An analysis of 2D object packing algorithms, created by foreign authors, and commercial two-dimensional stock packing software packages was performed in this work; also methods’ advantages and disadvantages were pointed out. A model of two-dimensional rectangular object packing into stock was formed, and the software solving 2D object packing problems was created according to this model. The tests proved that the suggested method is effective and beneficial.

Šio darbo tikslas – sukurti trimačių dėžių su papildomu orientacijos erdvėje apribojimu pakavimo optimizavimo algoritmą, o realizavus jį programinėmis priemonėmis – ištirti jo efektyvumą su atsitiktinai sugeneruotų kraunamų dėžių rinkiniais ir prie skirtingų algoritmo veikimo parametrų. Taip pat sukurti ir pakavimo optimizavimo sprendinio vizualizavimo trimatėje erdvėje programinę įrangą. / Presented work covers one of the most complex areas of combinatorial optimization – three dimensional bin packing problem. Solution methods of this problem are applied in the real world from logistics, packing optimization to VLSI circuit and automobile engineering. Several heuristic packing algorithms suggested by other authors are analyzed. Approach based on tree-search and wall building strategy is chosen to create a 3D packing optimization algorithm. A bin orientation in space restriction is added to classical 3D bin packing problem to make it more complex and more suited for real world applications. A prototype of created algorithm is created and tested with randomly generated data collections. Each data sample is processed with and without bin orientation in space restriction. Influence of restriction and maximal tree width on packing efficiency and computational time is statistically analyzed. Visualization tool based on Microsoft Direct X technology is created to view results of packing optimization.

Darbe trumpai apžvelgtos figūrų pakavimo ištakos, aprašyti keli figūrų pakavimui naudojami stochastinio modeliavimo algoritmai. Išnagrinėtas perturbacijos metodas, sukurtos dvi šiuo metodu vienetiniame kvadrate vienodus apskritimus pakuojan��ios programos, detaliai aprašyti jų algoritmai. Eksperimentiškai ištirtos programų galimybės: kiekviena programa po 30 kartų buvo pakuojami n apskritimų, kur 3 ≤ n ≤ 15 ir n = 25, 50, 75, 100. Buvo fiksuojami ir apibendrinami pakavimų rezultatai. Pastarieji lyginti tarpusavy ir kartu su Violetos Sabonienės magistriniame darbe ,,Biliardinio modeliavimo algoritmai ieškant talpiausio geometrinių figūrų pakavimo“ biliardiniu metodu atliktais pakavimo rezultatais. Prieduose pateikti programų tekstai ir skaičiavimų lentelės. / In this work are examined the sources of figure packing, described the stochastic simulation algorithms of finding the densest packing of geometric figures. Here is analysed the method of perturbation and made two programmes of equal circle packing in unit square and their algorithms are being described in detail. The possibilities of programmes were analysed experimentally: using each programme 30 times. In each experiment were packed n circles, were 3 ≤ n ≤ 15 end n = 25, 50, 75, 100. The results of packing were fixed and summarized. The latter rezults were compared between themselves and also with the results of Violeta Sabonienė master of science work “The billiarding simulation algorithms of finding the densest packing of geometric figures“. The text and the calculation charts of the program are giver in the appendices.

The essence of 3D object packing problem is to load a set of distinct boxes with given dimensions in containers to maximize volume utilization. The goal of this research is to support with algorithmic techniques the design of package layouts that meet the functional relationships between the parts and match market needs including cost, safety, comfort, as well as economic and environmental aspects. An analysis of 3D object packing algorithms, created by foreign authors, and commercial three-dimensional pallet packing software packages was performed in this work; also methods’ advantages and disadvantages were pointed out. A model of three-dimensional rectangular object packing into containers of the same shape was formed, and the software solving 3D object packing problems was created according to this model. The tests proved that the suggested method is effective and beneficial.

Darbe apžvelgiama trimačio pakavimo problemos tipologija. Nagrinėjama trimečio konteinerių pakavimo problema ir jos sprendimo būdai. Pateikiama šakos ir ribos, bei tabu paieškos algoritmų formulavimas ir jų rezultatų analizė. / The paper gives an overview of three-dimensional packing problem typology. There are investigating issue of container packing problem and its solutions. Branch and bound, TSpack algorithms formulation and analysis of their results.

Whether you are in industrial manufacturing striving to optimize your supply chain, international or domestic carrier committed to lower your operational costs, retailer dedicated to run your distribution network more efficiently, or anywhere else where the words "cargo", "freight", "shipment" are in your business language, automated load planning and optimization will significantly improve your business process. While the concept of computerized simulation of 3D load building is not new, with some companies offering software solutions for "virtual" loading, no one has a single product that is capable to handle complex variety of business rules and constraints of the modern transportation industry. We are analyzing the problems related with 3D box loading and then to analyze existing 3D load building systems. After accumulating all analyzes data we are having enough experience to create our own algorithm. And we did it! We create 3D box loading algorithm witch is fast and accurate and 3D box loading system which is using this new algorithm. To ensure that we succeeded we compare this new system with existing 3D box loading software to make sure that it’s really useful for solving logistic problems. After testing we are sure that we made a big job and we have created system, which can compete with the logistic IT leaders made solutions.