The Genetic Algorithm (GA) is a popular global search algorithm. Although it has been used successfully in many fields, there are still performance challenges that prevent GA’s further success. The performance challenges include: difficult to reach optimal solutions for complex problems and take a very long time to solve difficult problems. This dissertation is to research new ways to improve GA’s performance on solution quality and convergence speed. The main focus is to present the concept of shadow price and propose a two-measurement GA. The new algorithm uses the fitness value to measure solutions and shadow price to evaluate components. New shadow price Guided operators are used to achieve good measurable evolutions. Simulation results have shown that the new shadow price Guided genetic algorithm (SGA) is effective in terms of performance and efficient in terms of speed.

The doctorial thesis is focused on shadow pricing. The aim is to describe as complex and full description of the problem as possible. Briefly said, Shadow prices are prices of goods which would take a place on the efficient market, if such a market with the commodity existed. In the case of consumption benefits they in fact present monetary value of the utility increment resulted from additional consumption. They are basic information input into any socioeconomic evaluation. Research of shadow prices is underdeveloped in the Czech Republic. With respect to the fact the thesis contents description of basic theoretical concepts as well as list of attainable methods for shadow prices derivation. Main variables determining shadow prices (under condition of WTP, WTA and Social Opportunity Costs concepts) are the existed society welfare and social preferences. From this perspective if clear and evident that there would not be appropriate to use shadow prices conducted abroad for evaluation in the Czech economy. Each state has its own level of welfare as well as specific social and ethical values widespread among citizens and so specific shadow prices as well. Not just shadow prices them self are not simply applicable for evaluation in each country. Similar problem we have to face, if we try to use the same methods of deriving shadow prices in different areas. That is why the thesis also serves critical analysis of attainable methods and their assessment. Based on the assessment is stated, what methods are more or less appropriate and under which condition in the Czech area. In principal should shadow prices reflect Social Opportunity Costs of input usage for evaluated changes and Willingness to Pay of the society for the outputs of evaluated changes (or alternatively Willingness to Accept) with no respect to the fact if the good (or output or input) is market good or nonmarket good. Even though we differentiate in the methodological level between market and nonmarket good the theoretical and conceptual background is the same. The background is rooted in the neoclassical economics. For the practical reasons as a analyst time and budget constrain it is not too efficient in evaluation of marketed goods always perform deep empirical market analysis from primary data even though it would be theoretically ideal and correct. Fortunately we are usually not forced to do it. In majority of cases we can follow LMST methodology of shadow prices and derive so called Conversion Factors for transformation of market prices to shadow prices. The Conversion factors are usually derived for wider group of goods which is sold in the similar market. Such values we call Sector Conversion Factors. A Shadow price of an individual unique good we than receive by its market price multiplication by most appropriate sector conversion factor. With respect to current Czech evaluation practice situation, when sector conversion factor are very often used but their estimates are more less based on very poor quality of underlying theory and very often without sufficient data background, the quantification of SCF in the theses could be viewed as quite significant contribution. With respect to their specific characteristics nonmarket good as safety (VSL), time, noise, etc. should be valued separately. And the thesis is offering at least methodological contributive guidelines regarding theoretical validity and relevance as well as assessment of their applicability under Czech condition. For better imagination there is collected sample of results of selected externality values for foreign countries.

The diploma thesis describes portfolio management with proportional transaction costs. The main aim is to describe using of shadow prices to find the optimal Markov policies keeping the proportion of the investor's wealth invested in the risky asset within the corresponding interval in order to maximize the long run geometric growth rate. On the real market, the investor must pay transaction costs when he buys/sells shares. In the diploma thesis we transform these prices into the shadow price; when trading in the shadow price there are no transaction costs. The solution itself is based on Itô formula and the martingal theory. The prices of shares are modeled as geometric Brownian motion. Powered by TCPDF (www.tcpdf.org)

This thesis consists of four papers: two of them deal with the effects on the forest sector of an increase in the demand for forest fuels, and two of them concern the relation between economic growth and pollution. Paper [I] is a first, preliminary study of the potential effects on the Swedish forest sector of a continuing rise in the use of forest resources as a fuel in energy generation. Sweden has made a commitment that the energy system should be sustainable, i.e., it should be based on renewable resources. However, an increasing use of the forest resources as an energy input could have effects outside the energy sector. We consider this in a static model by estimating a system of demand and supply equations for the four main actors on the Swedish roundwood market; forestry, sawmills, pulpmills and the energy sector. We then calculate the industries' short run supply and demand elasticities. Paper [II], is a development of the former paper. In this paper, we estimate the dynamic effects on the forest sector of an increased demand for forest fuels. This is done by developing a partial adjustment model of the forest sector that enables short, intermediate, and long run price elasticities to be estimated. It is relevant to study the effects of increased demand for forest fuels as the Swedish government has committed to an energy policy that is likely to further increase the use of renewable resources in the Swedish energy system. Four subsectors are included in the model: forestry, sawmills, pulpmills and the energy industry. The results show that the short run elasticities are fairly consistent with earlier studies and that sluggish adjustment in the capital stock is important in determining the intermediate and long run responses. Simulation shows that an increase in the demand for forest fuels has a positive effect on the equilibrium price of all three types of wood, and a negative effect on the equilibrium quantities of sawtimber and pulpwood. In paper [III] a Shephard distance function approach is used to estimate time series of shadow prices for Swedish emissions of CO2, SO2, and VOC for the period 1918 - 1994. The shadow prices are in a next step regressed on GDP per capita. The objective of the study is closely linked to hypothesis of environmental Kuznets curves. We conclude that the time series of the shadow prices from this approach can not be used to explain the EKCs found for Swedish emissions. In paper [IV], we calculate time series of shadow prices for Swedish emissions of CO2, SO2, and VOC for the period 1918 - 1994. The shadow prices are in a next step related to income, to explain the EKCs previously found for Swedish data on the three emissions. Newly constructed historical emission time series enable studying a single country's emission paths through increasing levels of economic activity. A directional distance function approach is used to estimate the industry's production process in order to calculate the opportunity costs of a reduction in the emissions. The time series of the shadow prices show support for EKCs for the Swedish industry.

Pequenos e médios laticínios têm grandes dificuldades no planejamento da produção para maximizar o lucro. Além disso, a forma atual de precificar o leite cru no Brasil desestimula o produtor a melhorar sua qualidade, pois valoriza mais seu volume do que seus componentes sólidos. A composição do leite cru é muito importante para os laticínios, pois ela afeta diretamente o rendimento de produção e a qualidade dos produtos lácteos. Técnicas de otimização, como programação linear (PL), ajudam a resolver problemas relacionados à decisão do mix de produtos, além de fazer análise econômica dos recursos. Em razão disso, foi desenvolvido em PL um modelo para maximização da margem de contribuição total (MCT = receita total das vendas - custos e despesas diretas totais) e precificação do leite cru através da determinação do mix ótimo de produtos lácteos. O modelo foi simulado em cenários diários de alta (Janeiro) e baixa (Julho) disponibilidade de matéria prima comparando as soluções ótimas com resultados reais de um laticínio do sudeste do Brasil. Foram realizadas análises de sensibilidade dos componentes nutritivos de dois tipos de leite cru de diferentes composições (LC1, leite cru proveniente de um fornecedor, e LC50, leite cru proveniente de 50 fornecedores) para determinar seus preços-sombra. Foram observados preços-sombra para o quilograma da caseína em Janeiro e Julho e para o litro do LC50 em Julho. A MCT ótima e os preços calculados de ambos os tipos de leite cru foram maiores em Janeiro devido à maior disponibilidade de matéria prima. Em ambos os cenários, os preços calculados de ambos os tipos de leite cru foram maiores que os praticados pelo laticínio e o lucro antes de juros, impostos, depreciação e amortização (LAJIDA) diário real foi maior que o ótimo. A embaladora foi um recurso limitante atuante na produção do queijo Minas Frescal nos mixes ótimos. A relação entre margem de contribuição unitária (MCU = preço unitário de venda - custo e despesa diretos unitários) e quantidade necessária de matéria prima por unidade de produto e a disponibilidade de recursos são determinantes na definição do mix de produtos lácteos e da MCT do laticínio. A precificação do leite cru pelo modelo proposto remunera o produtor em função da quantidade de seus componentes. O laticínio pode maximizar seu LAJIDA planejando melhor seu mix de produtos com PL e remunerando melhor seus fornecedores em função da qualidade do leite cru. / Small and medium-sized dairies face great difficulties in production planning to maximize profit. In addition, the current way of pricing the raw milk in Brazil discourages producers to improve its quality because its volume values more than its solid components. The raw milk composition is very important for the dairies because it directly affects the yield and quality of dairy products. Optimization techniques, such as linear programming (LP), aid solve problems related to the decision of the product mix and perform economic analyzes of resources. For this reason, a model was developed in LP to maximizing total contribution margin (TCM = total sales revenues - total variable costs and expenses) and pricing the raw milk by determining the optimal mix of dairy products. The model was simulated in two daily scenarios of high (January) and low (July) availability of raw material comparing the optimal solutions with actual results from a dairy plant in Southeastern Brazil. Sensitivity analyzes of the nutritional components of two kinds of raw milk of different compositions (RM1 and RM50) were performed to determine their shadow-prices. Shadow-prices were observed for the kilogram of casein in January and July and for the liter of RM50 in July. The optimal TCM and the calculated prices of both types of raw milk were higher in January due the increased availability of raw materials. In both scenarios, the calculated prices of both types of raw milk were higher than those paid by the dairy plant and the actual daily earnings before interests, taxes, depreciation and amortization (EBITDA) were greater than the optimum ones. The wrapper was an active limiting resource in the production of Frescal Minas cheese in optimal mixes. The relationship between unit contribution margin (UCM = unit sales price - unit variable cost and expense) and required amount of raw material per unit of output and resource availability are crucial in defining the mix of dairy products and the dairy TCM. The proposed raw milk pricing model pays the producer by the quantity of its components. The dairies can maximize their EBITDA planning their product mixes with LP and remunerating their suppliers based on the quality of raw milk.

Pequenos e médios laticínios têm grandes dificuldades no planejamento da produção para maximizar o lucro. Além disso, a forma atual de precificar o leite cru no Brasil desestimula o produtor a melhorar sua qualidade, pois valoriza mais seu volume do que seus componentes sólidos. A composição do leite cru é muito importante para os laticínios, pois ela afeta diretamente o rendimento de produção e a qualidade dos produtos lácteos. Técnicas de otimização, como programação linear (PL), ajudam a resolver problemas relacionados à decisão do mix de produtos, além de fazer análise econômica dos recursos. Em razão disso, foi desenvolvido em PL um modelo para maximização da margem de contribuição total (MCT = receita total das vendas - custos e despesas diretas totais) e precificação do leite cru através da determinação do mix ótimo de produtos lácteos. O modelo foi simulado em cenários diários de alta (Janeiro) e baixa (Julho) disponibilidade de matéria prima comparando as soluções ótimas com resultados reais de um laticínio do sudeste do Brasil. Foram realizadas análises de sensibilidade dos componentes nutritivos de dois tipos de leite cru de diferentes composições (LC1, leite cru proveniente de um fornecedor, e LC50, leite cru proveniente de 50 fornecedores) para determinar seus preços-sombra. Foram observados preços-sombra para o quilograma da caseína em Janeiro e Julho e para o litro do LC50 em Julho. A MCT ótima e os preços calculados de ambos os tipos de leite cru foram maiores em Janeiro devido à maior disponibilidade de matéria prima. Em ambos os cenários, os preços calculados de ambos os tipos de leite cru foram maiores que os praticados pelo laticínio e o lucro antes de juros, impostos, depreciação e amortização (LAJIDA) diário real foi maior que o ótimo. A embaladora foi um recurso limitante atuante na produção do queijo Minas Frescal nos mixes ótimos. A relação entre margem de contribuição unitária (MCU = preço unitário de venda - custo e despesa diretos unitários) e quantidade necessária de matéria prima por unidade de produto e a disponibilidade de recursos são determinantes na definição do mix de produtos lácteos e da MCT do laticínio. A precificação do leite cru pelo modelo proposto remunera o produtor em função da quantidade de seus componentes. O laticínio pode maximizar seu LAJIDA planejando melhor seu mix de produtos com PL e remunerando melhor seus fornecedores em função da qualidade do leite cru. / Small and medium-sized dairies face great difficulties in production planning to maximize profit. In addition, the current way of pricing the raw milk in Brazil discourages producers to improve its quality because its volume values more than its solid components. The raw milk composition is very important for the dairies because it directly affects the yield and quality of dairy products. Optimization techniques, such as linear programming (LP), aid solve problems related to the decision of the product mix and perform economic analyzes of resources. For this reason, a model was developed in LP to maximizing total contribution margin (TCM = total sales revenues - total variable costs and expenses) and pricing the raw milk by determining the optimal mix of dairy products. The model was simulated in two daily scenarios of high (January) and low (July) availability of raw material comparing the optimal solutions with actual results from a dairy plant in Southeastern Brazil. Sensitivity analyzes of the nutritional components of two kinds of raw milk of different compositions (RM1 and RM50) were performed to determine their shadow-prices. Shadow-prices were observed for the kilogram of casein in January and July and for the liter of RM50 in July. The optimal TCM and the calculated prices of both types of raw milk were higher in January due the increased availability of raw materials. In both scenarios, the calculated prices of both types of raw milk were higher than those paid by the dairy plant and the actual daily earnings before interests, taxes, depreciation and amortization (EBITDA) were greater than the optimum ones. The wrapper was an active limiting resource in the production of Frescal Minas cheese in optimal mixes. The relationship between unit contribution margin (UCM = unit sales price - unit variable cost and expense) and required amount of raw material per unit of output and resource availability are crucial in defining the mix of dairy products and the dairy TCM. The proposed raw milk pricing model pays the producer by the quantity of its components. The dairies can maximize their EBITDA planning their product mixes with LP and remunerating their suppliers based on the quality of raw milk.