Análise de sensibilidade em modelos de programação linear com solução degenerada : revisão sistemática e estudo aplicado na Agência de Aviação Civil

Trabalho de Conclusão de Curso (graduação)—Universidade de Brasília, Faculdade de Economia, Administração, Contabilidade e Gestão de Políticas Públicas, Departamento de Administração, 2019.A utilização de modelos matemáticos como ferramenta de apoio a decisão possibilita que gestores avaliem as alternativas antes de implementá-las, proporcionando um melhor uso dos recursos disponíveis. Uma forma de aprofundar essa avaliação é por meio da análise de sensibilidade do modelo, em que é possível verificar como mudanças em seus parâmetros afetam a solução ótima. Porém, essa análise torna-se imprecisa quando o modelo apresenta soluções degeneradas. Dessa forma, o objetivo do presente trabalho foi estudar formas de realizar a análise de sensibilidade em modelos matemáticos de programação linear com soluções degeneradas. Assim, foi realizada uma revisão sistemática de artigos sobre o tema, seguindo o método proposto por Sampaio e Mancini (2007), e elaborado um quadro com os resumos dos métodos apresentados pelos autores. Em seguida, foi feito um estudo de caso, em que o método de problemas adicionais de programação linear proposto por Koltai e Tatay (2011) foi aplicado em um modelo matemático elaborado para auxiliar na designação de inspetores para missões de fiscalização da Superintendência de Padrões Operacionais (SPO) da ANAC, proposto por Pinheiro (2018). Por fim, a pesquisa atingiu seu objetivo ao realizar a análise de sensibilidade em um modelo real degenerado com sucesso, utilizando o método de Koltai e Tatay (2011) encontrado através da revisão sistemática

On the core of m-attribute games

We study a special class of cooperative games with transferable utility (TU), called (Formula presented.) -attribute games. Every player in an (Formula presented.) -attribute game is endowed with a vector of (Formula presented.) attributes that can be combined in an additive fashion; that is, if players form a coalition, the attribute vector of this coalition is obtained by adding the attributes of its members. Another fundamental feature of (Formula presented.) -attribute games is that their characteristic function is defined by a continuous attribute function (Formula presented.) —the value of a coalition depends only on evaluation of (Formula presented.) on the attribute vector possessed by the coalition, and not on the identity of coalition members. This class of games encompasses many well-known examples, such as queueing games and economic lot-sizing games. We believe that by studying attribute function (Formula presented.) and its properties, instead of specific examples of games, we are able to develop a common platform for studying different situations and obtain more general results with wider applicability. In this paper, we first show the relationship between nonemptiness of the core and identification of attribute prices that can be used to calculate core allocations. We then derive necessary and sufficient conditions under which every (Formula presented.) -attribute game embedded in attribute function (Formula presented.) has a nonempty core, and a set of necessary and sufficient conditions that (Formula presented.) should satisfy for the embedded game to be convex. We also develop several sufficient conditions for nonemptiness of the core of (Formula presented.) -attribute games, which are easier to check, and show how to find a core allocation when these conditions hold. Finally, we establish natural connections between TU games and (Formula presented.) -attribute games.</p

Conservation Prioritization Problems and their Shadow Prices

Systematic conservation planning is an essential part of biodiversity preservation

Distillers grains and the livestock industry in western Canada

The ethanol industry in Western Canada has seen significant growth in recent times spurred on mainly be environmental considerations. For a region with substantial grain production, increased prices from additional demand by the biofuel industry may inure to the benefit of grain farmers and land owners in the long term. The livestock industry however remains in a complex position facing the possibility of higher feed costs on the one hand and potential savings in feed cost on the other, with the availability of distillers grains- a by-product from ethanol production. The sectorial implications for the livestock sector could also be diverse and dependent upon the capacity to incorporate the distillers grains into the different feed rations. There is also the possibility of a spill-over effect from the US distillers grains market. This study therefore sought to complement current nutritional research by providing an economic perspective of the impact of distillers grains on the livestock industry in Western Canada. Focussing primarily on the beef cattle and hog industries, the study applied both linear programming and time-series techniques to assess potential benefits and costs. Potential positive economic benefits were observed for the inclusion of wheat and corn distillers grains with the former having a higher economic value in the high-protein feed segments. Dependent on market factors such as the price of substitute feeds, exchange rates and transportation considerations, the magnitude of these savings could range between $7.29 and$0.34/tonne. The study recommends an understanding of these dynamics in order for livestock and ethanol producers to derive mutual benefits from the fledging biofuel industry in the Western plains

Characterization of Petroleum Refinery Lp Results Under Conditions of Degeneracy

The phenomenon of degeneracy inevitably occurs in most large LP models. An LP could be primal degenerate, dual degenerate, or both primal and dual degenerate. Primal degeneracy of LP and its solution interpretation is well established in literature, but the notion of dual degeneracy (alternative optima) has received less attention. The condition of dual degeneracy or alternative optima leads to multiple optimal bases with multiple activity values or multiple primal solutions. Current refinery optimization practitioners are not fully aware of the consequences of degeneracy and business decisions are made using a single LP run. The purpose of this study is to investigate the effects of dual degeneracy in the context of petroleum refinery optimization and simultaneously to develop strategies to select a specific set of activity values for implementation based on business logic. When an LP has alternate optimal solutions or is dual degenerate, it will be primal degenerate in the dual space. This property of the dual degenerate problem is exploited in this research to derive businesslogic on the interpretation of LP solutions produced by a dual degenerate LP. This study developed a novel dual incremental analysis approach to choose a desired set of activity values based on small changes in the market price of activities when the LP is dual degenerate. Furthermore, a perturbation technique implementing parametric programming is developed to generate multiple optimal bases when the LP is dual degenerate. Results are presented, along with a simplified refinery model containing 33 decision variables and 37 constraints. Findings of this study indicated that for the dual degenerate refinery LP the magnitude of the difference among activity values obtained for each of the alternate optimal solutions is significant. Although the optimality criteria (primal and dual feasible) for the LP is satisfied for each of the alternate optimal solutions in the base case, the optimality criteria may not be satisfied even for an infinitesimal change in the market price of activities. The dual incremental analysis approach and the underlying business logic developed in this research serves two purposes for a dual degenerate LP: 1) characterize each of the activity values obtained for a single LP run, and 2) choose a desired set of activity values for implementation among multiple optimal solutions generated.School of Chemical Engineerin