A note on linear models for two-group and three-group two-dimensional guillotine cutting problems

Due to the particular characteristics of certain cutting machines, special classes of cutting patterns, such as 1-group, 2-group and 3-group, requiring shorter processing times appear in the furniture, hardboard and stone industries. In this study we present integer linear models to generate 2-group and 3-group constrained and unconstrained two-dimensional guillotine cutting patterns. The models are derived from the linear models for 1-group guillotine cutting patterns proposed in Yanasse, H.H. and Morabito, R., Linear models for one-group two-dimensional guillotine cutting problems. International Journal of Production Research, in press. The performances of the models were evaluated by solving a number of examples randomly generated and an actual example derived from a furniture company. These results were produced using GAMS modelling language and the CPLEX solver, and they show that the models are effective to solve problems of small and moderate size.     

Linear models for 1-group two-dimensional guillotine cutting problems

In this study we present integer linear and non-linear models to generate 1-group constrained and unconstrained two-dimensional guillotine cutting patterns, including exact and non-exact cases. These patterns appear in different cutting processes as, for example, in the furniture industry. The models are useful for research and development of more effective solution methods, exploring particular structures, model decomposition, model relaxations, etc. They are also helpful for the performance evaluation of heuristic methods, since they allow (at least for problems of moderate size) an estimation of the optimality gap of heuristic solutions. To demonstrate the effectiveness of the proposed models, we compare them with models of the literature by solving a number of examples randomly generated and an actual example derived from a furniture company. Such results were produced using a well-known commercial software (the modelling language GAMS and the solver CPLEX) and they show that the computational efforts required to solve the models can be very different.     

The constrained two-dimensional guillotine cutting problem with defects: an ILP formulation,a Benders decomposition and a CP-based algorithm

This paper addresses a variant of two-dimensional cutting problems in which rectangular small pieces are obtained by cutting a rectangular object through guillotine cuts. The characteristics of this variant are (i) the object contains some defects, and the items cut must be defective-free; (ii) there is an upper bound on the number of times an item type may appear in the cutting pattern; (iii) the number of guillotine stages is not restricted. This problem commonly arises in industrial settings that deal with defective materials, e.g. either by intrinsic characteristics of the object as in the cutting of wooden boards with knotholes in the wood industry, or by the manufacturing process as in the production of flat glass in the glass industry. We propose a compact integer linear programming (ILP) model for this problem based on the discretisation of the defective object. As solution methods for the problem, we develop a Benders decomposition algorithm and a constraint-programming (CP) based algorithm. We evaluate these approaches through computational experiments, using benchmark instances from the literature. The results show that the methods are effective on different types of instances and can find optimal solutions even for instances with dimensions close to real-size.     

Heuristic for two-dimensional homogeneous two-segment cutting patterns

This article deals with the guillotine-constrained two-dimensional cutting problem, where a guillotine is used to cut the stock plate into rectangular pieces, such that the pattern value (the total value of the pieces produced) is maximized, observing the constraint that the frequency of each piece type should not exceed the demand. Homogeneous two-segment (HTS) cutting patterns are considered to simplify the cutting process. Each HTS pattern includes two segments, each segment contains homogeneous strips of the same direction, and each homogeneous strip contains pieces of the same type. A heuristic is presented for generating HTS patterns. It is based on dynamic programming and branch-and-bound techniques. The computational results indicate that the heuristic is able to generate solutions close to optimal, and is adequate for solving large-scale instances.     

An algorithm for generating optimal constrained one-stage homogenous strip cutting patterns

The cutting and stamping process is often used to divide a stock plate into items to make products. It includes two phases. A guillotine machine cuts the plate orthogonally into homogenous strips at the cutting phase; then a stamping press stamps out the items from the strips at the stamping phase. A homogenous strip contains items of the same type. A one-stage homogenous strip cutting pattern (OSHSCP) contains parallel homogenous strips of the same length. The OSHSCP is useful because it can be used independently or as elements to compose other types of cutting patterns. This article presents a dynamic programming algorithm for generating the optimal constrained OSHSCP, where the maximum demand for each item type is specified and the objective is to maximize the total value of items included in the pattern. The computational results indicate that the computation time is reasonable.     

Sequence based heuristics for two-dimensional bin packing problems

This article addresses several variants of the two-dimensional bin packing problem. In the most basic version of the problem it is intended to pack a given number of rectangular items with given sizes in rectangular bins in such a way that the number of bins used is minimized. Different heuristic approaches (greedy, local search, and variable neighbourhood descent) are proposed for solving four guillotine two-dimensional bin packing problems. The heuristics are based on the definition of a packing sequence for items and in a set of criteria for packing one item in a current partial solution. Several extensions are introduced to deal with issues pointed out by two furniture companies. Extensive computational results on instances from the literature and from the two furniture companies are reported and compared with optimal solutions, solutions from other five (meta)heuristics and, for a small set of instances, with the ones used in the companies.     

满足“一刀切”要求的木工板排样优化研究

 针对木工板手工排样效率低和材料利用率低问题,提出木工板“一刀切”排样优化算法．在剩余矩形填充算法中添加启发式分块原则,改进的剩余矩形填充算法满足“一刀切”工艺要求．采用遗传算法对矩形件进行排样优化,以提高木工板利用率,降低企业生产成本．为提高算法的优化精度,使用基于指数变换的非线性动态适应度函数,引入精英保护策略,应用部分填充交叉（partially matched crossover）算子．结合剩余矩形填充“一刀切”算法对遗传种群进行解码计算原料利用率,并作为适应度函数值,进行迭代搜索最优解．排样实例表明木工板“一刀切”排样优化算法能够很好地解决多品种大规模木工板排样问题．     

Impact of the alignment between the strategic and operational levels of a manufacturing enterprise

In today's economic environment, manufacturing organisations compete against each other as part of supply chains (SC). As both the SC strategic level and production floor operational level are interdependent, a misalignment between them has a deep impact on the performance of the manufacturing organisation. For this reason, in this paper we develop an analytical expression of the impact such misalignment has on the manufacturing organisation performance, specifically, its demand fulfillment ability. The usefulness of the analytical expression is illustrated via the development, for the case of a local furniture company, of a system dynamics (SD) simulation model. The SD simulation model is tested under different operational conditions, so the case study company can derive conclusions regarding actions to improve its demand fulfillment ability.     

基于模糊聚类分析的家具零件成组研究

合理的零件分组是成组技术实施的关键因素之一,对山东省德州市某板式衣柜厂典型产品进行零件成组案例研究,通过生产流程分析,建立零件相似矩阵,利用传递闭包法求出等价矩阵,从而实现理性化的零件成组分类,进而通过Matlab的编程实现复杂零件系统的成组。结果表明：随着分组阈值的不断增加,分组数量随之增加,零件平均相似度也随分组阈值的不断增加而增加, 企业生产规模与选择的分组阈值、零件分组数量成反向关系,企业规模越小,分组数量应较小,从而实现组内零件较大批量的生产加工。     

A recursive algorithm for the rectangular guillotine strip packing problem

This article presents a recursive heuristic algorithm to generate cutting patterns for the rectangular guillotine strip packing problem in which a set of rectangular items must be cut from the strip such that the consumed strip length is minimized. The strip is placed with its length along the horizontal direction, and is divided into several segments with vertical cuts. The length of a segment is determined by the item placed at the bottom. Orthogonal cuts divide the segments into blocks and finished items. For the current block considered, the algorithm selects an item, puts it at the bottom-left corner of the block, and divides the unoccupied region into two smaller blocks with an orthogonal cut. Rotation of the items by 90 is allowed. Both lower and upper bounds are used to prune unpromising branches. The computational results indicate that the algorithm performs better than several recently published algorithms.     

中国传统家具图案在现代产品装饰设计中的应用

目的 对传统家具图案在现代产品装饰设计中的应用进行研究。方法 通过介绍传统家具图案的种类、图案纹样形式、图案应用位置及表现方法,分析并提出了传统家具图案应用于现代产品设计中的意义、原则和方法,从传统家具的植物图案、动物图案、云纹和吉祥图案,提取了设计要素,并应用于现代产品设计实践。结论 通过对设计原则、方法的实践,证明了使用传统家具图案进行现代设计是可行的、有效的。     

A Genetic-Algorithms-Based Multiobjective Approach for a Three-Dimensional Guillotine Cutting Problem

A novel method based upon multiobjective genetic algorithms is presented for simultaneously minimizing the amount of scrap and the number of turns in a three-dimensional guillotine cutting. The concept of best orientation between two cuboids has been used to improve the efficiency of the minimization process. Two different evolutionary algorithms have been used and also compared for effectiveness.     

传统纹样在藤制家具设计中的应用

目的 探究传统纹样在藤制家具设计中的应用策略。方法 基于当前的时代背景,结合藤制家具设计的实际情况,根据传统纹样在家具设计中的应用部位和作用,如结构装饰部件、面层编织、中国结饰、框体缠扎等部位,分析了传统纹样在藤制家具设计中的应用细节,从直接引用、变形重组、美好寓意和协调一致四个方面展开,并以具体的传统纹样为例,深入剖析了藤制家具的设计理念及方法。结论 传统纹样与藤制家具的结合不是简单地照搬照抄,而是要根据家具自身的特色进行合理简化、提炼,达到与家具整体风格的统一。传统纹样在藤制家具设计中的应用,不但为设计者提供了广泛的设计灵感和创作题材,而且增强了藤制家具中民族属性的审美特征,完成了对传统艺术文化的回归,为人们日常生活增添了情趣,旨在为藤制家具设计提供有价值的参考。     

凉山彝族建筑与家具纹样研究及创新应用

目的 将凉山彝族创新纹样应用于现代家具,延续凉山彝族文化。方法 以从凉山彝族地区采集到的纹样为数据基础,通过统计学方法汇总分析,并探究创新纹样在现代家具中的应用方法。结论 结合现有纹样数据的量化分析,总结不同类型纹样的常见装饰部位与构成方式,并归纳典型凉山彝族纹样的常见搭配纹样。通过对文化延续最大化的分析,提出凉山彝族纹样应以纹样组合为单元进行创新,并得出文化延续、功能延续与适于工业化生产的三大创新原则。以现代设计理念和大众审美为参考,通过研究各类纹样组合的文化内涵、比例尺寸与构成方式,产出适用于各类纹样的最优创新方法。结合现代家具的常见装饰部位与比例尺寸,提出各类创新纹样在现代家具中的应用方法,使彝族创新纹样以多样化的形式存在现代生活中并代代相传,从而延续凉山彝族文化。     

Multiple-choice knapsack-based heuristic algorithm for the two-stage two-dimensional cutting stock problem in the paper industry

This study examines a two-stage two-dimensional cutting stock problem encountered by a paper mill company. The problem includes various machine-related and operational constraints based on real-world situations. Paper products are manufactured using two major cutting processes. Each cutting machine has a specific minimum and maximum width for input and output rolls and is limited by the maximum number of rolls it can cut at the same time. A mathematical model is presented to formally address the problem and an efficient multiple-choice knapsack-based heuristic algorithm is proposed to solve the problem. To demonstrate the efficiency of the proposed heuristic algorithm, computational experiments are conducted on test data-set generated from real-world data provided by a large paper mill company in the Republic of Korea.     

文化元素在现代家具设计中的应用实践

目的 探索多样化且内涵丰富的文化元素在现代家具设计中的应用策略.方法 首先结合传统家具设计的主要特点,引出现代家具设计的现实追求.然后从现代家具对文化内涵的需求出发,就现代家具对文化元素所采用的直接应用、间接应用、解构应用和创新应用等手段进行分析.同时总结具体的应用方向,以中国结、水墨、剪纸、陶瓷等代表性文化元素在现代家具设计中的应用,展开深入的分析与探讨,挖掘切实可行的应用路径和创新策略.结论 在现代家具设计中创造性地融入优秀文化元素,能够使家具形成浓郁的民族特色和深厚的文化内涵,体现中国设计的独特风格,大大提升中国家具的社会地位.同时能够赋予家具更加旺盛且持久的生命力,为未来家具设计提供更多的思路和光明的发展前景.     

基于空间理论的“双面盒子”家具创意设计

目的以家具的空间利用、空间虚实关系、空间的设计维度为视角,以现代空间理论对空间与家具的关系、在产品设计中的运用上进行新的探索。方法在空间设计理论的视角下,以三元辩证法探索创意家具设计的模糊性与非指定性、创造性和开放性、科学性和继承性。结论注重创意家具设计分类方法,强调创意家具设计的系列化和主动性;从关注家具设计的形态,转向空间设计的介入,走向更为开放的亦此亦彼模式,保持开放与创新的姿态,加强对使用者的需求研究,主动让使用者参与空间设计;我国创意家具设计必须适应国际经济、设计思维和科技发展的形势,不断调整对于创意家具设计的认知,设计创新和转型将成为常态。     

传统吉祥纹样在新中式家具中的应用方法研究

目的探索传统吉祥纹样在新中式家具设计中的运用方法。方法从平面装饰、造型、功能和传统纹样的立体转化4个方面展开,研究了传统吉祥纹样在新中式家具设计中的创新方法,阐述了传统纹样在新中式家具设计中的应用细节,并结合具体的设计实例进行验证。结论传统吉祥纹样是我国传统文化的缩影,家具是技术与艺术的统一。将传统吉祥纹样与新中式家具相结合,不能照搬与模仿传统纹样,必须进行纹样的再设计,才能达到新中式家具的创新设计,更加直观、形象地表现我国传统文化,进一步推动家具设计的发展。     

传承视角下朝鲜族传统家具的数据库呈现与创新设计

目的 开展朝鲜族传统家具的数据库呈现与创新设计,为朝鲜族传统家具数字化设计的发展提供资源库。方法 通过对现存朝鲜族传统家具实物在装饰造型、图案、技艺、配饰、色彩与材质进行提取分析,利用可视化图像技术原理对其造型、材质、民族图腾纹样和色彩进行标注,数字化重组与创新设计应用。结果 建立朝鲜族传统家具的数据库,提出朝鲜族传统家具样式及工艺基础上数字化重组与创新设计思路,应用到朝鲜族家具设计中。结论 传承视角下对朝鲜族传统家具文化,进行数据库信息采集呈现,在公共空间拓展创新设计应用,为传统家具在民族生活环境空间的传承应用寻求新的思路与途径。     

家具包装的视觉传达设计

家具包装视觉传达设计是提升家具产品形象和企业形象、促进产品销售的重要手段。家具包装设计的视觉要素主要包括商标、造型、色彩、图形、文字等,家具包装设计者应综合利用这5个视觉要素,设计出符合消费者视觉审美需求和视觉消费需求的包装产品。某公司橱柜项目组"厨房板式家具包装设计"即在充分挖掘产品"环保"这一核心价值定位的基础上,以商标要素为核心,并结合图形要素、色彩要素、文字要素,突出产品"零甲醛排放"的环保特性,设计了一组家具包装方案。