A linear optimization approach to the combined production planning model

Two fundamental processes usually arise in the production planning of many industries. The first one consists of deciding how many final products of each type have to be produced in each period of a planning horizon, the well-known lot sizing problem. The other process consists of cutting raw materials in stock in order to produce smaller parts used in the assembly of final products, the well-studied cutting stock problem. In this paper the decision variables of these two problems are dependent of each other in order to obtain a global optimum solution. Setups that are typically present in lot sizing problems are relaxed together with integer frequencies of cutting patterns in the cutting problem. Therefore, a large scale linear optimizations problem arises, which is exactly solved by a column generated technique. It is worth noting that this new combined problem still takes the trade-off between storage costs (for final products and the parts) and trim losses (in the cutting process). We present some sets of computational tests, analyzed over three different scenarios. These results show that, by combining the problems and using an exact method, it is possible to obtain significant gains when compared to the usual industrial practice, which solve them in sequence. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

A game theoretical approach to the evolution of structured communication codes

Structured meaning-signal mappings, i.e., mappings that preserve neighborhood relationships by associating similar signals with similar meanings, are advantageous in an environment where signals are corrupted by noise and sub-optimal meaning inferences are rewarded as well. The evolution of these mappings, however, cannot be explained within a traditional language evolutionary game scenario in which individuals meet randomly because the evolutionary dynamics is trapped in local maxima that do not reflect the structure of the meaning and signal spaces. Here we use a simple game theoretical model to show analytically that when individuals adopting the same communication code meet more frequently than individuals using different codes-a result of the spatial organization of the population-then advantageous linguistic innovations can spread and take over the population. In addition, we report results of simulations in which an individual can communicate only with its K nearest neighbors and show that the probability that the lineage of a mutant that uses a more efficient communication code becomes fixed decreases exponentially with increasing K. These findings support the mother tongue hypothesis that human language evolved as a communication system used among kin, especially between mothers and offspring.

A quasispecies approach to the evolution of sexual replication in unicellular organisms

This study develops a simplified model describing the evolutionary dynamics of a population composed of obligate sexually and asexually reproducing, unicellular organisms. The model assumes that the organisms have diploid genomes consisting of two chromosomes, and that the sexual organisms replicate by first dividing into haploid intermediates, which then combine with other haploids, followed by the normal mitotic division of the resulting diploid into two new daughter cells. We assume that the fitness landscape of the diploids is analogous to the single-fitness-peak approach often used in single-chromosome studies. That is, we assume a master chromosome that becomes defective with just one point mutation. The diploid fitness then depends on whether the genome has zero, one, or two copies of the master chromosome. We also assume that only pairs of haploids with a master chromosome are capable of combining so as to produce sexual diploid cells, and that this process is described by second-order kinetics. We find that, in a range of intermediate values of the replication fidelity, sexually reproducing cells can outcompete asexual ones, provided the initial abundance of sexual cells is above some threshold value. The range of values where sexual reproduction outcompetes asexual reproduction increases with decreasing replication rate and increasing population density. We critically evaluate a common approach, based on a group selection perspective, used to study the competition between populations and show its flaws in addressing the evolution of sex problem.

A New Approach to the Prediction of Partition Coefficients in Water/Organic Interfaces

In the present work, a new approach for the determination of the partition coefficient in different interfaces based on the density function theory is proposed. Our results for log P(ow) considering a n-octanol/water interface for a large super cell for acetone -0.30 (-0.24) and methane 0.95 (0.78) are comparable with the experimental data given in parenthesis. We believe that these differences are mainly related to the absence of van der Walls interactions and the limited number of molecules considered in the super cell. The numerical deviations are smaller than that observed for interpolation based tools. As the proposed model is parameter free, it is not limited to the n-octanol/water interface.