A special case of the linear programming problem, the transportation problem, is the subject of this thesis. The development of a solution to the transportation problem is based on fundamental concepts from the theory of linear algebra and matrices.

Western Canada is in a post Canadian Wheat Board single-desk market, in which grain handlers face policy, allocation, and logistical changes to the transportation of grains. This research looks at the rails transportation problem for allocating wheat from Prairie to port position, offering a new allocation system that fits the evolving environment of Western Canada’s grain market. Optimization and analysis of the transport of wheat by railroads is performed using geographic information system software as well as spatial and historical data. The studied transportation problem searches to minimize the costs of time rather than look purely at locational costs or closest proximity to port. Through optimization three major bottlenecks are found to constrain the transportation problem; 1) an allocation preference towards Thunder Bay and Vancouver ports, 2) small capacity train inefficiency, and 3) a mismatched distribution of supply and demand between the Class 1 railway firms. Through analysis of counterfactual policies and a scaled sensitivity analysis of the transportation problem, the grains transport system of railroads is found to be dynamic and time efficient; specifically when utilizing larger train capacities, offering open access to rail, and under times of increased availability of supplies. Even under the current circumstances of reduced grain movement and inefficiencies, there are policies and logistics that can be implemented to offer grain handlers in Western Canada with the transportation needed to fulfill their export demands.

Main purpose of this thesis is finding the possibilities of operation analysis methods{\crq} use in logistics, proposition of specific situation{\crq}s optimal solution in specific company, confrontation of the above with reality and proposition of possible improvements. The use of scientific methods during decision making should have been the reason of this thesis. The theoretical knowledge that has been gained from literature research has been verified in factual conditions at company CSAD JIHOTRANS, Inc. To gain the knowledge of the environment I used the consultations with company management, system studying based on provided data and collective service{\crq}s trading conditions. ABC analysis and MODI and VAM methods were used as a scientific approach. In the thesis I processed data given to me concerning shipments that had been registered in collection centers for each month of the year 2008. 6 possible alternatives evaluating the basic and also sub-optimal solutions came out from solved problems of methods VAM and MODI. Option I is the most suitable from the point of optimization standard {--} minimal value of special-purpose function. Option VI will be the most suitable if I proceed from the current system functioning. But option VI satisfies the optimization standard the least. Therefore I suggest shifting the original pick-ups S5 into the competence of S2 and then to place it in between the 8 regional centers that are connected by the central trucktransport.

Apresentamos o problema do transporte ótimo de Monge-Kantorovich com duas medidas de probabilidade conhecidas e que possuem suporte em um conjunto de cardinalidade finita. O objetivo é determinar condições que permitam construir um acoplamento destas medidas que minimiza o valor esperado de uma função de custo conhecida e que assume valor nulo apenas nos elementos da diagonal. Apresentamos também um resultado relacionado com a solução do problema de Monge-Kantorovich em espaços produto finitos quando conhecemos soluções para o problema nos espaços marginais. / We present the Monge-Kantorovich optimal problem with two known probability measures on a finite set. The objective is to obtain conditions that allow us to build a coupling of these measures that minimizes the expected value of a cost function that is known and is zero only on the diagonal elements. We also present a result that is related with the solution of the Monge-Kantorovich problem in finite product spaces in the case that solutions to the problem in the marginal spaces are known.

We derive a technique for scaling the search directions of feasible direction methods when applied to optimization problems over Cartesian product sets. It is proved that when the scaling is included in a convergent feasible direction method, also the new method will be convergent. The scaling technique is applied to the Frank-Wolfe method, the partanized Frank-Wolfe method and a heuristic Frank-Wolfe method. The performance of  these algorithms with and without scaling is evaluated on the stochastic transportation problem. It is found that the scaling technique has the ability to improve the performance of some methods. In particular we observed a huge improvement in the performance of the partanized Frank-Wolfe method, especially when the scaling is used together with an exact line search and when the number of sets in the Cartesian product is large.

Apresentamos o problema do transporte ótimo de Monge-Kantorovich com duas medidas de probabilidade conhecidas e que possuem suporte em um conjunto de cardinalidade finita. O objetivo é determinar condições que permitam construir um acoplamento destas medidas que minimiza o valor esperado de uma função de custo conhecida e que assume valor nulo apenas nos elementos da diagonal. Apresentamos também um resultado relacionado com a solução do problema de Monge-Kantorovich em espaços produto finitos quando conhecemos soluções para o problema nos espaços marginais. / We present the Monge-Kantorovich optimal problem with two known probability measures on a finite set. The objective is to obtain conditions that allow us to build a coupling of these measures that minimizes the expected value of a cost function that is known and is zero only on the diagonal elements. We also present a result that is related with the solution of the Monge-Kantorovich problem in finite product spaces in the case that solutions to the problem in the marginal spaces are known.

[pt] As operações de importação de uma empresa com abrangência nacional apresentam custos de transporte muito significativos na composição do custo total de sua cadeia de suprimento. Esta dissertação de mestrado contribui para a criação de uma ferramenta de análise que irá favorecer o planejamento das operações de importação da empresa. Neste sentido, o objetivo deste trabalho é otimizar os fluxos de transportes internacionais realizados pela empresa no período de 2003 e 2004 englobando os custos, os modais e os prazos de transporte associados aos contratos logísticos existentes. A modelagem da rede e dos fluxos de transporte se baseou num problema de transporte não capacitado no qual foram testadas oito soluções para cada um dos 5857 embarques realizados. Alguns resultados se mostraram diferentes da solução original adotada pela empresa uma vez que os nós de passagem situados no estado de São Paulo se apresentam com maior oferta e menor custo associado aos serviços de transporte marítimo e aéreo quando comparados aos demais nós de passagem. / [en] The import operations of a company with national coverage present very significant transportation costs in its total cost composition supply chain. The present Master Dissertation contributes for the creation of an analysis tool that will favour the planning of the company import operations. Therefore, the present study aims at optimizing the company s international transportation flow in the period of 2003 and 2004 taking in consideration the costs, transportation modals and transportation deadlines associated with the existent logistical contracts. The network modeling and the transportation flows were based on a non-capacitated transportation problem, in which eight solutions were tested for each of the 5857 boarding performed. Some results obtained are different from the original solution adopted by the company, once the gateway nodes at the state of São Paulo have lower costs and greater service offer associated to the maritime and aerial transport system, when compared to the other gateway nodes.

No description available.

Various types of transportation issues are a common practice. The issue may be approached mainly as the distribution of products from suppliers to consumers while minimising distribution costs. The difference of real transportation issues predominantly relates to the considered restrictions, such as capacities of vehicles and orders, time windows and other special distribution restrictions. Transportation issues were already defined by F.L. Hitchcock in 1941 and since then, a wide range of stochastic and non- determinist methods providing solutions to transportation issues have been developed. Nevertheless, introducing distribution restrictions in resolving real-life problems makes it difficult for such methods to be applied. This thesis provides a compilation of the well-known determinist methods that may be used to resolve transportation issues. The methods that are appropriate for resolving real issues are discussed in more detail. The solution procedure of the selected method is demonstrated using simple examples and the results are compared with the results of other methods. An analysis of the above methods is used to design and implement new methods to resolve real transportation issues, their results being compared with the methods provided by the commercial software product.

This thesis concerns the development of novel feasible direction type algorithms for constrained nonlinear optimization. The new algorithms are based upon enhancements of the search direction determination and the line search steps. The Frank-Wolfe method is popular for solving certain structured linearly constrained nonlinear problems, although its rate of convergence is often poor. We develop improved Frank--Wolfe type algorithms based on conjugate directions. In the conjugate direction Frank-Wolfe method a line search is performed along a direction which is conjugate to the previous one with respect to the Hessian matrix of the objective. A further refinement of this method is derived by applying conjugation with respect to the last two directions, instead of only the last one. The new methods are applied to the single-class user traffic equilibrium problem, the multi-class user traffic equilibrium problem under social marginal cost pricing, and the stochastic transportation problem. In a limited set of computational tests the algorithms turn out to be quite efficient. Additionally, a feasible direction method with multi-dimensional search for the stochastic transportation problem is developed. We also derive a novel sequential linear programming algorithm for general constrained nonlinear optimization problems, with the intention of being able to attack problems with large numbers of variables and constraints. The algorithm is based on inner approximations of both the primal and the dual spaces, which yields a method combining column and constraint generation in the primal space. / The articles are note published due to copyright rextrictions.