Academic literature on the topic 'Geometric bin packing'

Resumo Estudos que visem otimizar a utilização da capacidade dos caminhões são importantes no Brasil, país em que o transporte rodoviário representa 61,1% da movimentação de cargas, pois contribuem para a redução da quantidade de caminhões nas estradas, melhorando a fluidez e a segurança. O objetivo deste trabalho é promover um estudo logístico por meio de um modelo matemático baseado no Three Dimensional Bin Packing Problem para arrumação da carga dentro dos veículos utilizados no transporte de produtos alimentícios de forma a otimizar a sua capacidade volumétrica. O modelo proposto visa um melhor aproveitamento da capacidade volumétrica dos veículos considerando a disposição em três dimensões das cargas, área de suporte, sequência de entrega das cargas, para evitar bloqueios, rotação das caixas no plano X-Y e caixas de geometria paralelepipédica. A solução alcançada pelo modelo apresentou ganhos importantes em relação ao planejamento manual realizado pela empresa, reduzindo a utilização de caminhões e gerando ganhos econômicos.

AbstractThis paper addresses the two-dimensional irregular bin packing problem, whose main aim is to allocate a given set of irregular pieces to larger rectangular containers (bins), while minimizing the number of bins required to contain all pieces. To solve the problem under study a dynamic hierarchical hyper-heuristic approach is proposed. The main idea of the hyper-heuristics is to search the space of low-level heuristics for solving computationally difficult problems. The proposed approach is “dynamic” since the low-level heuristic to be executed is chosen on the basis of the main characteristics of the instance to be solved. The term “hierarchical” is used to indicate the fact that the main hyper-heuristic can execute either simple heuristics or can run in a “recursive fashion” a hyper-heuristic. The developed solution strategy is evaluated empirically by performing extensive experiments on irregular packing benchmark instances. A comparison with the state-of-the-art approaches is also carried out. The computational results are very encouraging.

AbstractThe ubiquitous diffusion of cloud computing requires suitable management policies to face the workload while guaranteeing quality constraints and mitigating costs. The typical trade-off is between the used power and the adherence to a service-level metric subscribed by customers. To this aim, a possible idea is to use an optimization-based placement mechanism to select the servers where to deploy virtual machines. Unfortunately, high packing factors could lead to performance and security issues, e.g., virtual machines can compete for hardware resources or collude to leak data. Therefore, we introduce a multi-objective approach to compute optimal placement strategies considering different goals, such as the impact of hardware outages, the power required by the datacenter, and the performance perceived by users. Placement strategies are found by using a deep reinforcement learning framework to select the best placement heuristic for each virtual machine composing the workload. Results indicate that our method outperforms bin packing heuristics widely used in the literature when considering either synthetic or real workloads.

“...children’s play seems to become more and more a product of the educational and cultural orientation of parents...” — Stephen Kline, The Making of Children’s Culture We live in a world saturated by design and through design artefacts, one can glean unique insights into a culture's values and norms. In fact, some academics, such as British media and film theorist Ben Highmore, see the two areas so inextricably intertwined as to suggest a wholesale “re-branding of the cultural sciences as design studies” (14). Too often, however, everyday objects are marginalised or overlooked as objects of scholarly attention. The field of material culture studies seeks to change that by focussing on the quotidian object and its ability to reveal much about the time, place, and culture in which it was designed and used. This article takes on one such object, a mid-century children's toy tea set, whose humble journey from 1968 Sears catalogue to 2014 thrift shop—and subsequently this author’s basement—reveals complex rhetorical messages communicated both visually and verbally. As material culture studies theorist Jules Prown notes, the field’s foundation is laid upon the understanding “that objects made ... by man reflect, consciously or unconsciously, directly or indirectly, the beliefs of individuals who made, commissioned, purchased or used them, and by extension the beliefs of the larger society to which they belonged” (1-2). In this case, the objects’ material and aesthetic characteristics can be shown to reflect some of the pervasive stereotypes and gender roles of the mid-century and trace some of the prevailing tastes of the American middle class of that era, or perhaps more accurately the type of design that came to represent good taste and a modern aesthetic for that audience. A wealth of research exists on the function of toys and play in learning about the world and even the role of toy selection in early sex-typing, socialisation, and personal identity of children (Teglasi). This particular research area isn’t the focus of this article; however, one aspect that is directly relevant and will be addressed is the notion of adult role-playing among children and the role of toys in communicating certain adult practices or values to the child—what sociologist David Oswell calls “the dedifferentiation of childhood and adulthood” (200). Neither is the focus of this article the practice nor indeed the ethicality of marketing to children. Relevant to this particular example I suggest, is as a product utilising messaging aimed not at children but at adults, appealing to certain parents’ interest in nurturing within their child a perceived era and class-appropriate sense of taste. This was fuelled in large part by the curatorial pursuits of the Museum of Modern Art (MoMA) in New York, coupled with an interest and investment in raising their children in a design-forward household and a desire for toys that reflected that priority; in essence, parents wishing to raise modern children. Following Prown’s model of material culture analysis, the tea set is examined in three stages, through description, deduction and speculation with each stage building on the previous one. Figure 1: Porcelain Toy Tea Set. Description The tea set consists of twenty-six pieces that allows service for six. Six cups, saucers, and plates; a tall carafe with spout, handle and lid; a smaller vessel with a spout and handle; a small round bowl with a lid; a larger oval bowl with a lid, and a coordinated oval platter. The cups are just under two inches tall and two inches in diameter. The largest piece, the platter is roughly six inches by four inches. The pieces are made of a ceramic material white in colour and glossy in texture and are very lightweight. The rim or edge of each piece is decorated with a motif of three straight lines in two different shades of blue and in different thicknesses, interspersed with a set of three black wiggly lines. Figure 2: Porcelain Toy Tea Set Box. The set is packaged for retail purposes and the original box appears to be fully intact. The packaging of an object carries artefactual evidence just as important as what it contains that falls into the category of a “‘para-artefact’ … paraphernalia that accompanies the product (labels, packaging, instructions etc.), all of which contribute to a product’s discourse” (Folkmann and Jensen 83). The graphics on the box are colourful, featuring similar shades of teal blue as found on the objects, with the addition of orange and a silver sticker featuring the logo of the American retailer Sears. The cover features an illustration of the objects on an orange tabletop. The most prominent text that confirms that the toy is a “Porcelain Toy Tea Set” is in an organic, almost psychedelic style that mimics both popular graphics of this era—especially album art and concert posters—as well as the organic curves of steam that emanate from the illustrated teapot’s spout. Additional messages appear on the box, in particular “Contemporary DESIGN” and “handsome, clean-line styling for modern little hostesses”. Along the edges of the box lid, a detail of the decorative motif is reproduced somewhat abstracted from what actually appears on the ceramic objects. Figure 3: Sears’s Christmas Wishbook Catalogue, page 574 (1968). Sears, Roebuck and Co. (Sears) is well-known for its over one-hundred-year history of producing printed merchandise catalogues. The catalogue is another important para-artefact to consider in analysing the objects. The tea set first appeared in the 1968 Sears Christmas Wishbook. There is no date or copyright on the box, so only its inclusion in the catalogue allows the set to be accurately dated. It also allows us to understand how the set was originally marketed. Deduction In the deduction phase, we focus on the sensory aesthetic and functional interactive qualities of the various components of the set. In terms of its function, it is critical that we situate the objects in their original use context, play. The light weight of the objects and thinness of the ceramic material lends the objects a delicate, if not fragile, feeling which indicates that this set is not for rough use. Toy historian Lorraine May Punchard differentiates between toy tea sets “meant to be used by little girls, having parties for their friends and practising the social graces of the times” and smaller sets or doll dishes “made for little girls to have parties with their dolls, or for their dolls to have parties among themselves” (7). Similar sets sold by Sears feature images of girls using the sets with both human playmates and dolls. The quantity allowing service for six invites multiple users to join the party. The packaging makes clear that these toy tea sets were intended for imaginary play only, rendering them non-functional through an all-capitals caution declaiming “IMPORTANT: Do not use near heat”. The walls and handles of the cups are so thin one can imagine that they would quickly become dangerous if filled with a hot liquid. Nevertheless, the lid of the oval bowl has a tan stain or watermark which suggests actual use. The box is broken up by pink cardboard partitions dividing it into segments sized for each item in the set. Interestingly even the small squares of unfinished corrugated cardboard used as cushioning between each stacked plate have survived. The evidence of careful re-packing indicates that great care was taken in keeping the objects safe. It may suggest that even though the set was used, the children or perhaps the parents, considered the set as something to care for and conserve for the future. Flaws in the glaze and applique of the design motif can be found on several pieces in the set and offer some insight as to the technique used in producing these items. Errors such as the design being perfectly evenly spaced but crooked in its alignment to the rim, or pieces of the design becoming detached or accidentally folded over and overlapping itself could only be the result of a print transfer technique popularised with decorative china of the Victorian era, a technique which lends itself to mass production and lower cost when compared to hand decoration. Speculation In the speculation stage, we can consider the external evidence and begin a more rigorous investigation of the messaging, iconography, and possible meanings of the material artefact. Aspects of the set allow a number of useful observations about the role of such an object in its own time and context. Sociologists observe the role of toys as embodiments of particular types of parental messages and values (Cross 292) and note how particularly in the twentieth century “children’s play seems to become more and more a product of the educational and cultural orientation of parents” (Kline 96). Throughout history children’s toys often reflected a miniaturised version of the adult world allowing children to role-play as imagined adult-selves. Kristina Ranalli explored parallels between the practice of drinking tea and the play-acting of the child’s tea party, particularly in the nineteenth century, as a gendered ritual of gentility; a method of socialisation and education, and an opportunity for exploratory and even transgressive play by “spontaneously creating mini-societies with rules of their own” (20). Such toys and objects were available through the Sears mail-order catalogue from the very beginning at the end of the nineteenth century (McGuire). Propelled by the post-war boom of suburban development and homeownership—that generation’s manifestation of the American Dream—concern with home décor and design was elevated among the American mainstream to a degree never before seen. There was a hunger for new, streamlined, efficient, modernist living. In his essay titled “Domesticating Modernity”, historian Jeffrey L. Meikle notes that many early modernist designers found that perhaps the most potent way to “‘domesticate’ modernism and make it more familiar was to miniaturise it; for example, to shrink the skyscraper and put it into the home as furniture or tableware” (143). Dr Timothy Blade, curator of the 1985 exhibition of girls’ toys at the University of Minnesota’s Goldstein Gallery—now the Goldstein Museum of Design—described in his introduction “a miniaturised world with little props which duplicate, however rudely, the larger world of adults” (5). Noting the power of such toys to reflect adult values of their time, Blade continues: “the microcosm of the child’s world, remarkably furnished by the miniaturised props of their parents’ world, holds many direct and implied messages about the society which brought it into being” (9). In large part, the mid-century Sears catalogues capture the spirit of an era when, as collector Thomas Holland observes, “little girls were still primarily being offered only the options of glamour, beauty and parenthood as the stuff of their fantasies” (175). Holland notes that “the Wishbooks of the fifties [and, I would add, the sixties] assumed most girls would follow in their mother’s footsteps to become full-time housewives and mommies” (1). Blade grouped toys into three categories: cooking, cleaning, and sewing. A tea set could arguably be considered part of the cooking category, but closer examination of the language used in marketing this object—“little hostesses”, et cetera—suggests an emphasis not on cooking but on serving or entertaining. This particular category was not prevalent in the era examined by Blade, but the cultural shifts of the mid-twentieth century, particularly the rapid popularisation of a suburban lifestyle, may have led to the use of entertaining as an additional distinct category of role play in the process of learning to become a “proper” homemaker. Sears and other retailers offered a wide variety of styles of toy tea sets during this era. Blade and numerous other sources observe that children’s toy furniture and appliances tended to reflect the style and aesthetic qualities of their contemporary parallels in the adult world, the better to associate the child’s objects to its adult equivalent. The toy tea set’s packaging trumpets messages intended to appeal to modernist values and identity including “Contemporary Design” and “handsome, clean-line styling for modern little hostesses”. The use of this coded marketing language, aimed particularly at parents, can be traced back several decades. In 1928 a group of American industrial and textile designers established the American Designers' Gallery in New York, in part to encourage American designers to innovate and adopt new styles such as those seen in the L’ Exposition Internationale des Arts Decoratifs et Industriels Modernes (1925) in Paris, the exposition that sparked international interest in the Art Deco or Art Moderne aesthetic. One of the gallery founders, Ilonka Karasz, a Hungarian-American industrial and textile designer who had studied in Austria and was influenced by the Wiener Werkstätte in Vienna, publicised her new style of nursery furnishings as “designed for the very modern American child” (Brown 80). Sears itself was no stranger to the appeal of such language. The term “contemporary design” was ubiquitous in catalogue copy of the nineteen-fifties and sixties, used to describe everything from draperies (1959) and bedspreads (1961) to spice racks (1964) and the Lady Kenmore portable dishwasher (1961). An emphasis on the role of design in one’s life and surroundings can be traced back to efforts by MoMA. The museum’s interest in modern design hearkens back almost to the institution’s inception, particularly in relation to industrial design and the aestheticisation of everyday objects (Marshall). Through exhibitions and in partnership with mass-market magazines, department stores and manufacturer showrooms, MoMA curators evangelised the importance of “good design” a term that can be found in use as early as 1942. What Is Good Design? followed the pattern of prior exhibitions such as What Is Modern Painting? and situated modern design at the centre of exhibitions that toured the United States in the first half of the nineteen-fifties. To MoMA and its partners, “good design” signified the narrow identification of proper taste in furniture, home decor and accessories; effectively, the establishment of a design canon. The viewpoints enshrined in these exhibitions and partnerships were highly influential on the nation’s perception of taste for decades to come, as the trickle-down effect reached a much broader segment of consumers than those that directly experienced the museum or its exhibitions (Lawrence.) This was evident not only at high-end shops such as Bloomingdale’s and Macy’s. Even mass-market retailers sought out well-known figures of modernist design to contribute to their offerings. Sears, for example, commissioned noted modernist designer and ceramicist Russel Wright to produce a variety of serving ware and decor items exclusively for the company. Notably for this study, he was also commissioned to create a toy tea set for children. The 1957 Wishbook touts the set as “especially created to delight modern little misses”. Within its Good Design series, MoMA exhibitions celebrated numerous prominent Nordic designers who were exploring simplified forms and new material technologies. In the 1968 Wishbook, the retailer describes the Porcelain Toy Tea Set as “Danish-inspired china for young moderns”. The reference to Danish design is certainly compatible with the modernist appeal; after the explosion in popularity of Danish furniture design, the term “Danish Modern” was commonly used in the nineteen-fifties and sixties as shorthand for pan-Scandinavian or Nordic design, or more broadly for any modern furniture design regardless of origin that exhibited similar characteristics. In subsequent decades the notion of a monolithic Scandinavian-Nordic design aesthetic or movement has been debunked as primarily an economically motivated marketing ploy (Olivarez et al.; Fallan). In the United States, the term “Danish Modern” became so commonly misused that the Danish Society for Arts and Crafts called upon the American Federal Trade Commission (FTC) to legally restrict the use of the labels “Danish” and “Danish Modern” to companies genuinely originating in Denmark. Coincidentally the FTC ruled on this in 1968, noting “that ‘Danish Modern’ carries certain meanings, and... that consumers might prefer goods that are identified with a foreign culture” (Hansen 451). In the case of the Porcelain Toy Tea Set examined here, Sears was not claiming that the design was “Danish” but rather “Danish-inspired”. One must wonder, was this another coded marketing ploy to communicate a sense of “Good Design” to potential customers? An examination of the formal qualities of the set’s components, particularly the simplified geometric forms and the handle style of the cups, confirms that it is unlike a traditional—say, Victorian-style—tea set. Punchard observes that during this era some American tea sets were actually being modelled on coffee services rather than traditional tea services (148). A visual comparison of other sets sold by Sears in the same year reveals a variety of cup and pot shapes—with some similar to the set in question—while others exhibit more traditional teapot and cup shapes. Coffee culture was historically prominent in Nordic cultures so there is at least a passing reference to that aspect of Nordic—if not specifically Danish—influence in the design. But what of the decorative motif? Simple curved lines were certainly prominent in Danish furniture and architecture of this era, and occasionally found in combination with straight lines, but no connection back to any specific Danish motif could be found even after consultation with experts in the field from the Museum of Danish America and the Vesterheim National Norwegian-American Museum (personal correspondence). However, knowing that the average American consumer of this era—even the design-savvy among them—consumed Scandinavian design without distinguishing between the various nations, a possible explanation could be contained in the promotion of Finnish textiles at the time. In the decade prior to the manufacture of the tea set a major design tendency began to emerge in the United States, triggered by the geometric design motifs of the Finnish textile and apparel company Marimekko. Marimekko products were introduced to the American market in 1959 via the Cambridge, Massachusetts-based retailer Design Research (DR) and quickly exploded in popularity particularly after would-be First Lady Jacqueline Kennedy appeared in national media wearing Marimekko dresses during the 1960 presidential campaign and on the cover of Sports Illustrated magazine. (Thompson and Lange). The company’s styling soon came to epitomise a new youth aesthetic of the early nineteen sixties in the United States, a softer and more casual predecessor to the London “mod” influence. During this time multiple patterns were released that brought a sense of whimsy and a more human touch to classic mechanical patterns and stripes. The patterns Piccolo (1953), Helmipitsi (1959), and Varvunraita (1959), all designed by Vuokko Eskolin-Nurmesniemi offered varying motifs of parallel straight lines. Maija Isola's Silkkikuikka (1961) pattern—said to be inspired by the plumage of the Great Crested Grebe—combined parallel serpentine lines with straight and angled lines, available in a variety of colours. These and other geometrically inspired patterns quickly inundated apparel and decor markets. DR built a vastly expanded Cambridge flagship store and opened new locations in New York in 1961 and 1964, and in San Francisco in 1965 fuelled in no small part by the fact that they remained the exclusive outlet for Marimekko in the United States. It is clear that Marimekko’s approach to pattern influenced designers and manufacturers across industries. Design historian Lesley Jackson demonstrates that Marimekko designs influenced or were emulated by numerous other companies across Scandinavia and beyond (72-78). The company’s influence grew to such an extent that some described it as a “conquest of the international market” (Hedqvist and Tarschys 150). Subsequent design-forward retailers such as IKEA and Crate and Barrel continue to look to Marimekko even today for modern design inspiration. In 2016 the mass-market retailer Target formed a design partnership with Marimekko to offer an expansive limited-edition line in their stores, numbering over two hundred items. So, despite the “Danish” misnomer, it is quite conceivable that designers working for or commissioned by Sears in 1968 may have taken their aesthetic cues from Marimekko’s booming work, demonstrating a clear understanding of the contemporary high design aesthetic of the time and coding the marketing rhetoric accordingly even if incorrectly. Conclusion The Sears catalogue plays a unique role in capturing cross-sections of American culture not only as a sales tool but also in Holland’s words as “a beautifully illustrated diary of America, it’s [sic] people and the way we thought about things” (1). Applying a rhetorical and material culture analysis to the catalogue and the objects within it provides a unique glimpse into the roles these objects played in mediating relationships, transmitting values and embodying social practices, tastes and beliefs of mid-century American consumers. Adult consumers familiar with the characteristics of the culture of “Good Design” potentially could have made a connection between the simplified geometric forms of the components of the toy tea set and say the work of modernist tableware designers such as Kaj Franck, or between the set’s graphic pattern and the modernist motifs of Marimekko and its imitators. But for a much broader segment of the population with a less direct understanding of modernist aesthetics, those connections may not have been immediately apparent. The rhetorical messaging behind the objects’ packaging and marketing used class and taste signifiers such as modern, contemporary and “Danish” to reinforce this connection to effect an emotional and aspirational appeal. These messages were coded to position the set as an effective transmitter of modernist values and to target parents with the ambition to create “appropriately modern” environments for their children. References Ancestry.com. “Historic Catalogs of Sears, Roebuck and Co., 1896–1993.” <http://search.ancestry.com/search/db.aspx?dbid=1670>. Baker Furniture Inc. “Design Legacy: Our Story.” n.d. <http://www.bakerfurniture.com/design-story/ legacy-of-quality/design-legacy/>. Blade, Timothy Trent. “Introduction.” Child’s Play, Woman’s Work: An Exhibition of Miniature Toy Appliances: June 12, 1985–September 29, 1985. St. Paul: Goldstein Gallery, U Minnesota, 1985. Brown, Ashley. “Ilonka Karasz: Rediscovering a Modernist Pioneer.” Studies in the Decorative Arts 8.1 (2000-1): 69–91. Cross, Gary. “Gendered Futures/Gendered Fantasies: Toys as Representatives of Changing Childhood.” American Journal of Semiotics 12.1 (1995): 289–310. Dolansky, Fanny. “Playing with Gender: Girls, Dolls, and Adult Ideals in the Roman World.” Classical Antiquity 31.2 (2012): 256–92. Fallan, Kjetil. Scandinavian Design: Alternative Histories. Berg, 2012. Folkmann, Mads Nygaard, and Hans-Christian Jensen. “Subjectivity in Self-Historicization: Design and Mediation of a ‘New Danish Modern’ Living Room Set.” Design and Culture 7.1 (2015): 65–84. Hansen, Per H. “Networks, Narratives, and New Markets: The Rise and Decline of Danish Modern Furniture Design, 1930–1970.” The Business History Review 80.3 (2006): 449–83. Hedqvist, Hedvig, and Rebecka Tarschys. “Thoughts on the International Reception of Marimekko.” Marimekko: Fabrics, Fashions, Architecture. Ed. Marianne Aav. Bard. 2003. 149–71. Highmore, Ben. The Design Culture Reader. Routledge, 2008. Holland, Thomas W. Girls’ Toys of the Fifties and Sixties: Memorable Catalog Pages from the Legendary Sears Christmas Wishbooks, 1950-1969. Windmill, 1997. Hucal, Sarah. "Scandi Crush Saga: How Scandinavian Design Took over the World." Curbed, 23 Mar. 2016. <http://www.curbed.com/2016/3/23/11286010/scandinavian-design-arne-jacobsen-alvar-aalto-muuto-artek>. Jackson, Lesley. “Textile Patterns in an International Context: Precursors, Contemporaries, and Successors.” Marimekko: Fabrics, Fashions, Architecture. Ed. Marianne Aav. Bard. 2003. 44–83. Kline, Stephen. “The Making of Children’s Culture.” The Children’s Culture Reader. Ed. Henry Jenkins. New York: NYU P, 1998. 95–109. Lawrence, Sidney. “Declaration of Function: Documents from the Museum of Modern Art’s Design Crusade, 1933-1950.” Design Issues 2.1 (1985): 65–77. Marshall, Jennifer Jane. Machine Art 1934. Chicago: U of Chicago P, 2012. McGuire, Sheila. “Playing House: Sex-Roles and the Child’s World.” Child’s Play, Woman’s Work: An Exhibition of Miniature Toy Appliances : June 12, 1985–September 29, 1985. St. Paul: Goldstein Gallery, U Minnesota, 1985. Meikel, Jeffrey L. “Domesticating Modernity: Ambivalence and Appropriation, 1920–1940.” Designing Modernity; the Arts of Reform and Persuasion. Ed. Wendy Kaplan. Thames & Hudson, 1995. 143–68. O’Brien, Marion, and Aletha C. Huston. “Development of Sex-Typed Play Behavior in Toddlers.” Developmental Psychology, 21.5 (1985): 866–71. Olivarez, Jennifer Komar, Jukka Savolainen, and Juulia Kauste. Finland: Designed Environments. Minneapolis Institute of Arts and Nordic Heritage Museum, 2014. Oswell, David. The Agency of Children: From Family to Global Human Rights. Cambridge UP, 2013. Prown, Jules David. “Mind in Matter: An Introduction to Material Culture Theory and Method.” Winterthur Portfolio 17.1 (1982): 1–19. Punchard, Lorraine May. Child’s Play: Play Dishes, Kitchen Items, Furniture, Accessories. Punchard, 1982. Ranalli, Kristina. An Act Apart: Tea-Drinking, Play and Ritual. Master's thesis. U Delaware, 2013. Sears Corporate Archives. “What Is a Sears Modern Home?” n.d. <http://www.searsarchives.com/homes/index.htm>. "Target Announces New Design Partnership with Marimekko: It’s Finnish, Target Style." Target, 2 Mar. 2016. <http://corporate.target.com/article/2016/03/marimekko-for-target>. Teglasi, Hedwig. “Children’s Choices of and Value Judgments about Sex-Typed Toys and Occupations.” Journal of Vocational Behavior 18.2 (1981): 184–95. Thompson, Jane, and Alexandra Lange. Design Research: The Store That Brought Modern Living to American Homes. Chronicle, 2010.

The bin packing problem has been the corner stone of approximation algorithms and has been extensively studied starting from the early seventies. In the classical bin packing problem, we are given a list of real numbers in the range (0, 1], the goal is to place them in a minimum number of bins so that no bin holds numbers summing to more than 1. In this thesis we study approximation algorithms for three generalizations of bin packing: geometric bin packing, vector bin packing and weighted bipartite edge coloring. In two-dimensional (2-D) geometric bin packing, we are given a collection of rectangular items to be packed into a minimum number of unit size square bins. Geometric packing has vast applications in cutting stock, vehicle loading, pallet packing, memory allocation and several other logistics and robotics related problems. We consider the widely studied orthogonal packing case, where the items must be placed in the bin such that their sides are parallel to the sides of the bin. Here two variants are usually studied, (i) where the items cannot be rotated, and (ii) they can be rotated by 90 degrees. We give a polynomial time algorithm with an asymptotic approximation ratio of $\ln(1.5) + 1 \approx 1.405$ for the versions with and without rotations. We have also shown the limitations of rounding based algorithms, ubiquitous in bin packing algorithms. We have shown that any algorithm that rounds at least one side of each large item to some number in a constant size collection values chosen independent of the problem instance, cannot achieve an asymptotic approximation ratio better than 3/2. In d-dimensional vector bin packing (VBP), each item is a d-dimensional vector that needs to be packed into unit vector bins. The problem is of great significance in resource constrained scheduling and also appears in recent virtual machine placement in cloud computing. Even in two dimensions, it has novel applications in layout design, logistics, loading and scheduling problems. We obtain a polynomial time algorithm with an asymptotic approximation ratio of $\ln(1.5) + 1 \approx 1.405$ for 2-D VBP. We also obtain a polynomial time algorithm with almost tight (absolute) approximation ratio of $1+\ln(1.5)$ for 2-D VBP. For $d$ dimensions, we give a polynomial time algorithm with an asymptotic approximation ratio of $\ln(d/2) + 1.5 \approx \ln d+0.81$. We also consider vector bin packing under resource augmentation. We give a polynomial time algorithm that packs vectors into $(1+\epsilon)Opt$ bins when we allow augmentation in (d - 1) dimensions and $Opt$ is the minimum number of bins needed to pack the vectors into (1,1) bins. In weighted bipartite edge coloring problem, we are given an edge-weighted bipartite graph $G=(V,E)$ with weights $w: E \rightarrow [0,1]$. The task is to find a proper weighted coloring of the edges with as few colors as possible. An edge coloring of the weighted graph is called a proper weighted coloring if the sum of the weights of the edges incident to a vertex of any color is at most one. This problem is motivated by rearrangeability of 3-stage Clos networks which is very useful in various applications in interconnected networks and routing. We show a polynomial time approximation algorithm that returns a proper weighted coloring with at most $\lceil 2.2223m \rceil$ colors where $m$ is the minimum number of unit sized bins needed to pack the weight of all edges incident at any vertex. We also show that if all edge weights are $>1/4$ then $\lceil 2.2m \rceil$ colors are sufficient.

Bio-based polymers offer a broad range of applications in pharmaceutical engineering. However, their assortment gets constrained owing to variations in structural conformation, which affects the thermomechanical properties during complex formulation. The thermomechanical property of pharmaceutically inactive ingredients provides insight into the thermal expansion, glass transitions temperature, softening point, compositional, and phase changes of biomaterials with different geometries on the application of constant force as a function of temperature. In addition, thermomechanical properties provide fundamental information on network chemical structure, crosslink density, rubbery modulus, failure strain, and toughness. Moreover, the structural composition of polysaccharides also affects the composite’s mechanical properties. Hence, analysis of thermomechanical properties provides valuable information that is applicable in different sectors including aviation, quasistatic loading, electroplating technology, micro-electric, construction, cosmetics, food packaging, and pharmaceutical products. This compilation highlights the basics of thermal and mechanical experiments on bio-based polymers with different fabrication for both technical and pharmaceutical formulations.

The understanding of the engineering performance of green laminated composites is necessary to the design of load bearing components in building and infrastructure construction, and packaging applications. These components are made of outer thin laminae called skins or faces and a thick inner layer called core. The use of bonding is unavoidable in the assembling of these composite products. Like all materials, the bonding materials have finite mechanical properties, e.g. stiffness, but when used in the literature, they are assumed perfectly rigid. That is an unrealistic assumption. Our analytical solutions change this assumption by using the real properties of bonding. In general, the analytical formulations are based on the equilibrium equations of forces, the compatibility of interlaminar stresses and deformation, and the geometrical conditions of the panels. Once solutions are obtained, the next step is to evaluate them. The numerical evaluations proved that perfect rigid bonding in laminated composites greatly underestimates the true performance. At low values of adhesive stiffness, the serviceability is multiple orders of magnitude of that at high values. The logical question is thus: what constitutes perfect bonding? The answer to this question lies in the core-to-adhesive stiffness. The lower the ration is the higher the error in using the rigid-bond theories. It is worth noting that green-composites in this chapter refer to components made of traditional materials such as wood, in addition to newly developed bio-based and bio-degradable and bio-based composites, made of renewable resources. In addition, bonding and adhesive are used interchangeably.

This paper presents a residual stress analyses based on two bonding systems, silicon-aluminum-glass and silicon-aluminum-quartz, for MEMS packaging applications: The predicted residual stress generated in the Pyrex glass bonding system is 60 to 74 GPa that is close to the fracture strength of Pyrex glass at 69 GPa. In the quartz bonding system, the predicted residual stress is 100 to 207 GPa that far exceeds the fracture strength of Quartz at 48 GPa. Experimental results are consistent with analytical predictions that small cracks are found in the glass bonding system and big fracture lines are observed in the quartz bonding system. As such, this residual stress analysis model serves as an excellent tool to assist the development of new bonding systems in the areas of material selection, geometrical design of the bonding area and the dimensions of the bonding solders.

Micro cantilevers are significant structure for MEMS devices, such as bio-chips, sensors and STEM/AFM probes. The beam deflection and its characteristics have been studied for various purposes. In this study, expending bubbles from thermal surface exert force on micro-cantilever beam and causes deflection of the beam. Cantilevers were fabricated by classic MEMS fabrication method; photolithography and dry etching. The micro-beam was fabricated from &lt;100&gt; n-type silicon wafer and its thickness varies from 10 micron to 30micron with various geometry (length, width and tip shapes). The distance from thermal surface and cantilever beam is also significant variables for analysis of bubble-beam interaction. We observed beam deflection with respect to various bubble generation conditions (bubble size, contact area and generating frequency). Simple analysis of bubble-beam interaction were performed and compared with experimental results.

Modeling of fan failures in networking chassis is a challenging task. There is not enough data or literature available to accurately model fan failures. This paper embarks on a study consisting of both modeling and experimental cases to investigate how to accurately model fan failures. The study will include CFD simulations in different ways to model fan failures and also real life experimental measurements to verify the simulation concepts. Recommendations will then be made about the exact and accurate ways of modeling fan failures. Normally the fans have been modeled as a two dimensional entity. The fan curve measured by the vendor is used in the fan during modeling. The problem that arises with this kind of a fan modeling especially during fan failures is that the three dimensional effect of the rotor and stator blades of the fan is not taken into account. In reality, the fan blades provide a big obstruction to the flow reversal that happens due to pressure imbalance during fan failures. In this paper, we start with modeling a single fan in an AMCA wind tunnel. The complete rotor and stator geometry of the fan is modeled. We run a MRF (Multiple Reference Frame) model to generate the fan curve for the fan and compare it with the experimental fan curve. After we validate the fan curve in an AMCA model for a single fan, the paper discusses three different sets of temperature and flow data: i. Temperature and flow data in a real system with four fans modeled with two dimensional fans. ii. Temperature and flow data in a real system with four fans modeled with MRF fans (full 3 dimensional rotor and stator blade geometry). iii. Experimental comparisons with the simulated data Conclusions will be drawn based on this modeling and experimental data about accurate ways of modeling fans during fan failures in real systems.

PLA (Poly Lactic Acid) is a bio-sourced and a biodegradable polymer. It represents an interesting substitute for some petrochemical based polymers, especially because of its wide range of applications in the biomedical, agriculture and packaging fields. Unfortunately, PLA exhibits slow crystallization kinetics, limiting the amount of crystallinity in the final product, which is a handicap in order to extend its use. Many authors have investigated the crystallization of polymers; nevertheless several physical mechanisms remain not yet understood. This work aims a complete characterization of PLA in order to improve the understanding of its crystallization kinetics. The quiescent crystallization was investigated using Differential Scanning Calorimetry (DSC) measurements in isothermal and non-isothermal conditions for PLA and PLA with 5wt % talc. The flow effect on crystallization was studied using a thermocontrolled hot-stage shearing device (Linkam) coupled with an optical microscope. The number of activated nuclei and the growth rate were measured as functions of temperature. In addition, the linear viscoelastic properties were obtained from a rheometer with plate-plate geometry. The enhancement of the crystallization was quantified and analyzed in terms of the half crystallization time t1/2. This characteristic time t1/2 is found to be drastically decreased by both the talc and the flow which promote supplementary nucleation leading to various crystalline microstructures. The flow is known to orient and stretch molecules leading to an extra nucleation. An original description of this phenomenon is proposed using two characteristic Weissenberg numbers; based on the definition of Rousse and reptation times. Finally, we have proposed a semi-empirical model to quantify the thermal and flow contributions on the crystallization.

Flexible electronics provide new design options not afforded by rigid electronics in a variety of applications including wearable electronics, robotics and automotive systems. However, the processes for the manufacturing of complex electronic assemblies using fine-pitch components are not as well developed as those for rigid electronics. The lack of structural rigidity of flexible printed circuit cards requires attention to assembly configuration for double-sided flexible assemblies. In addition, mechanisms are needed to compensate for the deformation and warpage of the flexible substrate and components during assembly. In this paper, the stresses in solder joints of double-sided flexible assemblies have been measured during thermal excursions using x-ray micro-computed tomography in conjunction with digital volume correlation. The method allows for non-invasive measurement and does not require cross-sectioning of the part for the purpose of deformation and strain measurement. In addition, the measurements are not limited to the joints in the line of sight. The three-dimensional measurements of deformation and strain have been visualized on the geometry of the solder joints in the package. Digital volume correlation (DVC) method has been used to find the displacements and strains in interconnects of operational electronics. The x-ray microscopic computed tomography (μCT) system has been used to generate the 16 bit digital volume data. The x-ray detector has ability to image the x-ray attenuation of x-rays through the object. Reliability testing of SAC 305 solder interconnects has been performed on double-sided flexible circuit board using x-ray μCT by heating the package to 100°C. The flexible circuit board used in this experiment is of BGA 256-144 combination, two packages, A-PBGA256-1.0mm-17mm and A-CABGA144-1.0mm-13mm. A 3D printed fixture has also been used to support the flexible board and keep it flat while in the CT scan machine. The reference and deformed scans are then re-constructed 3D using Volume Graphics, and Digital Volume Correlation performed using MATLAB modules. Reliability of double-sided flexible printed circuit boards will be discussed and any crack, defects, or deformation in the solder interconnectivity which might occur while heating the package on flexible board is presented. The solder joint strains during thermal excursions are also compared between the flexible and rigid printed circuit assemblies.