Gemi üretiminde bilgisayar destekli optimum malzeme kullanımı
Computer aided optimum material utilization in shipbuilding
- Tez No: 19364
- Danışmanlar: PROF.DR. REŞAT BAYKAL
- Tez Türü: Doktora
- Konular: Gemi Mühendisliği, Marine Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1991
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Belirtilmemiş.
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 295
Özet
ÖZET Kesilerek üretilen parçaların, levhalara en az kayıp verecek şekilde yerleştirilmesi problemi ile, gemi inşaatı mühendisliğinde olduğu gibi uçak, deri, kağıt, konfeksiyon, çelik konstrüksiyon, cam ve mobilya endüstrisi gibi birçok sektörde karşılaşılmaktadır. Genelde, kayıp oranlarının en küçük düzeyde olması amaçlanan çalışmalarda, en iyi cüzüm değerini bulabilen analitik çözüm yöntemleri yanında; kabul edilebilir düzeyde bir çözüm bulan sezgisel yaklaşımlarda kullanılmaktadır. Problem bağımlı olan sezgisel yaklaşımlar, durum uzayı araştırması ve problem indirgeme olmak üzere iki şekilde ele alınabilirler. Çeşitli çalışmalarda, dikdörtgen ve dik dörtgen olmayan parçaların, bir, iki ve üç boyutlu olmak üzere, kesme düzeneklerine bağlı olarak, giyotin kesime uygun olan veya olmayan yerleşimlerinin gerçeklenmesi ele alınmaktadır. Çalışmanın ilk aşamasında, dikdörtgen parçaların levhalara yerleştirilmesinde, geleneksel çözüm yaklaşımına örnek teşkil eden, sayımlama ve lineer programlama ile sonuca ulaşan Maak Yöntemi ele alınarak geliştirilmiştir. Parçaların gruplara ayrılarak incelemeye alınması ile, iki aşamalı, üc kademeli kesme planlarının elde edilmesi sağlanmış» sonrada probleme dinamik bir yapı kazandırılmıştır. Bu şekilde, analitik yöntemlerin ortak özelliği olan ve parça çeşit sayılarının küçük değerle rinde bile ortaya çıkan büyük işlem yükü önemli oranda azaltılmış, çözüm hızı arttırılmış, tamsayılı çözüme geçilmesi ve parçaların istenilen talep miktarlarında üretilmesinin sağlanması ile en iyi çözüme yakın, kabul edilebilir çözümlerin elde edilmesi mümkün olmuştur. Dikdörtgen parçaların yerleştirilmesi probleminde bile kullanımı parça çeşit sayısına bağlı olan analitik yöntemlerin yerini sezgisel yaklaşımlar almaktadır. Dik dörtgen olmayan parçaların levhalara yerleştirilmesinde otomatik olarak yerleşimi gerçekleyen ve sezgisel yaklaşımların kullanıldığı çalışmaların yanında interaktif çalışmalara da yer verilmektedir. iki parçanın en iyi yerleşiminin bulunması ve par çaların ele alınma sırasının belirlenmesi şeklinde iki temel üzerine kurulu bu çalışmada, çözüm mertebesi ve çözüm taraması gibi iki kavram geliştirilerek, eldeki mevcut bilgisayar olanaklarına göre alternatif yerleşimlerin elde edilmesi sağlanmıştır. En iyi yerleşimin bulunmasında kullanılan karmaşıklık değerine ek olarak poligon karmaşıklık değeride tanımlanarak, aynı karmaşıklık değerine sahip yerleşimler arasında eleme yapma olanağına kavuşulmuştur. Hesaplamalarda çokgen olarak ele alınan, gemi üretiminde kullanılan parçaların bilgisayar ortamın da tanımlı şekilleri, çözüm sonunda yerleştirme işlemine katı1maktadır.
Özet (Çeviri)
COMPUTER AIDED OPTIMUM MATERIAL UTILIZATION IN SHIPBUILDING SUMMARY In shipbuilding, the procedure of obtaining the most beneficial configuration of steel plate pieces on standard sized plates for cutting with the least possible material loss is known as the nesting problem. The methods for the solution of the nesting problem are generally classified in three groups» which are the analytical methods, heuristic approaches and others. A survey of the related literature indicates that the analytical methods are mostly used in the nesting of rectangular elements. The basic approach used in the present study is a conventional one which finds a possible solution to the nesting problem by determining all of the combinations first, then establishing the mathematical model and object function and finally obtaining the solution by utilizing linear programming. This approach is known to yield reasonable results when a small number of pieces is used repetatively during the nesting. When the number of repetitive usage of identical pieces is small and/or when the number of different pieces to be nested on one plate is great, the procedure yields too many possible alternatives in the stage of the“determination of all the combinations”, which renders the mathematical modelling and its solution impossible. To improve on this aspect of the procedure, this study utilizes the Maak method which is a known example of the conventional methods, and the shortcomings of the above procedure are eliminated by two different measures. Firstly, a two staged solution technique is used which is capable of handling an increased number of pieces with different geometries to be nested on one plate. In the first stage, the pieces are classified in groups of numbers prescribed by the user according to their widths or, if they are permitted to rotate, according to their lengths. Since every group of pieces is treated as a different problem, the number of combinations is then considerably reduced. After determining the types and the areas of strips, which assures the nesting of each xiand &very group, all of the groups are then gathered to arrive at the solution. In this manner of reaching a solution, the procedure for setting up the longitudinal nesting which is checked in every transversal nesting, is therefore abandoned. Moreover, by obtaining all the alternative solutions and by reducing the number of alternative nesting drawings, the material loss is reduced, albeit not very significantly. In this procedure, the results, obtained in real numbers by utilizing Simplex Method in linear programming, are then expressed in integer numbers. This, in turn, increases the amount of material loss depending on the number of elements and the number of types of nesting plans. Despite the fact that the capability of handling geometrically different pieces is increased and the material loss is reduced as described in the previous paragraph, the solution may become useless due to very high number of possible nestings even the number of types of pieces remains low, i.e. lO - 20. According to the calculations of the present study, the number of possible nestings, in which 40 different pieces are considered with at least two edges equal to each other, is, for an average case, 10 million and it may be as high as lOO million for an extreme case. Accordingly, in the nesting procedure of rectangular pieces, the heuristic approach is preferred in order to obtain acceptable solutions although the analytical methods give the solution much more precisely. In the present study, however, it is thought that to model the problem mathematically by discarding the large number of probable nestings, the computer time and memory space required are still too high even for this elimination procedure to make the solution economic and useful. By making some modifications to the above mentioned method, the procedure is dynamically restructured which enables the results to be given in terms of integer numbers and makes the process of necessary eliminations possible without deriving all of the nestings according to the rules specified. The fundamental idea described here aims to determine the priority in the nesting of a piece, while all the pieces are to be nested in specified numbers. From this point of view, the difference in the present study is that the piece With the higher priority is taken into consideration with its position linked to other pieces rather than, as in other studies, it is xiithought of as a stand-alone piece. As a direct benefit of this idea, it is possible to obtain results which are either equal to or very close to the analytical solution with integer results. The piece with the highest priority is always chosen as the largest piece which bears some difficulties in nesting. Therefore during the scanning of various configurations, the nesting procedure is stopped when the highest priority piece is found to be absent in a configuration. Although, only the required number of pieces is considered during the mathematical modelling in other studies; the number of combinations is reduced in the presently developed method, since the demanded numbers of pieces are considered together with the nesting-possibilities. By classifying the elements group by group, by terminating the procedure when the preferential piece is found to be absent in a configuration and by considering the demanded numbers when nesting the pieces, the conventional method, which uses the analytical method in the nesting of rectangular elements, is improved in order to reach the solution quicker and to increase the number of types of pieces. If the results of other heuristic approaches are considered, it can be said that acceptable and, in some cases, the same results with those of analytical methods are obtained. Three different computer programmes are developed related with the present topic. QuickBASIC 4. 0 is used for computations, and AutoCAD 2.6 is used for plotting purposes. In the procedures for nesting of rectangular plate elements, dependent on the dimensions of uncut plates and cut pieces as well as the quantities demanded, there has been a move from analytical methods to various heuristic techniques. Nevertheless, the drawings of the rectangular pieces nested on an uncut plate are prepared automatically. When the nesting of polygonal shapes is considered, automatic nesting and interactive manual nesting concepts appear to gain significance. In this area, the manual nesting techniques are used most frequently, mostly because they provide acceptable solutions within acceptable time limits. Although the development of the automatic nesting techniques are continuing, they, in comparison to the manual approach, do not yet achieve the same quality of solution both in terms of the processing speeds and resulting material losses. Especially in recent xiiiyears, these studies have used new tecniques where the automatic and manual nesting methods are utilized together to obtain a common procedure. In these procedures, the initial nesting is done automatically, later the final configuration is determined manually. The studies which aim at automatic nesting of non-rectangular pieces on uncut plates consist of two fundamental operations: - the positioning together of two pieces in the most beneficial configuration, and - the determination of the most beneficial order with which the pieces are nested. In the present study, further operational properties such as the plate areas lost due to the cutting allowances and whether a particular piece is rotatable, are taken into consideration. In the initial stage, where the best configuration for two pieces is determined, the total number of alternatives C solutions]» is increased from 2. m. n to 4. m. n where m and n are the number of corners for the first and second pieces respectively. In effect, the total number of alternative configurations that are investigated is determined implicitly by the user who specifies a“ solution search number ”CCT3, where CT e < 1,2,3,4 >. The existing procedures select as the best configuration the solution which has the lowest“ complexity value ”CKEÛ, but they do not offer any preference as to which, amongst the solutions with equal complexity values, is the most beneficial configuration. Not only these studies mention this shortcoming explicitly, but also their results exhibit clear indications that this is a severe disadvantage. In order to remove this shortcoming a new complexity value CPKD3 is defined for polygons so that the alternatives with equal KD values are classified according to their KDxPKD values. In addition, if more than one solution still have equal KDxPKD values, the configuration which has the maximum sum of the lengths of the coinciding sides and the maximum sum of the internal angles of the coinciding corners, is declared as the best solution. This approach ensures that the area remaining for a third piece is the most suitable one amongst the alternatives. xi vThe second stage of the nesting process for non-rectangular pieces is the determination of the handling order. In this stage, pieces with the smallest KD value and those with the largest area amongst the pieces of equal KD values are given priority to be processed. These criteria make it possible to speed up the initial stages of the nesting procedure as well as to obtain a relatively more uniform configuration in the beginning. The positioning of more complex pieces is left for later stages of nesting. This approach is used in many existing studies but it leads to the following point open to questioning: the first two pieces can be nested with the best possible configuration where as the quality of the solution for the third, fourth and more pieces is completely ignored. In order to avoid this problem, the concept of“order of solution”CCÎO is developed. In this approach, depending on the selected order of solution, all the solutions found by investigating every variation in the handling priorities of a number of pieces equal to CM are grouped together and the groups of pieces thus obtained are included in the nesting procedure as individual pieces. Obviously, the process of setting up these groups takes time. However, because the nesting procedure now involves groups of pieces each with CM items, there is a considerable time saved in the later stages. Additionally, the solutions obtained for various CM values provide acceptable alternatives which are considerably closer to the best nesting configuration. Theoretically, this approach indicates that the solution most similar to the best configuration is obtained when the CM value is equal to the number of pieces. This, in reality, is never realised due to the excessive processing time required. For the reduction of time required to obtain a solution, it is suggested that the studies should continue on two fronts. Firstly, rules have to be developed which ensure that, before the nesting process, the conf igurationwise compatible pieces are identified with respect to their geometrical properties. Secondly, during the initial stage of configuring two pieces, new rules should be available to eliminate a significant number of the 4. m. n alternatives before the start of the evaluation of the possible configurations. xv
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