Thesis (PhD (Logistics))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: Packing problems are common in industry and there is a large body of literature on the subject. Two packing problems are considered in this dissertation: the strip packing problem and the bin packing problem. The aim in both problems is to pack a speci ed set of small items, the dimensions of which are all known prior to packing (hence giving rise to an o ine problem), into larger objects, called bins. The strip packing problem requires packing these items into a single bin, one dimension of which is unbounded (the bin is therefore referred to as a strip). In two dimensions the width of the strip is typically speci ed and the aim is to pack all the items into the strip, without overlapping, so that the resulting packing height is a minimum. The bin packing problem, on the other hand, is the problem of packing the items into a speci ed set of bins (all of whose dimensions are bounded) so that the wasted space remaining in the bins (which contain items) is a minimum. The bins may all have the same dimensions (in which case the problem is known as the single bin size bin packing problem), or may have di erent dimensions, in which case the problem is called the multiple bin size bin packing problem (MBSBPP). In two dimensions the wasted space is the sum total of areas of the bins (containing items) not covered by items. Many solution methodologies have been developed for above-mentioned problems, but the scope of the solution methodologies considered in this dissertation is restricted to heuristics. Packing heuristics follow a xed set of rules to pack items in such a manner as to nd good, feasible (but not necessarily optimal) solutions to the strip and bin packing problems within as short a time span as possible. Three types of heuristics are considered in this dissertation: (i) those that pack items into levels (the heights of which are determined by the heights of the tallest items in these levels) in such a manner that all items are packed along the bottom of the level, (ii) those that pack items into levels in such a manner that items may be packed anywhere between the horizontal boundaries that de ne the levels, and (iii) those heuristics that do not restrict the packing of items to levels. These three classes of heuristics are known as level algorithms, pseudolevel algorithms and plane algorithms, respectively. A computational approach is adopted in this dissertation in order to evaluate the performances of 218 new heuristics for the strip packing problem in relation to 34 known heuristics from the literature with respect to a set of 1 170 benchmark problem instances. It is found that the new level-packing heuristics do not yield signi cantly better solutions than the known heuristics, but several of the newly proposed pseudolevel heuristics do yield signi cantly better results than the best of the known pseudolevel heuristics in terms of both packing densities achieved and computation times expended. During the evaluation of the plane algorithms two classes of heuristics were identi ed for packing problems, namely sorting-dependent and sortingindependent algorithms. Two new sorting techniques are proposed for the sorting-independent algorithms and one of them yields the best-performing heuristic overall. A new heuristic approach for the MBSBPP is also proposed, which may be combined with level and pseudolevel algorithms for the strip packing problem in order to nd solutions to the problem very rapidly. The best-performing plane-packing heuristic is modi ed to pack items into the largest bins rst, followed by an attempted repacking of the items in those bins into smaller bins with the aim of further minimising wasted space. It is found that the resulting plane-packing algorithm yields the best results in terms of time and packing density, but that the solution di erences between pseudolevel algorithms are not as marked for the MBSBPP as for the strip packing problem. / AFRIKAANSE OPSOMMING: Inpakkingsprobleme kom algemeen in die industrie voor en daar is 'n aansienlike volume literatuur oor hierdie onderwerp. Twee inpakkingsprobleme word in hierdie proefskrif oorweeg, naamlik die strook-inpakkingsprobleem en die houer-inpakkingsprobleem. In beide probleme is die doel om 'n gespesi seerde versameling klein voorwerpe, waarvan die dimensies almal voordat inpakking plaasvind, bekend is (en die probleem dus 'n sogenaamde a yn-probleem is), in een of meer groter houers te pak. In die strook-inpakkingsprobleem word hierdie voorwerpe in een houer, waarvan een dimensie onbegrens is, ingepak (hierdie houer word dus 'n strook genoem). In twee dimensies word die wydte van die strook gewoonlik gespesi seer en is die doel om al die voorwerpe sonder oorvleueling op s o 'n manier in die strook te pak dat die totale inpakkingshoogte geminineer word. In die houer-inpakkingsprobleem, daarenteen, is die doel om die voorwerpe op s o 'n manier in 'n gespesi seerde aantal houers (waarvan al die dimensies begrens is) te pak dat die vermorste of oorblywende ruimte in die houers (wat wel voorwerpe bevat) 'n minimum is. Die houers mag almal dieselfde dimensies h^e (in welke geval die probleem as die enkelgrootte houer-inpakkingsprobleem bekend staan), of mag verskillende dimensies h^e (in welke geval die probleem as die veelvuldige-grootte houer-inpakkingsprobleem bekend staan, afgekort as VGHIP). In twee dimensies word die vermorste ruimte geneem as die somtotaal van daardie deelareas van die houers (wat wel voorwerpe bevat) waar daar geen voorwerpe geplaas word nie. Verskeie oplossingsmetodologie e is al vir die bogenoemde twee inpakkingsprobleme ontwikkel, maar die bestek van die metodologie e wat in hierdie proefskrif oorweeg word, word beperk tot heuristieke. 'n Inpakkingsheuristiek volg 'n vaste stel re els waarvolgens voorwerpe in houers gepak word om so spoedig moontlik goeie, toelaatbare (maar nie noodwendig optimale) oplossings tot die strook-inpakkingsprobleem en die houer-inpakkingsprobleem te vind. Drie tipes inpakkingsheuristieke word in hierdie proefskrif oorweeg, naamlik (i) heuristieke wat voorwerpe langs die onderste randte van horisontale vlakke in die houers pak (die hoogtes van hierdie vlakke word bepaal deur die hoogtes van die hoogste item in elke vlak), (ii) heuristieke wat voorwerpe op enige plek binne horisontale stroke in die houers pak, en (iii) heuristieke waar inpakking nie volgens horisontale vlakke of stroke beperk word nie. Hierdie drie klasse heuristieke staan onderskeidelik as vlakalgoritmes, pseudo-vlakalgoritmes en platvlakalgoritmes bekend. 'n Berekeningsbenadering word in hierdie proefskrif gevolg deur die werkverrigting van die 218 nuwe heuristieke vir die strook-inpakkingsprobleem met die werkverrigting van 34 bekende heuristieke uit die literatuur te vergelyk, deur al die heuristieke op 1 170 toetsprobleme toe te pas. Daar word bevind dat die nuwe vlakalgoritmes nie 'n noemenswaardige verbetering in oplossingskwaliteit in vergeleke met soortgelyke bestaande algoritmes in die literatuur lewer nie, maar dat verskeie nuwe pseudo-vlakalgoritmes wel noemenswaardige verbeteringe in terme van beide inpakkingsdigthede en oplossingstye in vergeleke met die beste bestaande algoritmes in die literatuur lewer. Assessering van die platvlakalgoritmes het gelei tot die identi kasie van twee deelklasse van algoritmes, naamlik sorteringsafhanklike- en sorteringsonafhanklike algoritmes. Twee nuwe sorteringstegnieke word ook vir die deelklas van sorteringsonafhanklike algoritmes voorgestel, en een van hulle lewer die algeheel beste inpakkingsheursitiek. 'n Nuwe heuristiese benadering word ook vir die VGHIP ontwikkel. Hierdie benadering kan met vlak- of pseudo-vlakalgoritmes vir die strook-inpakkingsprobleem gekombineer word om baie vinnig oplossings vir die VGHIP te vind. Die beste platvlakheuristiek vir die strookinpakkingsprobleem word ook aangepas om voorwerpe eers in die grootste houers te pak, en daarna in kleiner houers te herpak met die doel om vermorste ruimte verder te minimeer. Daar word bevind dat die resulterende platvlakalgoritme die beste resultate in terme van beide inpakkingsdigtheid en oplossingstyd lewer, maar dat oplossingsverskille tussen die pseudovlakalgoritmes nie so opmerklik vir die VGHIP is as wat die geval met die strookinpakkingsprobleem was nie.

O problema de empacotamento em faixas de peças irregulares consiste em cortar um conjunto de peças bidimensionais a partir de um objeto de largura fixa utilizando o menor comprimento possível. Apesar de sua importância econômica para diversos setores industriais, há poucos trabalhos que abordam o problema de forma exata devido a sua dificuldade de resolução. Recentemente, Toledo et al. (2013) propuseram um modelo inteiro misto para este problema, no qual as peças são posicionadas em uma malha de pontos. Este modelo obteve bons resultados, provando a otimalidade para instâncias com até 21 peças. No entanto, o modelo possui um grande número de restrições de não-sobreposição, que cresce rapidamente de acordo com a discretização utilizada e a quantidade de peças distintas que devem ser alocadas. Neste trabalho, são propostas novas formulações matemáticas baseadas neste modelo, com o objetivo de reduzir o número de restrições. Na primeira abordagem, são propostos dois modelos reduzidos que mostraram ser eficientes para instâncias com poucas repetições de peças. Na segunda abordagem, foi proposto um modelo de cobertura por cliques para o problema. Este modelo obteve desempenho igual ou superior ao modelo da literatura para todas as instâncias avaliadas, obtendo uma solução ótima para instâncias com até 28 peças. / The irregular strip packing problem consists of cutting a set of two-dimensional pieces from an object of fixed width using the smallest possible length. Despite its economic importance for many industrial sectors, few exact studies have been made on this problem due to its difficulty of resolution. Recently, Toledo et al. (2013) proposed a mixed-integer model to this problem in which the pieces are placed on a grid. This model has worked successfully proving the optimality for instances up to 21 pieces. However, the model has a large number of non-overlapping constraints, which grows quickly in accordance with the discretization resolution and number of distinct pieces. In this work, we propose new mathematical formulations based on this model in order to reduce the number of constraints. In the first approach, we present two reduced models that have shown to be effective for instances with few repetitions of pieces. In the second approach, it was proposed a clique covering model for the problem. This model achieved a greater or equal performance than the literature for all instances, getting an optimal solution for instances up to 28 pieces.

O problema de empacotamento em faixas de peças irregulares consiste em cortar um conjunto de peças bidimensionais a partir de um objeto de largura fixa utilizando o menor comprimento possível. Apesar de sua importância econômica para diversos setores industriais, há poucos trabalhos que abordam o problema de forma exata devido a sua dificuldade de resolução. Recentemente, Toledo et al. (2013) propuseram um modelo inteiro misto para este problema, no qual as peças são posicionadas em uma malha de pontos. Este modelo obteve bons resultados, provando a otimalidade para instâncias com até 21 peças. No entanto, o modelo possui um grande número de restrições de não-sobreposição, que cresce rapidamente de acordo com a discretização utilizada e a quantidade de peças distintas que devem ser alocadas. Neste trabalho, são propostas novas formulações matemáticas baseadas neste modelo, com o objetivo de reduzir o número de restrições. Na primeira abordagem, são propostos dois modelos reduzidos que mostraram ser eficientes para instâncias com poucas repetições de peças. Na segunda abordagem, foi proposto um modelo de cobertura por cliques para o problema. Este modelo obteve desempenho igual ou superior ao modelo da literatura para todas as instâncias avaliadas, obtendo uma solução ótima para instâncias com até 28 peças. / The irregular strip packing problem consists of cutting a set of two-dimensional pieces from an object of fixed width using the smallest possible length. Despite its economic importance for many industrial sectors, few exact studies have been made on this problem due to its difficulty of resolution. Recently, Toledo et al. (2013) proposed a mixed-integer model to this problem in which the pieces are placed on a grid. This model has worked successfully proving the optimality for instances up to 21 pieces. However, the model has a large number of non-overlapping constraints, which grows quickly in accordance with the discretization resolution and number of distinct pieces. In this work, we propose new mathematical formulations based on this model in order to reduce the number of constraints. In the first approach, we present two reduced models that have shown to be effective for instances with few repetitions of pieces. In the second approach, it was proposed a clique covering model for the problem. This model achieved a greater or equal performance than the literature for all instances, getting an optimal solution for instances up to 28 pieces.

Scheduling in the context of manufacturing systems has become increasingly impor- tant in order for organizations to achieve success in dynamic and competitive scenarios. Scheduling can be described as allocation of available jobs over resources to meet the performance criteria defined in a domain. Our research work fo cuses on scheduling a given set of three-dimensional cylindrical items, each characterized by width wj , height hj, and depth dj , onto parallel non-identical rectangular heat treatment kilns, such that the capacities of the kilns is optimally used. The problem is strongly NP-hard as it generalizes the (one-dimensional) Bin Packing Problem (1BP), in which a set of n positive values wj has to be partitioned into the minimum number of subsets so that the total value in each subset does not exceed the bin capacity W. The problem has been formulated as a variant of the 3D-BPP by following the MILP approach, and we propose a weight optimization heuristic that produces solutions comparable to that of the LP problem, in addition to reducing the computational complexity. Finally, we also propose a Decomposition Algorithm (DA) and validate the perfor- mance effectiveness of our heuristic. The numerical analyses provides useful insights that influence the shop-floor decision making process.

Ο όγκος των δεδομένων που απαιτούνται για τον έλεγχο της ορθής λειτουργίας ενός συστήματος που υλοποιείται σε ένα ολοκληρωμένο κύκλωμα είναι πάρα πολύ μεγάλος. Αυτό συνεπάγεται ότι ο χρόνος που απαιτείται για τον έλεγχο της ορθής λειτουργίας του ολοκληρωμένου κυκλώματος μπορεί να είναι απαγορευτικά μεγάλος. Για τη μείωση του απαιτούμενου χρόνου χρησιμοποιούνται διάφορες τεχνικές συμπίεσης των δεδομένων δοκιμής. Κάποιες από αυτές τις τεχνικές βασίζονται στην αποστολή κοινών δεδομένων δοκιμής ταυτόχρονα σε περισσότερες από μία μονάδες του ολοκληρωμένου κυκλώματος. Στην εργασία αυτή υλοποιούμε μια από αυτές τις τεχνικές που βασίζεται στην ύπαρξη μονοπατιών ολίσθησης (scan paths) στις μονάδες του ολοκληρωμένου κυκλώματος. Για την περαιτέρω μείωση του χρόνου που απαιτείται για τον έλεγχο της ορθής λειτουργίας του ολοκληρωμένου κυκλώματος γίνεται χρονοπρογραμματισμός της σειράς με την οποία θα ελεγχθεί η ορθή λειτουργία των διαφόρων μονάδων του ολοκληρωμένου κυκλώματος. / The volume of data that is required to test a SoC is too much big. This means that the time that is required for testing can be prohibitorily big. For the reduction of required time are used various techniques of data compaction.Some of these techniques are based on broadcasting the same value to all of the cores on a SoC.In this work we use one of these techniques that are based on the existence of scan chains in the core (broadcast scan).For further reduction of time that is required for testing a circuit we use a core testing schedule algorithm.