This thesis deals with the placement of irregular shapes on a fixed width plane, which is a problem whose solution can be used, for example, when placing sewing patterns on fabric so that its length is as small as possible. A continuity of shapes depending on ma- terial patterns are also taken into account. The thesis uses evolutionary algorithms with heuristic functions that assign positions to individual shapes depending on the individual being developed by the relevant evolution. Patterned fabrics are treated differently using special heuristic functions types that are able to adjust the layout. 1

AN ABSTRACT OF THE DISSERTATION OFDinush Lanka Panditharathna Jayasooriya Arachchilage, forthe Doctor of Philosophy degree in MATHEMATICS, presented on June 22, 2020 at SouthernIllinois University Carbondale.TITLE: SPIN NETWORK EVALUATION AND THE ASYMPTOTIC BEHAVIORMAJOR PROFESSOR: Dr. Jerzy KocikGraphically, a spin network is a trivalent graph with weights on each edge. At anyof the vertices, the sum of all three weights is even and the sum of any two weights isgreater than or equal to the remaining weight. If the spin network has no free ends, thenwe can evaluate the spin network. Here, we propose a method to evaluate some basic spinnetworks using the idea of Stirling triangle.Tangent circles with integer curvatures are a natural source to make a spin network.In particular, there are spin networks corresponding the Apollonian circle packing and theFord circle packing. We obtain the recurrence relations using the Descartes circle theoremand we evaluate the Apollonian spin network and the Ford circle spin network. We alsodiscuss the asymptotic behavior of the Ford circle spin network.

This research has been conducted at Hunter Engineering Company. It aims to Design a Kit Packing Weighing System which performs a Quality Assessment of tool-kits while packing them on weighing scales. The main aspects of Kit-Packing are documented and suitable terminologies to address the process are established. The kits are categorized and a process for packing kits of different categories is suggested. A system to weigh Heavy, Medium and Light kits is presented. A Monte-Carlo Simulation Tool is developed and an Analysis using the Risk Solver Software is conducted to select the preferable method of establishing Tolerance Limits. A design for a Visual Basic coded Interface is outlined that will guide the Operator through the kit packing process and indicate whether to Accept or Inspect the kit. A Windows application of the Software was prototyped to demonstrate the System’s functionality which also is documented herein.

No description available.

O problema de empacotamento de cilindros em níveis é comumente encontrado nas indústrias de cerâmica. Solucionar este problema significa encontrar o posicionamento ideal dos itens cerâmicos cilíndricos dentro do forno de modo que o menor número de fornos seja utilizado e os itens não se sobreponham e obedeçam aos limites do recipiente. Também é considerado o uso de prateleiras para que haja uma melhor ocupação do espaço do forno. Propomos uma formulação matemática não-linear inteira mista e métodos de resolução heurísticos e exato para o problema. Os métodos heurísticos consistem em escolher uma estratégia de ordenação, posicionar os itens em cada nível por meio da heurística Bottom-Left e posicionar os níveis no recipiente utilizando as estratégias Best-Fit, First-Fit ou Worst-Fit. Ao total, propomos seis variações heurísticas para resolução do problema. O método exato consiste em estimar o número de níveis e recipientes necessários e resolver o problema por meio de um solver de otimização global. Os experimentos computacionais foram realizados para um conjunto de instâncias que criamos. Os resultados mostraram que o método exato é capaz de encontrar a solução ótima em um curto período de tempo para instâncias de pequeno porte e que as heurísticas são capazes de resolver o problema em um tempo computacional baixo, para instâncias de pequeno, médio e grande porte, sendo que algumas heurísticas apresentam melhor desempenho que outras. / The cylinder packing problem in levels is commonly found in ceramic industries. Solving this problem consists in finding the ideal position of items inside furnaces so that the minimum number of furnaces is used and the items do not overlap and obeying furnaces size. In this case, it is possible to add levels to the furnace. We proposed a non-linear integer mixed mathematical model for the problem and heuristic and exact resolution methods. Heuristic methods consist of choosing a sorting strategy, packing the items at each level by a Bottom-Left heuristic, and positioning the levels in the furnace using Best-Fit, First- Fit or Worst-Fit strategy. In total, it is proposed six heuristic variations to solve the problem. The exact method consists in solving the problem by a global optimization solver. The computational experiments were run over a set of new proposed instances. The results have shown that the exact method is able to find an optimal solution in a short period of time for small instances and that the proposed heuristics are capable of solving the problem in a low computational time for small, medium and large instances. Furthermore, some of them have performed better than others.

O problema de empacotamento de cilindros em níveis é comumente encontrado nas indústrias de cerâmica. Solucionar este problema significa encontrar o posicionamento ideal dos itens cerâmicos cilíndricos dentro do forno de modo que o menor número de fornos seja utilizado e os itens não se sobreponham e obedeçam aos limites do recipiente. Também é considerado o uso de prateleiras para que haja uma melhor ocupação do espaço do forno. Propomos uma formulação matemática não-linear inteira mista e métodos de resolução heurísticos e exato para o problema. Os métodos heurísticos consistem em escolher uma estratégia de ordenação, posicionar os itens em cada nível por meio da heurística Bottom-Left e posicionar os níveis no recipiente utilizando as estratégias Best-Fit, First-Fit ou Worst-Fit. Ao total, propomos seis variações heurísticas para resolução do problema. O método exato consiste em estimar o número de níveis e recipientes necessários e resolver o problema por meio de um solver de otimização global. Os experimentos computacionais foram realizados para um conjunto de instâncias que criamos. Os resultados mostraram que o método exato é capaz de encontrar a solução ótima em um curto período de tempo para instâncias de pequeno porte e que as heurísticas são capazes de resolver o problema em um tempo computacional baixo, para instâncias de pequeno, médio e grande porte, sendo que algumas heurísticas apresentam melhor desempenho que outras. / The cylinder packing problem in levels is commonly found in ceramic industries. Solving this problem consists in finding the ideal position of items inside furnaces so that the minimum number of furnaces is used and the items do not overlap and obeying furnaces size. In this case, it is possible to add levels to the furnace. We proposed a non-linear integer mixed mathematical model for the problem and heuristic and exact resolution methods. Heuristic methods consist of choosing a sorting strategy, packing the items at each level by a Bottom-Left heuristic, and positioning the levels in the furnace using Best-Fit, First- Fit or Worst-Fit strategy. In total, it is proposed six heuristic variations to solve the problem. The exact method consists in solving the problem by a global optimization solver. The computational experiments were run over a set of new proposed instances. The results have shown that the exact method is able to find an optimal solution in a short period of time for small instances and that the proposed heuristics are capable of solving the problem in a low computational time for small, medium and large instances. Furthermore, some of them have performed better than others.

Die vorliegende Thesis befasst sich mit der Mischungsentwicklung eines zementreduzierten Ökobetons für die Verwendung in einem ökologisch verbesserten Deckensystem. Dafür wurden mithilfe eines in Microsoft Excel aufgestellten physikalischen Analysemodells – dem Compaction-Interaction Packing Model nach FENNIS – Rezepturen entwickelt, die durch eine optimierte Packungsdichte einen geringeren Zementleimbedarf aufweisen. Dabei gelang es, Zement teilweise durch feine Kalksteinmehle zu ersetzen und eine CO2-sparende Mischung mit einem reduzierten Zementgehalt von 150 kg je Kubikmeter Beton herzustellen, welche die an sie gestellten Anforderungen erfüllt – u. a. bezogen auf Festigkeit (Festigkeitsklasse C 20/25), Verarbeitbarkeit (Konsistenzklasse C3) und Alkalität (pH-Wert > 10). Diese Eigenschaften wurden experimentell geprüft. Zwar wurden bei der auf empirischen Daten beruhenden Prognose von Festigkeit und Konsistenz im Modell nur teilweise realitätsnahe Werte ermittelt, das Modell stellte sich insgesamt jedoch als zielführendes Instrument bei der Mischungsentwicklung von Ökobetonen heraus.:1 Einleitung 2 Verringerung der Umwelteinwirkungen bei der Betonherstellung 3 Methodik der Mischungsentwicklung zementreduzierter Ökobetone 4 Packungsdichteberechnung mit dem Compaction-Interaction Packing Model nach FENNIS 5 Mischungsentwicklung eines Ökobetons im Rahmen des Forschungsvorhabens GRO-COCE 6 Herstellung der Auswahlmischungen und experimentelle Ermittlung von Betoneigenschaften 7 Eingrenzung einer Zielmischung 8 Diskussion der Ergebnisse 9 Zusammenfassung und Ausblick / The present thesis deals with the mix development of a cement-reduced eco-concrete for the use in an ecologically improved ceiling system. For this purpose, a physical analysis model built in Microsoft Excel – the Compaction-Interaction Packing Model according to FENNIS – was used to develop recipes which, due to an optimised packing density, have a low cement paste requirement. It was possible to partially replace cement with fine limestone powders and to produce a CO2-saving mixture with a reduced cement content of 150 kg per cubic metre of concrete, which meets the requirements placed on it – among other things with regard to strength (strength class C 20/25), workability (consistency class C3) and alkalinity (pH-value > 10). These properties were tested experimentally. Although only partially realistic values were determined in the model for the prediction of strength and consistency based on empirical data, the model turned out to be a suitable instrument for mix developments of eco-concretes.:1 Einleitung 2 Verringerung der Umwelteinwirkungen bei der Betonherstellung 3 Methodik der Mischungsentwicklung zementreduzierter Ökobetone 4 Packungsdichteberechnung mit dem Compaction-Interaction Packing Model nach FENNIS 5 Mischungsentwicklung eines Ökobetons im Rahmen des Forschungsvorhabens GRO-COCE 6 Herstellung der Auswahlmischungen und experimentelle Ermittlung von Betoneigenschaften 7 Eingrenzung einer Zielmischung 8 Diskussion der Ergebnisse 9 Zusammenfassung und Ausblick

Call number: LD2668 .T4 1963 A54 / Master of Science

Thesis (MComm)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Table grapes are the second-largest contributor to the perishable product export in South Africa. The table grape industry also experienced considerable growth in the past ten years. The industry contributes toward employment in South Africa. The South African table grape industry experiences quality-related problems with exporting table grapes to the European market. Examples of quality related problems can range from chemical damage, chilling injury/freezing damage, heavy bruising and decay. A great amount of table grapes is basically wasted. The postharvest loss of table grapes during transportation can range from 1%-25% per day depending on the degree of temperature fluctuation. Therefore, it is important to minimize waste and increase the export volumes in order to utilise the potential profit possibilities. Based on data analysis for this case, results indicated that packaging is preventing cool air from flowing through the pallet during transportation and preventing the table grapes to cool evenly. The fluctuation in temperature contributes to the qualityrelated problems of these table grapes. The primary research goal is to identify packaging-related problems and propose possible solutions to improve the packaging-related conditions in which table grapes arrive at the destination. This study therefore investigated and evaluated the performance of the current packaging system of table grapes within a South African context for exporting to Europe for a specific case. Further analyses of the data received from Dole South Africa, a fruit marketing and distribution company, revealed that the following two types of packaging showed serious quality-related problems: 1) A04I: The 4.5kg box with the grapes in plastic bags. 2) A05E: The 5kg box with 500g punnets (10 x 500g punnets). A questionnaire combining with the Packaging Portfolio Evaluation Model and the Packaging Scorecard was developed and used to evaluate the two identified packaging systems in the following stages: Stage 1: Development of a new questionnaire by combining the Packaging Portfolio Evaluation Model and the Packaging Scorecard. Stage 2: Survey with the questionnaire developed in Stage 1. The identified types of packaging were evaluated with a new questionnaire with specific criteria. Members of the table grape supply chain from the farmer in South Africa to consumer in Sweden were used during the evaluation process. Descriptive statistics were calculated for each criteria or question in order to describe the performance and importance of the different packaging criteria. Data were also analysed with the use of box plots. The box plots and data visualisation methods were used to make conclusions and recommendations regarding the different categories of each type of packaging. It was clear that the major problem areas of both packaging systems involved were related to the environmental aspect of the packaging. The marketing and the logistics of the plastic bag also underperformed. However, individual criteria regarding the other business areas can also be improved. Possible solutions to these problem areas are also suggested in this thesis. The possible solutions include the Tali Grape Basket, Perforated Plastic Liners, New Generation Pack (NGP), Vinguard TM , Easypunnet and the Sulphur Dioxide Liner Bag. / AFRIKAANSE OPSOMMING: Tafeldruiwe is die tweede grootste bydraende faktor tot bederfbare produkuitvoere in Suid-Afrika. Die tafeldruifindustrie het ook aansienlike groei die afgelope tien jaar beleef. Die industrie dra tot werkskepping in Suid-Afrika by. Die Suid-Afrikaanse tafeldruifindustrie ervaar kwaliteitsverwante probleme met die uitvoer van tafeldruiwe na die Europese mark. Voorbeelde van hierdie kwaliteitsverwante probleme kan wissel van chemiese skade, koueskade / vries skade, swaar kneusing en bederf. ‘n Groot hoeveelheid tafeldruiwe word vermors. Die oes verlies van tafeldruiwe tydens vervoer kan wissel van 1% -25% per dag, afhangende van die mate van temperatuur verandering. Daarom is dit belangrik om vermorsing te beperk en uitvoerhoeveelhede te verhoog om sodoende potensiële winsmoontlikhede te benut. Volgens data-analise blyk dit dat huidige verpakking tans verhoed dat koel lug tydens die vervoer van die produk deur die palet vloei, en dit veroorsaak dat die tafeldruiwe nie eweredig afkoel nie. Die wisseling in temperatuur dra grootliks tot die kwaliteitsverwante probleme van die tafeldruiwe by. Die primêre navorsingsdoelwit is om die verpakkingsverwante probleme te identifiseer en moontlike oplossings voor te stel om sodoende die toestand te verbeter waarin tafeldruiwe by die eindbestemming aankom. Daarom ondersoek en evalueer hierdie studie die prestasie van die huidige verpakkingsisteem van tafeldruiwe binne ʼn Suid-Afrikaanse konteks vir uitvoere na Europa; met betrekking tot ʼn spesifieke situasie. Verdere analise van data soos ontvang vanaf Dole Suid-Afrika, ‘n vrugtebemarkingsen verspreidingsmaatskappy, het getoon dat ernstige kwaliteitsverwante probleme veral by die volgende twee tipes verpakkingsisteme voorkom: 1) A04I: Die 4.5kg karton met druiwe in plastieksakkies. 2) A05E: Die 5kg karton met 500g bakkies (10 x 500g bakkies). ʼn Vraelys, gebaseer op die kombinasie van die Verpakkingportefeulje Evalueringsmodel model en die Verpakkingstelkaart, is ontwikkel en gebruik om die bogenoemde verpakkingsisteme te evalueer en wel in die volgende fases: Fase 1: Ontwikkeling van ʼn gekombineerde Verpakkingsportefeulje Evalueringsmodel en die Verpakkingstelkaart tot ʼn nuwe vraelys. Fase 2: Opname met die vraelys soos ontwikkel in Fase 1. Die twee geïdentifiseerde tipes verpakking is geëvalueer met die nuwe vraelys met spesifieke kriteria. Die lede van die tafeldruiwe voorsieningsketting van die boer in Suid-Afrika tot die verbruiker in Swede is gebruik tydens die evaluasieproses. Beskrywende statistiek vir elke kriteria of vraag was bereken sodat die prestasie en belangrikheid van die verskillende verpakkingskriteria beskryf kan word. Data was ook beskryf met behulp van ‘n houer-en-puntstipping. Data visualiseringmetodes en die houer-en-puntstippings was gebruik om gevolgtrekkings en aanbevelings rakende die verskillende kategorieë van die tipes verpakking te maak. Dit was duidelik dat die omgewingsaspek van beide tipes verpakking ‘n groot probleem was. Die bemarking en logistiek van die plastieksakkie het ook onderpresteer. Individuele kriteria van ander besigheidsareas kan egter ook verbeter word. Moontlike oplossings vir hierdie probleem-areas word ook in hierdie tesis aangedui. Die moontlike oplossings sluit die “Tali Grape Basket”, “Perforated Plastic Liners”, “New Generation Pack (NGP)”, “Vinguard TM ”, “Easypunnet” en die “Sulphur Dioxide Liner Bag” in

Thesis (MCom)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Kohler Signs (PTY) Ltd is a sign production company located in Cape Town, South Africa. They manufacture and install signs for the City of Cape Town and private companies as well as manufacture advertisement signs to be placed on vehicles. Road signs consist of steel sheets that are cut and bent to the appropriate size and frame, and an image design, which is cut from re ective vinyl, are applied to the bent steel sheet. The image design consists of various letters, numbers and symbols which are categorised as irregular items. When these irregular items are combined in a distinctive way, with the use of di erent coloured vinyl, they convey a message to the road user which may be to yield for pedestrians crossing the street, or indicate to the road user the various highway exits that exist on the interchange ahead. These irregular items are placed upon re ective vinyl for cutting which results in vinyl o cuts that are wasted. The focus of this thesis is to minimise the waste incurred by placing these irregular items upon the vinyl in an optimal and timely manner for industry use. The vinyl printer, which cuts the irregular items out of the vinyl, consists of a xed width and is only limited in height by the vinyl itself. Thus, this problem may be described as a Two Dimensional Irregular Strip Packing Problem. These irregular items have only a few possible heights for each type of irregular item packed, which allows these irregular items to be packed as a level packing problem. The items are packed within levels as though they are regular items with the assistance of a prede ned rule-set. In this thesis various packing algorithms and image processing methodologies from the literature are researched and used to develop a new packing algorithm for this speci c problem. The newly developed algorithm is put through various benchmarks to test its performance. Some of these benchmarks are procured from Kohler Signs themselves, whereas others are randomly generated under certain conditions. These benchmarks reveal that the newly developed algorithm performs better for both the minimisation of waste and the minimisation of algorithm running time than the tried and trusted techniques utilised in industry by Kohler Signs. / AFRIKAANSE OPSOMMING: Kohler Signs (EDMS) Bpk is 'n padteken produksie maatskappy gele e in Kaapstad, Suid-Afrika. Hulle vervaardig en installeer tekens vir die Stad van Kaapstad en privaat maatskappye, sowel as advertensietekens wat op voertuie geplaas word. Padtekens bestaan uit staalplate wat gesny en gebuig word tot die toepaslike grootte en vorm. 'n Beeldontwerp, wat gesny is uit re ektiewe viniel, word vasgesit op die gebuigde staalplaat. Die beeldontwerp bestaan uit verskeie letters, getalle en simbole wat geklassi seer word as onre elmatige items. Wanneer hierdie onre elmatige items gekombineer word op 'n eiesoortige manier, met die gebruik van verskillende kleure viniel, dra hulle 'n boodskap oor aan die padgebruiker, soos byvoorbeeld om toe te gee aan voetgangers by 'n voetoorgang of dit dui aan die padgebruiker die verskillende snelweguitgange wat bestaan op die wisselaar wat voorl^e. Hierdie onre elmatige items word op re ektiewe viniel geplaas en uitgesny wat lei tot die vermorsing van stukkies viniel. Die fokus van hierdie tesis is om die onre elmatige items op 'n optimale en tydige wyse vir gebruik in industrie, op die viniel te plaas sodat die afval stukkies viniel geminimeer word. Die vinieldrukker, wat die onre elmatige items sny uit die viniel, bestaan uit 'n vaste wydte en is slegs beperk in hoogte deur die viniel self. Dus kan hierdie probleem beskryf word as 'n Twee-Dimensionele Onre elmatige Strookverpakkingsprobleem. Hierdie onre elmatige items het slegs 'n paar moontlike hoogtes vir elke tipe van onre elmatige item wat verpak word, wat dit moontlik maak om hierdie onre elmatige items te verpak as 'n strook verpakkingsprobleem. Die items word met behulp van 'n gede nieerde stel re els binne vlakke verpak asof hulle re elmatige items is. In hierdie tesis is verskeie verpakkingsalgoritmes en beeldverwerkingsmetodes van die literatuur nagevors en gebruik om 'n nuwe verpakkingsalgoritme vir hierdie spesi eke probleem te ontwikkel. Die nuut ontwikkelde algoritme se prestasie is deur middel van verskeie normbepalingsvoorbeelde getoets. Sommige van hierdie normbepalingsvoorbeelde is verkry van Kohler Signs self, terwyl ander lukraak gegenereer is onder sekere voorwaardes. Hierdie normbepalingsvoorbeelde toon dat die nuut ontwikkelde algoritme beter vaar as die beproefde tegnieke gebruik in industrie deur Kohler Signs vir beide die minimering van vermorsde viniel sowel as die minimering van die algoritme se uitvoertyd.