Journal articles: 'Cutting stock problem Mathematical models'

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Poltroniere, Sônia Cristina, Silvio Alexandre Araujo, and Kelly Cristina Poldi. "Optimization of an Integrated Lot Sizing and Cutting Stock Problem in the Paper Industry." TEMA (São Carlos) 17, no. 3 (December 20, 2016): 305. http://dx.doi.org/10.5540/tema.2016.017.03.0305.

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Two important optimization problems occur in the planning and production scheduling in paper industries: the lot sizing problem and the cutting stock problem. The lot sizing problem must determine the quantity of jumbos of different types of paper to be produced in each machine over a finite planning horizon.These jumbos are then cut in order to meet the demand of items for each period. In this paper, we deal with the integration of these two problems, aiming to minimize costs of production and in- ventory of jumbos, as well as the trim loss of paper generated during the cutting process. Two mathematical models for the integrated problem are considered, and these models are solved both heuristically and using an optimization package. Attempting to get lower bounds for the problem, relaxed versions of the models also have been solved. Finally, computational experiments are presented and discussed.

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Farley, Alan A. "Mathematical Programming Models for Cutting-Stock Problems in the Clothing Industry." Journal of the Operational Research Society 39, no. 1 (January 1988): 41. http://dx.doi.org/10.2307/2581997.

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Farley, Alan A. "Mathematical Programming Models for Cutting-Stock Problems in the Clothing Industry." Journal of the Operational Research Society 39, no. 1 (January 1988): 41–53. http://dx.doi.org/10.1057/jors.1988.6.

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Delorme, Maxence, Manuel Iori, and Silvano Martello. "Bin packing and cutting stock problems: Mathematical models and exact algorithms." European Journal of Operational Research 255, no. 1 (November 2016): 1–20. http://dx.doi.org/10.1016/j.ejor.2016.04.030.

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Poldi, Kelly Cristina, and Silvio Alexandre de Araujo. "Mathematical models and a heuristic method for the multiperiod one-dimensional cutting stock problem." Annals of Operations Research 238, no. 1-2 (January 18, 2016): 497–520. http://dx.doi.org/10.1007/s10479-015-2103-2.

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Wang, Fu-Kwun, and Feng-Tai Liu. "Flexible Stock Allocation and Trim Loss Control for Cutting Problem in the Industrial-Use Paper Production." Mathematical Problems in Engineering 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/521386.

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We consider a one-dimensional cutting stock problem (CSP) in which the stock widths are not used to fulfill the order but kept for use in the future for the industrial-use paper production. We present a new model based on the flexible stock allocation and trim loss control to determine the production quantity. We evaluate our approach using a real data and show that we are able to solve industrial-size problems, while also addressing common cutting considerations such as aggregation of orders, multiple stock widths, and cutting different patterns on the same machine. In addition, we compare our model with others, including trim loss minimization problem (TLMP) and cutting stock problem (CSP). The results show that the proposed model outperforms the other two models regarding total flexibility and trim loss ratio.

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Sá Santos, José Victor, and Napoleão Nepomuceno. "Computational Performance Evaluation of Column Generation and Generate-and-Solve Techniques for the One-Dimensional Cutting Stock Problem." Algorithms 15, no. 11 (October 25, 2022): 394. http://dx.doi.org/10.3390/a15110394.

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The Cutting Stock Problem (CSP) is an optimisation problem that roughly consists of cutting large objects in order to produce small items. The computational effort for solving this problem is largely affected by the number of cutting patterns. In this article, in order to cope with large instances of the One-Dimensional Cutting Stock Problem (1D-CSP), we resort to a pattern generating procedure and propose a strategy to restrict the number of patterns generated. Integer Linear Programming (ILP) models, an implementation of the Column Generation (CG) technique, and an application of the Generate-and-Solve (G&S) framework were used to obtain solutions for benchmark instances from the literature. The exact method was capable of solving small and medium sized instances of the problem. For large sized instances, the exact method was not applicable, while the effectiveness of the other methods depended on the characteristics of the instances. In general, the G&S method presented successful results, obtaining quasi-optimal solutions for the majority of the instances, by employing the strategy of artificially reducing the number of cutting patterns and by exploiting them in a heuristic framework.

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Li, Yan Cang, Juan Juan Suo, and Shu Jing Zhou. "Improved ACO for Dimensional Cutting-Stock Problem." Applied Mechanics and Materials 26-28 (June 2010): 277–80. http://dx.doi.org/10.4028/www.scientific.net/amm.26-28.277.

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In order to find an effective method for solving the NP problem-dimensional cutting stock problem, the improved ACO based on entropy was introduced．After introducing the basic knowledge of the improved ACO, the dimensional cutting-stock problem’s mathematical model was set up．And the improved ACO was employed to optimize the problem．Computed results indicate that the ant colony algorithm can approach the theoretical optimal solution，and its astringency is good．This study provides a new approach for the optimization of the NP hard problems.

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Arenales, Marcos Nereu, Adriana Cristina Cherri, Douglas N. do Nascimento, and Andréa Vianna. "A NEW MATHEMATICAL MODEL FOR THE CUTTING STOCK/LEFTOVER PROBLEM." Pesquisa Operacional 35, no. 3 (December 2015): 509–22. http://dx.doi.org/10.1590/0101-7438.2015.035.03.0509.

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Sugi, Masao, Yusuke Shiomi, Tsuyoshi Okubo, Kazuyoshi Inoue, and Jun Ota. "A Solution for 2D Rectangular Cutting Stock Problems with 3-Stage Guillotine-Cutting Constraint." International Journal of Automation Technology 4, no. 5 (September 5, 2010): 461–68. http://dx.doi.org/10.20965/ijat.2010.p0461.

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The cutting stock problem (CSP) adversely affecting processing industry profits has been studied aggressively in mathematical planning but the results are not often used at real production sites and solutions are often still found manually by experienced personnel because real processing constraints have not been focused on. This paper deals with the 2-dimensional rectangular cutting stock problem (2DRCSP) in which the shape of a cut piece is rectangular, assuming a roll-shaped stock often used in actual processing and proposing a solution taking processing called 3-stage guillotine cutting into account.

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Powar, P. L., Ravi Vishwakarma, and Chandrashekhar Meshram. "Effective Mathematical Simulation for One-Dimensional Cutting Stock Problem using Heuristics Approach." International Journal of Hybrid Information Technology 10, no. 1 (January 31, 2017): 111–24. http://dx.doi.org/10.14257/ijhit.2017.10.1.10.

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Furini, Fabio, and Enrico Malaguti. "Models for the two-dimensional two-stage cutting stock problem with multiple stock size." Computers & Operations Research 40, no. 8 (August 2013): 1953–62. http://dx.doi.org/10.1016/j.cor.2013.02.026.

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Zastempowski, Marcin, Andrzej Bochat, Lubomir Hujo, Juraj Jablonicky, and Maciej Janiec. "Impact of Cutting Units’ Design on Biomass Cutting Resistance." Acta Mechanica et Automatica 16, no. 3 (September 1, 2022): 259–65. http://dx.doi.org/10.2478/ama-2022-0031.

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Abstract The paper presents mathematical models describing the moments of resistance to cutting on the cutting drum shafts in the biomass cutting process. The mathematical procedures described in the paper have been verified on a test stand developed and constructed by the authors, which reflects real conditions of the process of cutting plant material into pieces of specified lengths. Experimental verification proved that the developed mathematical models are adequate for drums of both cylindrical and conical constructions. The value of the average error did not exceed 13%. Following the mathematical elaboration and verification studies, the authors carried out calculations for machines currently available on the market that are equipped with drum cutting units. The calculations were carried out for the most commonly cut material, i.e. for maize, straw and green plant materials. The obtained results confirm the complexity of the problem arising from a wide range of numerical values of cutting resistance, which is contained in the range of 400–1,800 nm. The compiled database can be practically applied in the selection of machines for specific field works, and the mathematical models developed and verified in the study can be applied at the stage of designing new designs of cutting drums used in forage harvesters.

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Parreño, F., and R. Alvarez-Valdes. "Mathematical models for a cutting problem in the glass manufacturing industry." Omega 103 (September 2021): 102432. http://dx.doi.org/10.1016/j.omega.2021.102432.

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Vishwakarma, Ravi, and P. L. Powar. "An efficient mathematical model for solving one-dimensional cutting stock problem using sustainable trim." Advances in Industrial and Manufacturing Engineering 3 (November 2021): 100046. http://dx.doi.org/10.1016/j.aime.2021.100046.

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Rao, Yunqing, Dezhong Qi, and Jinling Li. "An Improved Hierarchical Genetic Algorithm for Sheet Cutting Scheduling with Process Constraints." Scientific World Journal 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/202683.

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For the first time, an improved hierarchical genetic algorithm for sheet cutting problem which involvesncutting patterns formnon-identical parallel machines with process constraints has been proposed in the integrated cutting stock model. The objective of the cutting scheduling problem is minimizing the weighted completed time. A mathematical model for this problem is presented, an improved hierarchical genetic algorithm (ant colony—hierarchical genetic algorithm) is developed for better solution, and a hierarchical coding method is used based on the characteristics of the problem. Furthermore, to speed up convergence rates and resolve local convergence issues, a kind of adaptive crossover probability and mutation probability is used in this algorithm. The computational result and comparison prove that the presented approach is quite effective for the considered problem.

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Chen, W.-F. "A mathematical solution to the design and manufacturing problems of ball-end cutters having a cutting edge with constant angle to the axis." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 218, no. 3 (March 1, 2004): 301–8. http://dx.doi.org/10.1243/095440604322900426.

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This paper considers two of the major problems associated with the design and manufacture of ball-end cutters whose cutting edge lies at a constant angle to the axis. The first problem involves the inability to solve the mathematical description of the cutting edge at the top of the ball-end cutter, while the second problem relates to the tendency of the grinding wheel feeding speed description to approach infinity in the same region. Mathematical models are developed to overcome these problems. These models provide a valuable reference for the future design and manufacture of cutters of this type.

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Li, Shengguo, Jin Peng, and Bo Zhang. "A Stock Model with Varying Stock Diffusion for Uncertain Market." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 26, no. 04 (July 12, 2018): 679–92. http://dx.doi.org/10.1142/s0218488518500319.

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The option-pricing problem is an important topic in modern finance. In this paper, we propose a stock model with varying stock diffusion based on uncertainty theory. The European option pricing formulas are derived from the proposed uncertain stock model, and some mathematical properties of these formulas are investigated. Moreover, extended uncertain stock models are introduced and discussed. Finally, numerical examples are given to illustrate the proposed model.

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Zhang, Chun Liang, and Li Ping Chen. "Real Time Monitoring of Cutting Chatter Based on Fuzzy Hidden Markov Models." Materials Science Forum 532-533 (December 2006): 1160–63. http://dx.doi.org/10.4028/www.scientific.net/msf.532-533.1160.

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The full automation of machine tools has gained substantial importance in manufacturing industries in recent years, as machining technology has progressed from manually operated production machines to highly advanced and sophisticated CNC machine tool. Whereas manufacturing technology has moved to the stage of automation, there is still an unsolved problem in metal cutting processes: cutting chatter. Due to its complexity, thus cutting chatter is still the primary problem in metal cutting processes. According to the characteristic of cutting chatter, a real time monitoring technique of cutting chatter based on fuzzy hidden Markov model (FHMM) was presented. Hidden Markov model (HMM) is a state-of-the-art technique for speech recognition because of its elegant mathematical structure and the availability of computer implementation of these models. In this paper, the fuzzy EM algorithm was used to the Baum-Welch algorithm in the HMM method, and the strategy of time frequency feature extraction to non-stability signal was described. The experimental results show that the proposed method is feasible and effective for the monitoring of cutting chatter in the metal cutting processes.

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Khan, Razaullah, Catalin Iulian Pruncu, Abdul Salam Khan, Khawar Naeem, Muhammad Abas, Qazi Salman Khalid, and Asnaf Aziz. "A Mathematical Model for Reduction of Trim Loss in Cutting Reels at a Make-to-Order Paper Mill." Applied Sciences 10, no. 15 (July 30, 2020): 5274. http://dx.doi.org/10.3390/app10155274.

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One of the main issues in a paper mill is the minimization of trim loss when cutting master reels and stocked reels into reels of smaller required widths. The losses produced in trimming at a paper mill are reprocessed by using different chemicals which contributes to significant discharge of effluent to surface water and causes environmental damage. This paper presents a real-world industrial problem of production planning and cutting optimization of reels at a paper mill and differs from other cutting stock problems by considering production and cutting of master reels of flexible widths and cutting already stocked over-produced and useable leftover reels of smaller widths. The cutting process of reels is performed with a limited number of cutting knives at the winder. The problem is formulated as a linear programming model where the generation of all feasible cutting patterns determines the columns of the constraint matrix. The model is solved optimally using simplex algorithm with the objective of trim loss minimization while satisfying a set of constraints. The solution obtained is rounded in a post-optimization procedure in order to satisfy integer constraints. When tested on data from the paper mill, the results of the proposed model showed a significant reduction in trim loss and outperformed traditional exact approaches. The cutting optimization resulted in minimum losses in paper trimming and a lesser amount of paper is reprocessed to make new reels which reduced the discharge of effluent to the environment.

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Bonfatti Júnior, Eraldo Antonio, Elaine Cristina Lengowski, Tamires De Almeida Sfeir, Bruno Gruber Nisponginski, Kaio Fanes, and Kauana Melissa Cunha Dickow. "Mathematical modeling to optimize pine lumber yield." Advances in Forestry Science 7, no. 1 (April 3, 2020): 877. http://dx.doi.org/10.34062/afs.v7i1.9767.

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In Brazil, only 4% of the 7.84 million hectares of planted forests is devoted to the production of lumber wood, being in Santa Catarina state most of the wood used for this purpose is of the Pinus genus. This work aims to estimate the maximum utilization of logs due to the production of wood boards in the city of Canoinhas, Santa Catarina. For that, a sawmill of the region were consulted and the dimensions of the pieces produced were verified. The dimensions and classes of logs commonly traded in the region were also raised. As a result, 82 models were created in Maxitora software in diagram format. With the cutting models the sawmill had its performance optimized with the use of techniques of operational research in a cutting problem. The whole linear programming technique was used for an estimated demand for the quantity of each of the pieces produced. The results showed that only five models are required to meet such demand, so the yield is 43.18%.

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Melega, Gislaine Mara, Silvio Alexandre de Araujo, and Raf Jans. "COMPARISON OF MIP MODELS FOR THE INTEGRATED LOT-SIZING AND ONE-DIMENSIONAL CUTTING STOCK PROBLEM." Pesquisa Operacional 36, no. 1 (April 2016): 167–96. http://dx.doi.org/10.1590/0101-7438.2016.036.01.0167.

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Tran, Bong Dang, Tuan Ngoc Pham, Nguyen Dai Tran, and Tuan Minh Ho. "OPTIMAL STRIP LAYOUT OF IRREGULAR SHAPES CUTTING FROM RECTANGULAR SHEET." Science and Technology Development Journal 13, no. 1 (March 30, 2010): 39–48. http://dx.doi.org/10.32508/stdj.v13i1.2068.

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This article deals with optimal nesting problem when parts are cut from rectangular sheet in the footwear industry. The objective of the research is minimizing the waste of material or maximizing the number of parts to be cut from sheet materials. By generating the mathematical models and building up their algorithms, the software for solving problem dedicates to a number of industries for saving time and minimizing waste of material, and increasing the cutting productivity.

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Kwon, Sue-Jeong, Seulgi Joung, and Kyungsik Lee. "Comparative analysis of pattern-based models for the two-dimensional two-stage guillotine cutting stock problem." Computers & Operations Research 109 (September 2019): 159–69. http://dx.doi.org/10.1016/j.cor.2019.05.005.

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Sotova, E. S., and M. N. Lazareva. "Increasing of cutting efficiency of heat-treated steel through the application of cutting tools of high-strength composite ceramic with coating E. S. Sotova, M. N. Lazareva." Izvestiya MGTU MAMI 6, no. 2-2 (March 20, 2012): 184–89. http://dx.doi.org/10.17816/2074-0530-68500.

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In the paper there is investigated the cutting tool properties of high-strength composite ceramics with multi-coated cutting hardened steel. Mathematical models of cutting are obtained. They establish the dependence of the wear and tear on the back of the instrument, roughness of the machined surface of the parts, the tangent component of the cutting forces, as well as cutting power on the modes of turning. A problem of cutting tools modes optimization is made of high-strength composite ceramics. It is established that the application of the multi-functional coatings on ceramic cutting tool allows you to increase the efficiency of processing.

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Tung, Pham Dinh. "Mathematical modeling and parametric identification of dynamic properties of mechanical subsystems tool and workpiece in turning process." MATEC Web of Conferences 226 (2018): 02017. http://dx.doi.org/10.1051/matecconf/201822602017.

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Research and modeling of dynamic structures of the subsystems tool and the workpiece is given continued attention. This is due to the fact that the analysis of the stability of the cutting process and the self-oscillation is necessary, first of all, to have a model of the dynamics of interacting subsystems tool and workpiece through the cutting process. A similar problem is in the study of the machining accuracy, particularly in cases where the workpiece has significant deformation displacement varying along the trajectory of the tool relative to the workpiece. This paper considers the problem of mathematical modeling and identification of inertial, damping, and stiffness properties of the subsystems tool and workpiece in the dynamics exercises of the cutting process. The algorithms and the results of the identification of parameters in mathematical models of mechanical subsystems tool and workpiece for the case of turning are resulted.

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Hnatushenko, V. V., T. A. Zheldak, and L. S. Koriashkina. "Mathematical model of steel consumption minimization considering the two-stage billets cutting." Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, no. 2 (2021): 118–24. http://dx.doi.org/10.33271/nvngu/2021-2/118.

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Purpose. To achieve a decrease in energy and resource costs in the multi-stage production of rolled products within a given plan through the development of appropriate mathware. Methodology. The multi-stage problem mathware for producing rolling steel products is developed on the basis of system approach applying fundamental principles of the optimization and operation research theory. Realization of the developed mathematical model allows discovering such a strategy of using steel during the whole manufacturing process, which minimizes not only the steel waste at the moment of its casting in a mold, but also the offcuts in the process of cutting the obtained ingots into the billets. Findings. A mathematical task model is built to minimize the amount of steel for producing a certain order of size of one cast volume only. The developed model specifies the possibility to pre-evaluate the billet optimal size, based on the necessary cutting along the final product length, appropriate for the certain billet form of section, and ingot weight limits. Originality. A mathematical model is provided for the optimal metal distribution process when implementing the plan of manufacturing rolling products. The model, in contrast to the existing ones, shifts the emphasis on forming the optimal ingot weight, which has a pre-calculated optimal cutting plan. Practical value. The use of the developed mathematical optimization model (minimizing the amount of steel for producing a certain order) as part of an automated decision support system for management of rolling production will reduce the number of cutting machine changeover and minimize resources use and stock balance.

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Aldaihani, Majid M., and Talla M. Al Deehani. "Mathematical models and a tabu search for the portfolio management problem in the Kuwait stock exchange." International Journal of Operational Research 7, no. 4 (2010): 445. http://dx.doi.org/10.1504/ijor.2010.032421.

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Суслов, Анатолий, Anatoliy Suslov, Дмитрий Петрешин, Dmitriy Petreshin, Олег Федонин, Oleg Fedonin, Виктор Хандожко, and Viktor Khandozhko. "Control automation of surface layer quality parameters and machinery operation properties at cutting." Science intensive technologies in mechanical engineering 2019, no. 8 (August 16, 2019): 28–36. http://dx.doi.org/10.30987/article_5d2635cb62fb56.07245294.

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A problem in the control automation of surface layer quality parameters and machinery operation properties at cutting is considered. For this purpose there are used corresponding control systems. The substantiation for the formation of the control system of surface layer quality parameters and machinery operation properties is shown. An algorithm of systems functioning is described, and mathematical models are shown.

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Koriashkina, Larysa, Volodymyr Saveliev, and Aleksey Zhelo. "On Mathematical Models of Some Optimization Problems Arising in the Production of Autoclaved Aerated Concrete." Advanced Engineering Forum 22 (May 2017): 173–81. http://dx.doi.org/10.4028/www.scientific.net/aef.22.173.

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A mathematical model of an optimization problem to define a short-term (one month) production plan which implements the best use of the production capacity with the condition of meeting the demand is proposed. Long-term planning of autoclaved production (up to six months) with the account of the dynamics of demand and possible residual products in stock are also considered. The results of computational experiments are presented.

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Satyanarayana, Kosaraju, Anne Venu Gopal, and Popuri Bangaru Babu. "Experimental Investigations and Modeling of Machining Titanium Alloy – Ti-6Al-4V." Applied Mechanics and Materials 315 (April 2013): 562–66. http://dx.doi.org/10.4028/www.scientific.net/amm.315.562.

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The problem of machining titanium is one of ever-increasing magnitude due to its low thermal conductivity and work hardening characteristic of the titanium alloy. The efficient machining of titanium alloy with coated carbides involves a proper selection of process parameters to minimizing the surface roughness and cutting force. In the present work, experimental studies have been carried out to obtain the optimum conditions for machining titanium alloy. The effect of machining parameters such speed, feed and depth of cut on the cutting force, surface roughness were investigated. The significance of these parameters, on cutting force and surface roughness has been established using the analysis of variance. Mathematical models have also been developed for estimating the cutting force and surface roughness on the basis of experimental results.

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Madić, Miloš, Srđan Mladenović, Marin Gostimirović, Miroslav Radovanović, and Predrag Janković. "Laser cutting optimization model with constraints: Maximization of material removal rate in CO2 laser cutting of mild steel." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 234, no. 10 (April 13, 2020): 1323–32. http://dx.doi.org/10.1177/0954405420911529.

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Taking full advantage of what laser cutting technology offers in terms of achieving superb quality cuts at low cost and high production rates requires the optimization of laser cutting parameters. This implies the need to formulate and solve different laser cutting optimization problems. In this article, an optimization model for CO2 laser cutting of mild steel is developed. The laser cutting optimization problem was explicitly formulated as a single-objective optimization problem with five non-linear constraints of the equality, inequality and range type. The goal was to determine the laser cutting parameter values so as to maximize the material removal rate while simultaneously considering practical process constraints related to dross formation, kerf width, perpendicularity deviation, surface roughness and severance energy. Two crossed experimental designs of different resolutions were performed in order to define six mathematical models, which were used in the formulation of the optimization problem. For the purpose of optimization, the exhaustive iterative search algorithm was applied, since it determines solutions whose optimality is guaranteed in the given discrete space of input variable values. The practical usability of the developed laser cutting optimization model and the effectiveness of the applied optimization approach were proved while solving a real case study aimed at the optimization of laser cutting parameters for cutting parts for the furnace industry.

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Ali, Musrrat, Chang Wook Ahn, and Millie Pant. "Trim Loss Optimization by an Improved Differential Evolution." Mathematical Problems in Engineering 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/706350.

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The “trim loss problem” (TLP) is one of the most challenging problems in context of optimization research. It aims at determining the optimal cutting pattern of a number of items of various lengths from a stock of standard size material to meet the customers’ demands that the wastage due to trim loss is minimized. The resulting mathematical model is highly nonconvex in nature accompanied with several constraints with added restrictions of binary variables. This prevents the application of conventional optimization methods. In this paper we use synergetic differential evolution (SDE) for the solution of this type of problems. Four hypothetical but relevant cases of trim loss problem arising in paper industry are taken for the experiment. The experimental results compared with those of the other techniques show the competence of the SDE to solve the problem.

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Lascsáková, Marcela. "Improving Accuracy of the Numerical Model Forecasting Commodity Prices." Applied Mechanics and Materials 708 (December 2014): 251–56. http://dx.doi.org/10.4028/www.scientific.net/amm.708.251.

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In mathematical models, for forecasting prices on commodity exchanges different mathematical methods are used. In the paper the numerical model based on the exponential approximation of commodity stock exchanges was derived. The price prognoses of aluminium on the London Metal Exchange were determined as numerical solution of the Cauchy initial problem for the 1st order ordinary differential equation. To make the numerical model more accurate the idea of the modification of the initial condition value by the stock exchange was realized. The derived numerical model was observed to determine the influence of the decreased size of the limiting value error causing the modification of the initial condition value by the chosen stock exchange on the accuracy of the obtained prognoses. The advantage of the chosen sizes of the limiting value error 7 % and 8 % within different movements of aluminium prices was studied.

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GU, EN-GUO. "STOCK-HARVEST DYNAMICS IN MULTIAGENT FISHERIES." International Journal of Bifurcation and Chaos 21, no. 01 (January 2011): 363–72. http://dx.doi.org/10.1142/s0218127411028477.

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In this work, we build a two-dimensional dynamical fishery model in which the total harvest is obtained by a multiagent game with best reply strategy and naive expectations, i.e. each agent decides the harvest quantity by solving a profit maximization problem. Special attention is paid to the global dynamic analysis in the light of feasible domains (initial conditions giving non-negative trajectories converging to an equilibrium), which is related to the crisis of extinction. We also study the existence and stability of non-negative equilibria for models through mathematical analysis and numerical simulations. We discover the increase in the margin price of fish stock may lead to instability of the fixed point and make the system sink into chaotic attractors. Thus the fishery resource may fluctuate in a stochastic form.

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Baykasoğlu, Adil, and Burcu Kubur Özbel. "Modeling and solving a real-world cutting stock problem in the marble industry via mathematical programming and stochastic diffusion search approaches." Computers & Operations Research 128 (April 2021): 105173. http://dx.doi.org/10.1016/j.cor.2020.105173.

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Chang, Chun-Tao, Yi-Ju Chen, Tzong-Ru Tsai, and Wu Shuo-Jye. "Inventory models with stock- and price-dependent demand for deteriorating items based on limited shelf space." Yugoslav Journal of Operations Research 20, no. 1 (2010): 55–69. http://dx.doi.org/10.2298/yjor1001055c.

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This paper deals with the problem of determining the optimal selling price and order quantity simultaneously under EOQ model for deteriorating items. It is assumed that the demand rate depends not only on the on-display stock level but also the selling price per unit, as well as the amount of shelf/display space is limited. We formulate two types of mathematical models to manifest the extended EOQ models for maximizing profits and derive the algorithms to find the optimal solution. Numerical examples are presented to illustrate the models developed and sensitivity analysis is reported.

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Shimada, Takumi, and Haruhiko Suwa. "Optimization of Cutting Tool Allocation to Enhance Workload Balance and Total Completion Time in Parallel-Type FMS." International Journal of Automation Technology 15, no. 6 (November 5, 2021): 804–12. http://dx.doi.org/10.20965/ijat.2021.p0804.

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This study aims to build a machine scheduling method that involves the cutting tool management in parallel-type flexible manufacturing systems. These systems consist of multi-axis CNC machine tools and are equipped with an automated tool changer and a large-capacity tool magazine. The target scheduling problem could be described as a multi-objective parallel scheduling problem. We consider the availability of cutting tools stored in the magazine as so-called “machine eligibility,” and propose a two-phase scheduling method for tool allocation and job sequencing on machines to minimize the workload balance between machines and the total completion time. Two mathematical models for tool allocation are provided: a machine-eligibility-based model and an enhanced version of the model that considers each cutting tool. A series of computational experiments demonstrates the effectiveness of the proposed method. We also clarify the relationship between schedule performance measures and job routing flexibility in the system.

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Schnute, Jon T., and Laura J. Richards. "Use and abuse of fishery models." Canadian Journal of Fisheries and Aquatic Sciences 58, no. 1 (January 1, 2001): 10–17. http://dx.doi.org/10.1139/f00-150.

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Recent failures of important fish stocks give mathematical models a poor reputation as tools for fishery management. This paper examines the role of models in fish stock assessment and identifies reasons why they can fail. Starting with laws of arithmetic, models attempt to relate observed data to unknown quantities, such as the stock biomass and abundance. Typically, the number of unknowns greatly exceeds the number of observations, and models must impose hypothetical constraints to give useful estimates. We use the word "fishmetic" (rhymes with arithmetic) to represent uncertainty in the conversion of arithmetic to practical fishery models. Arbitrary assumptions cannot be avoided, even though different choices can greatly influence the outcome of the analysis. We compare the modeling process in fisheries with that in other sciences. World literature also offers useful analogies. Potential reasons for failure suggest possible improvements to the application of fishery models. We recommend that modelers remain skeptical, expand their knowledge base, apply common sense, and implement robust strategies for fishery management. Particularly creative thought must be applied to the problem of translating scientific knowledge into management practice. Comparisons between fish stocks and financial stocks illustrate some possibilities.

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Al Hazza, Muataz H. F., Erry Yulian Triblas Adesta, Muhammad Riza, and M. Y. Suprianto. "Surface Roughness Optimization in End Milling Using the Multi Objective Genetic Algorithm Approach." Advanced Materials Research 576 (October 2012): 103–6. http://dx.doi.org/10.4028/www.scientific.net/amr.576.103.

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In finishing end milling, not only good accuracy but also good roughness levels must be achieved. Therefore, determining the optimum cutting levels to achieve the minimum surface roughness is important for it is economical and mechanical issues. This paper presents the optimization of machining parameters in end milling processes by integrating the genetic algorithm (GA) with the statistical approach. Two objectives have been considered, minimum arithmetic mean roughness (Ra) and minimum Root-mean-square roughness (Rq). The mathematical models for the surface roughness parameters have been developed, in terms of cutting speed, feed rate, and axial depth of cut by using Response Methodology Method (RSM). Due to complexity of this machining optimization problem, a multi objective genetic algorithm (MOGA) has been applied to resolve the problem, and the results have been analyzed.

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Chen, Hui Xian, Gong Chu, Meng Pei Wu, and Hui Jun Yang. "Research on Geometric Modeling Method of Finishing Milling Cutter with Fir-Slot." Key Engineering Materials 589-590 (October 2013): 438–43. http://dx.doi.org/10.4028/www.scientific.net/kem.589-590.438.

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Because of the influence of tool geometry, when the fine slotting cutter is cutting, the cutting condition at every point of the type line cutting edge varies, which will lead to uneven loading on the whole cutting edge. Finally, partial earlier failure of the cutter would be initiated. To solve this problem, this paper presented a cutting simulation of the slotting cutter with zero rake angle, which could draw the variation law of cutting force at different locations on the type line. On the basis of micro-elemental milling force model, this paper established mathematical models of different sections along the turning axis of cutting tool, in which the relief angle changed to adapt to the variation of cutting force. The variation law of relief angle could be found by utilizing liner regression analysis. Then the 3D model of tool could be reconstructed. According to cutting experiment analysis of the reconstructed model, the distribution of cutting force at every point of the cutting edge tended to be reasonable, and the rationality of the optimal model was proved. This will offer a new idea to improve the level of slotting cutter design as well as a reference of complex forming cutter design that was completed by using the modern design method.

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Yan, Yingying, and Daguang Yang. "A Stock Trend Forecast Algorithm Based on Deep Neural Networks." Scientific Programming 2021 (July 3, 2021): 1–7. http://dx.doi.org/10.1155/2021/7510641.

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As a recognized complex dynamic system, the stock market has many influencing factors, such as nonstationarity, nonlinearity, high noise, and long memory. It is difficult to explain it simply through mathematical models. Therefore, the analysis and prediction of the stock market have been a very challenging job since long time. Therefore, this paper adopts an encoder-decoder model of attention mechanism, adding attention mechanism from two aspects of feature and time. Both encoder and decoder use LSTM neural network. This method solves two problems in time series prediction; the first problem is that multiple input features have different degrees of influence on the target sequence, the feature attention mechanism is used to deal with this problem, and the weights of different input features can be obtained. A more robust feature association relationship is obtained; the second problem is that the data before and after the sequence have a strong time correlation. The time attention mechanism is used to deal with this problem, and the weights at different time points can be obtained to obtain more robustness and good timing dependencies. The simulation and experimental results show that the introduction of the attention mechanism can obtain lower forecast errors, which proves the effectiveness of the model in dealing with stock forecasting problems.

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Schadner, Wolfgang, and Joshua Traut. "Estimating Forward-Looking Stock Correlations from Risk Factors." Mathematics 10, no. 10 (May 12, 2022): 1649. http://dx.doi.org/10.3390/math10101649.

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This study provides fully mathematically and economically feasible solutions to estimating implied correlation matrices in equity markets. Factor analysis is combined with option data to receive ex ante beliefs for cross-sectional correlations. Necessary conditions for implied correlation matrices to be realistic, both in a mathematical and in an economical sense, are developed. An evaluation of existing models reveals that none can comply with the developed conditions consistently. This study overcomes this pitfall and provides two estimation models via exploiting the underlying factor structure of returns. The first solution reformulates the task into a constrained nearest correlation matrix problem. This method can be used either as a stand-alone instrument or as a repair tool to re-establish the feasibility of another model’s estimate. One of these properties is matrix invertibility, which is especially valuable for portfolio optimization tasks. The second solution transforms common risk factors into an implied correlation matrix. The solutions are evaluated upon empirical experiments of S&P 100 and S&P 500 data. They turn out to require modest computational power and comply with the developed constraints. Thus, they provide practitioners with a reliable method to estimate realistic implied correlation matrices.

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Eskicioğlu, A. M., and H. Eskicioğlu. "Application of Three Non-Linear Programming Techniques in Optimizing Machining Conditions." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 206, no. 3 (August 1992): 183–89. http://dx.doi.org/10.1243/pime_proc_1992_206_072_02.

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Mathematical models used for determining optimal machining conditions are non-linear functions subject to non-linear constraints. In this paper models for unit production cost and unit production time for multi-pass milling operations are developed, taking cutting speed, depth of cut, feed and number of passes as design variables. The problem is then solved by three non-linear programming methods, namely the generalized reduced gradient (GRG) method, the sequential unconstrained minimization technique (SUMT) and the flexible tolerance method. The efficiency of the methods in obtaining the solution is discussed. It is shown through computational experience that their usefulness differs considerably, some parameters in the computer codes used requiring careful selection for the models in question.

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Batig, А. V., and A. Ya Kuzyshyn. "NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS." Criminalistics and Forensics, no. 65 (May 18, 2020): 442–51. http://dx.doi.org/10.33994/kndise.2020.65.43.

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One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

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Pikhalov, Anatoly, and Anton Zabelin. "Applying models of spatial interpolation for the approximation of responses in the refinement of parameters of finite element models." MATEC Web of Conferences 212 (2018): 01021. http://dx.doi.org/10.1051/matecconf/201821201021.

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The numerical experiment on refining the parameters of the finite element model of the beam by the method of approximating the responses is presented in the article. As mathematical models of joint-stock companies are used: linear combinations of radial-basis functions, and Kriging-models. These models are generated in the work on the basis of Latin squares and depend on the parameters to be refined (the moduli of elasticity of finite element groups of the beam). To obtain optimal values of the parameters, a genetic optimization method was used. The results of solving the optimization problem showed a high level of coincidence of the parameter values with a combination of response models obtained from dynamic and static types of calculations. It was also shown that when solving the problems of finite element models, it is sufficient to use models constructed only on the basis of radial-basis functions.

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Stevic, Stevo. "Asymptotic behavior of a class of nonlinear difference equations." Discrete Dynamics in Nature and Society 2006 (2006): 1–10. http://dx.doi.org/10.1155/ddns/2006/47156.

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Motivated by some results of L. Berg (2002), in this paper we find the second member in the asymptotic development of some of the positive solutions of a class of difference equations of second and third orders. The main result in this paper partially solves an open problem by S. Stević (2003), and it is applied to some classes of mathematical biology models, for example, generalized Beverton-Holt stock recruitment model, flour beetle population model, mosquito population equations, and discrete delay logistic difference equation.

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Ghosh, Tamal, Yi Wang, Kristian Martinsen, and Kesheng Wang. "A surrogate-assisted optimization approach for multi-response end milling of aluminum alloy AA3105." International Journal of Advanced Manufacturing Technology 111, no. 9-10 (October 27, 2020): 2419–39. http://dx.doi.org/10.1007/s00170-020-06209-6.

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Abstract Optimization of the end milling process is a combinatorial task due to the involvement of a large number of process variables and performance characteristics. Process-specific numerical models or mathematical functions are required for the evaluation of parametric combinations in order to improve the quality of the machined parts and machining time. This problem could be categorized as the offline data-driven optimization problem. For such problems, the surrogate or predictive models are useful, which could be employed to approximate the objective functions for the optimization algorithms. This paper presents a data-driven surrogate-assisted optimizer to model the end mill cutting of aluminum alloy on a desktop milling machine. To facilitate that, material removal rate (MRR), surface roughness (Ra), and cutting forces are considered as the functions of tool diameter, spindle speed, feed rate, and depth of cut. The principal methodology is developed using a Bayesian regularized neural network (surrogate) and a beetle antennae search algorithm (optimizer) to perform the process optimization. The relationships among the process responses are studied using Kohonen’s self-organizing map. The proposed methodology is successfully compared with three different optimization techniques and shown to outperform them with improvements of 40.98% for MRR and 10.56% for Ra. The proposed surrogate-assisted optimization method is prompt and efficient in handling the offline machining data. Finally, the validation has been done using the experimental end milling cutting carried out on aluminum alloy to measure the surface roughness, material removal rate, and cutting forces using dynamometer for the optimal cutting parameters on desktop milling center. From the estimated surface roughness value of 0.4651 μm, the optimal cutting parameters have given a maximum material removal rate of 44.027 mm3/s with less amplitude of cutting force on the workpiece. The obtained test results show that more optimal surface quality and material removal can be achieved with the optimal set of parameters.

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Kalchenko, V. V., V. I. Kalchenko, S. D. Tsybulya, A. V. Kolohoida, and Ye Yu Sakhno. "Simulation of the process of milling and grinding cylindrical surfaces by an oriented tool in one setup." Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, no. 4 (August 30, 2022): 66–70. http://dx.doi.org/10.33271/nvngu/2022-4/066.

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Purpose. Improvement of schemes for processing the cylindrical surfaces of the shafts of gearboxes and transmissions of large-sized equipment. Development of modular spatial models of the processes of milling and grinding of the cylindrical surfaces of the shafts of gearboxes and transmissions of military and civil vehicles. Development of a model for dressing a grinding wheel with a diamond tool. Methodology. Creation of general and particular modular mathematical models of the processes of removal of allowance and shaping during rough and finish milling and finishing grinding of non-rigid cylindrical surfaces was carried out using a matrix apparatus for transforming coordinate systems. This made it possible to describe the treatment process using standard matrices. The calculations were carried out in the mathematical package Mathcad. To obtain a graphic display of the mathematical model of the instrumental and machined surfaces, the standard functions of the software package and the developed logical blocks were used. Findings. A technique for processing cylindrical surfaces of revolution with an oriented tool is proposed. Roughing, finishing and polishing are carried out in one setup. Roughing and finishing are carried out with an oriented cutter with replaceable multifaceted carbide inserts. The angle of orientation of the cutter is selected from the condition of maximum loading of the end section. Thus, the roughing stock is removed by the end face and by the finishing periphery, while the maximum component of the cutting force is directed along the axis of the part and does not cause deformations in the radial direction. Final finishing is carried out with a wide grinding wheel. The angle of orientation of the grinding wheel is selected from the condition of uniform distribution of the allowance along the periphery. A scheme for dressing the working surface of a grinding wheel with a diamond pencil with a constant feed is proposed. Originality. Modular spatial models of the processes of milling and grinding of the cylindrical surfaces of the shafts of gearboxes and transmissions of military and civil vehicles were developed. A model for dressing a grinding wheel is proposed. The use of the proposed models makes it possible to conduct a more detailed analysis of the processes of stock removal and shaping. Practical value. Dependencies are proposed for choosing the optimal angles of orientation of the cutter for roughing and finishing milling and the grinding wheel for finishing. The accuracy of parts is increased due to the elimination of the resetting error. The cost of manufacturing is reduced due to the maximum full use of cutting carbide inserts, by turning them and operating the worn finishing edge in the rough milling mode, as well as by increasing the resource of the grinding wheel.

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Rudikov, D. A., and A. S. Ilinykh. "Error analysis of the cutting machine step adjustable drive." Journal of Physics: Conference Series 2131, no. 2 (December 1, 2021): 022046. http://dx.doi.org/10.1088/1742-6596/2131/2/022046.

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Abstract The implementation precision of a number of adjustment bodies of a metal-cutting machine is also the most important indicator of its quality, a strictly standardized industry standard, technical conditions for manufacturing and acceptance. Moreover, the standard for limiting the error is set depending on the used denominator of the series. An essential feature of the precision of the series being implemented is that it is determined not by an error in parts’ manufacturing, but by the disadvantages of the used method of kinematic calculation. The established modes largely determine the efficiency of processing on metal-cutting machines. If the setting is set to an underestimated mode, then the performance is reduced accordingly. In the case of the mode overestimation, this leads to a decrease in durability and losses due to increased regrinding and tool changes. Creation of a complex of mathematical models for the design kinematic calculation of the metal-cutting machines’ main movement drive, which allows reducing the error in the implementation of a series of preferred numbers and increasing machining precision. The article provides a mathematical complex for analyzing the total error components, which allows determining and evaluating the total error of the drive of a metal-cutting machine by analyzing its constituent values with high precision: errors of a permanent part, errors of a multiplier part, rounding errors of standard numbers, errors in the electric motor and belt transmission. The presented complex helps to identify the role of the rounding error of preferred numbers in the total relative error formation and makes it possible to reduce it, which allows solving the problem of increasing the step adjustable drive precision. When using a mathematical complex, a fundamentally new opportunity for creating a scientific base appears, developing algorithms and programs for engineering calculation of tables that facilitate the selection of the numbers of teeth for multiple groups, structures and guaranteeing high precision of the implemented series.

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Journal articles on the topic 'Cutting stock problem Mathematical models'

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