Os problemas de corte e empacotamento são frequentes em diferentes processos produtivos, por exemplo, na produção de roupas, de calçados, de peças metálicas e de móveis. Seu objetivo mais frequente e a minimização do desperdício de matéria-prima. No entanto, em algumas situações, o problema de determinação do caminho de corte e fundamental para eciência do planejamento da produção. Este problema consiste em determinar a trajetória de corte que minimize, por exemplo, o tempo total de corte de um plano de corte previamente estabelecido. Devido a existência de poucas abordagens para este problema, nosso objetivo e propor modelos matemáticos para resolver o problema de determinação do caminho de corte. Além disso, uma variação do problema que considera a utilização de grafos dinâmicos também é abordada. Os resultados obtidos são comparados com resultados da literatura. / Cutting and packing problems are frequent in dierent productive process, for example, in the garment, shoe, metallic pieces and furniture production. Its most common objective is the minimization of the raw material waste. However, in some situations, the cutting path determination problem is fundamental to the eciency of the production planning. This problem consists in determining the cutting trajectory that minimizes, for example, the total cutting time of a previously established cutting plane. Due to the few existing approaches to this problem, our objective is to propose mathematical models to solve the cutting path determination problem. Furthermore, a variation of the problem that considers the use of dynamic graphs is also adressed. The obtained results are compared with those from the literature.

<p>Division of labor and division of knowledge are so important andcommon in society today that it is almost impossible to imagine asociety where everyone knows the same things and perform the sametasks. This would be a society where everyone grows, or gathers, andprepares their own food, makes their own tools, builds their ownhouse, and so on.</p><p>Cultural evolution is the field of research that studies the creationand diffusion of ideas and societies. It is very uncommon for thesestudies to take into account the effects of specialization. Thisthesis will show that specialization is of great importance tocultural evolution.</p><p>The thesis is divided into three parts: one introduction and two papers. The introduction covers the mathematical models used byeconomists to study the relation between the market and division oflabor. The first paper is an interdisciplinary survey of the researchon division of labor and specialization, including both theoretic andempirical studies. The second paper is a mathematical model of howspecialization of knowledge (i.e. higher education) leads to socialstratification. The model is tested against statistical data fromseveral countries and found to be a good predictor of the differencesin income between people of high and low education.</p>

Division of labor and division of knowledge are so important andcommon in society today that it is almost impossible to imagine asociety where everyone knows the same things and perform the sametasks. This would be a society where everyone grows, or gathers, andprepares their own food, makes their own tools, builds their ownhouse, and so on. Cultural evolution is the field of research that studies the creationand diffusion of ideas and societies. It is very uncommon for thesestudies to take into account the effects of specialization. Thisthesis will show that specialization is of great importance tocultural evolution. The thesis is divided into three parts: one introduction and two papers. The introduction covers the mathematical models used byeconomists to study the relation between the market and division oflabor. The first paper is an interdisciplinary survey of the researchon division of labor and specialization, including both theoretic andempirical studies. The second paper is a mathematical model of howspecialization of knowledge (i.e. higher education) leads to socialstratification. The model is tested against statistical data fromseveral countries and found to be a good predictor of the differencesin income between people of high and low education.

Os problemas de corte e empacotamento são frequentes em diferentes processos produtivos, por exemplo, na produção de roupas, de calçados, de peças metálicas e de móveis. Seu objetivo mais frequente e a minimização do desperdício de matéria-prima. No entanto, em algumas situações, o problema de determinação do caminho de corte e fundamental para eciência do planejamento da produção. Este problema consiste em determinar a trajetória de corte que minimize, por exemplo, o tempo total de corte de um plano de corte previamente estabelecido. Devido a existência de poucas abordagens para este problema, nosso objetivo e propor modelos matemáticos para resolver o problema de determinação do caminho de corte. Além disso, uma variação do problema que considera a utilização de grafos dinâmicos também é abordada. Os resultados obtidos são comparados com resultados da literatura. / Cutting and packing problems are frequent in dierent productive process, for example, in the garment, shoe, metallic pieces and furniture production. Its most common objective is the minimization of the raw material waste. However, in some situations, the cutting path determination problem is fundamental to the eciency of the production planning. This problem consists in determining the cutting trajectory that minimizes, for example, the total cutting time of a previously established cutting plane. Due to the few existing approaches to this problem, our objective is to propose mathematical models to solve the cutting path determination problem. Furthermore, a variation of the problem that considers the use of dynamic graphs is also adressed. The obtained results are compared with those from the literature.

This work concerns new borders, heuristics, algoritms and mathematic models of pallet loading problem (PLP). We try to describe these computational methods and find out if we can use them in real. We maximalize number of boxes placed on rectangular pallets in a particular warehouse by using chosen heuristics. Every box has a rectangular form with the same lenght and width and is fully placed on the pallet. We can rotate with the box by 90% degree until it is fixed as we want and its side lies parallelly with side of the pallet. All instances are setted in model (X, Y, a, b), where X is lenght, Y width of the pallet, a lenght and b width of the box.