Optimal Scrap Combination for Steel Production

. In steel production, scrap metal is used for cooling the enormous quantity of heat producedby blowing oxygenon hot metal. Scrap differs in regard to the content of iron and of some tramp elements. The price depends on these attributes. Each melting bath unit of steel has its own material constraints for the amount of iron and tramp elements in order to guarantee the desired quality. In addition, the transportation of scrap is restricted because it needs time and space: the scrap is kept in some railroad cars in the scrap hal

A unified framework for shared protection schemes in optical mesh network

While the advantages of p-cycles and FIPP p-cycles are well established, there has been no systematic analysis of how much bandwidth they consume in comparison with the classical shared link and path protection schemes. It was recently observed that, even enumerating a huge number of cycles, is not necessarily a guarantee for obtaining good quality solutions with the ILP models if tools for large scale programming are not used. We propose to investigate the bandwidth protection costs of p-cycles and FIPP p-cycles in comparison with those of shared link and path protection by applying the column generation technique to solve relaxed LP models for the four protection schemes, and then solving the resulting ILP models. Provably near-optimal solutions allow us to perform accurate quantitative comparisons on real-world networks.<br>Embora as vantagens dos p-ciclos e FIPP p-ciclos estejam bem estabelecidas, não existe uma análise sistemática de quanta largura de banda eles consomem em comparação aos mecanismos clássicos de proteção compartilhada por caminhos e por links. Foi observado recentemente que a enumeração de um enorme número de ciclos não é necessariamente uma garantia de se obter soluções de boa qualidade se ferramentas para programação de larga escala não forem usadas. Nós propomos investigar os custos de proteção de largura de banda dos p-ciclos e FIPP p-ciclos em comparação com aqueles de proteção compartilhada por links e por caminhos, através da aplicação da técnica de geração de colunas para resolver modelos relaxados para os quatro esquemas de proteção. Em seguida, resolvemos os modelos de programação inteira resultantes. Soluções próximas da otimalidade nos permitem desempenhar comparações quantitativas exatas em redes reais

An inexact bundle variant suited to column generation

International audienceWe give a bundle method for constrained convex optimization. Instead of using penalty functions, it shifts iterates towards feasibility, by way of a Slater point, assumed to be known. Besides, the method accepts an oracle delivering function and subgradient values with unknown accuracy. Our approach is motivated by a number of applications in column generation, in which constraints are positively homogeneous--so that zero is a natural Slater point--and an exact oracle may be time consuming. Finally, our convergence analysis employs arguments which have been little used so far in the bundle community. The method is illustrated on a number of cutting-stock problems