swarm optimization are Meta heuristic optimization method, which are used for clustering and pattern recognition applications are abundantly. These algorithms in multimodal optimization problems are more efficient than genetic algorithms. A major drawback in these algorithms is their slow convergence to global optimum and their weak stability can be considered in various running of these algorithms. In this paper, improved Particle swarm optimization is introduced for the first time to overcome its problems. The fuzzy cellular automata is used for improving the algorithm efficiently. The credibility of the proposed approach is evaluated by simulations, and it is shown that the proposed approach achieves better results can be achieved compared to the Particle swarm optimization algorithms.

Keywords: cellular automata, cellular learning automata, local search, optimization, particle swarm optimization

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Authors: María L. Jalón, Feargal Brennan

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A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: non-stationary stochastic optimization, oscillating water, temporal variability, wave energy

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Authors: Liudmyla Koliechkina, Olena Dvirna

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The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: discrete set, linear combinatorial optimization, multi-objective optimization, Pareto solutions, partial permutation set, structural graph

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Authors: Mohammad Y. Badiee, Saeed Golestani, Mir Saman Pishvaee

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In recent years consumers and governments have been pushing companies to design their activities in such a way as to reduce negative environmental impacts by producing renewable product or threat free disposal policy more and more. It is therefore important to focus more accurate to the optimization of various aspect of total supply chain. Modeling a supply chain can be a challenging process due to the fact that there are a large number of factors that need to be considered in the model. The use of multi-objective optimization can lead to overcome those problems since more information is used when designing the model. Uncertainty is inevitable in real world. Considering uncertainty on parameters in addition to use multi-objectives are ways to give more flexibility to the decision making process since the process can take into account much more constraints and requirements. In this paper we demonstrate a stochastic scenario based robust model to cope with uncertainty in a closed-loop multi-objective supply chain. By applying the proposed model in a real world case, the power of proposed model in handling data uncertainty is shown.

Keywords: supply chain management, closed-loop supply chain, multi-objective optimization, goal programming, uncertainty, robust optimization

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Authors: R. M. Rizk-Allah

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This paper presents co-evolutionary fruit fly optimization algorithm based on firefly algorithm (CFOA-FA) for solving unconstrained optimization problems. The proposed algorithm integrates the merits of fruit fly optimization algorithm (FOA), firefly algorithm (FA) and elite strategy to refine the performance of classical FOA. Moreover, co-evolutionary mechanism is performed by applying FA procedures to ensure the diversity of the swarm. Finally, the proposed algorithm CFOA- FA is tested on several benchmark problems from the usual literature and the numerical results have demonstrated the superiority of the proposed algorithm for finding the global optimal solution.

Keywords: firefly algorithm, fruit fly optimization algorithm, unconstrained optimization problems

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Authors: Yani Shi, Jiaqi Yan

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A new product is important for companies to extend consumers and manifest competitiveness. New product often involves new features that consumers might not be familiar with while it may also have a competitive advantage to attract consumers compared to established products. However, although most online retailers employ recommendation agents (RA) to influence consumers’ product choice decision, recommended new products are not accepted and chosen as expected. We argue that it might also be caused by providing a new product recommendation in the wrong way at the wrong time. This study seeks to discuss how new product evaluations sourced from third parties could be employed in RAs as evidence of the superiority for the new product and how the new product recommendation could be provided to a consumer at the right time so that it can be accepted and finally chosen during the consumer’s decision-making process. A 2*2 controlled laboratory experiment was conducted to understand the selection of new product recommendation sources and recommendation timing. Human subjects were randomly assigned to one of the four treatments to minimize the effects of individual differences on the results. Participants were told to make purchase choices from our product categories. We find that a new product recommended right after a similar existing product and with the source of the expert review will be more likely to be accepted. Based on this study, both theoretical and practical contributions are provided regarding new product recommendation.

Keywords: new product recommendation, recommendation timing, recommendation source, recommendation agents

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Authors: K. K. Lee, H. W. Han, H. L. Kang, T. A. Kim, S. H. Han

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For the robust optimization of the manufacturing product design, there are design objectives that must be achieved, such as a minimization of the mean and standard deviation in objective functions within the required sensitivity constraints. The authors utilized the sensitivity of objective functions and constraints with respect to the effective design variables to reduce the computational burden associated with the evaluation of the probabilities. The individual mean and sensitivity values could be estimated easily by using the 9 level orthogonal array based response surface models optimized by the stepwise regression. The present study evaluates a proposed procedure from the robust optimization of rubber domes that are commonly used for keyboard switching, by using the 9 level orthogonal array and stepwise regression along with a desirability function. In addition, a new robust optimization process, i.e., the I2GEO (Identify, Integrate, Generate, Explore and Optimize), was proposed on the basis of the robust optimization in rubber domes. The optimized results from the response surface models and the estimated results by using the finite element analysis were consistent within a small margin of error. The standard deviation of objective function is decreasing 54.17% with suggested sensitivity based robust optimization. (Business for Cooperative R&D between Industry, Academy, and Research Institute funded Korea Small and Medium Business Administration in 2017, S2455569)

Keywords: objective function, orthogonal array, response surface model, robust optimization, stepwise regression

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Authors: Mohita Gangwar Sharma

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Different factors are compelling manufacturers to move towards the phenomenon of servitization i.e. when firms go beyond giving support to the customers in operating the equipment. The challenges that are being faced in this transition by the manufacturing firms from being a product provider to a product- service provider are multipronged. Product-Service Systems (PSS) lies in between the pure-product and pure-service continuum. Through this study, we wish to understand the dimensions of ‘PSS-quality’. We draw upon the quality literature for both the product and services and through an expert survey for a specific transportation sector using analytical hierarchical process (AHP) derive a conceptual model that can be used as a comprehensive measurement tool for PSS offerings.

Keywords: servitisation, quality, product-service system, AHP

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Authors: Pham Van Nha, Le Cam Binh

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Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO’s ideas are simple and easy to understand but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply in the multivariate data classification. First, PSOs general mathematical model (MPSO) is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.

Keywords: analysis of optimization, artificial intelligence based optimization, optimization for learning and data analysis, global optimization

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Authors: Yousuf Alkhezi

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Since most of the literature on algebra does not make much deal with the special case of mapping cone. This paper is an alternative way to examine the special tensor product and mapping cone. Also, we show that the isomorphism that implies the mapping cone commutes with the tensor product for the ordinary tensor product no longer holds for the pinched tensor product. However, we show there is a morphism. We will introduce an alternative way of mapping cone. We are looking for more properties which is our future project. Also, we want to apply these new properties in some application. Many results and examples with classical algorithms will be provided.

Keywords: complex, tensor product, pinched tensore product, mapping cone

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