Models for capacitated lot-sizing problem with backlogging,setup carryover and crossover

Setup operations are significant in some production environments. It is mandatory that their production plans consider some features, as setup state conservation across periods through setup carryover and crossover. The modelling of setup crossover allows more flexible decisions and is essential for problems with long setup times. This paper proposes two models for the capacitated lot-sizing problem with backlogging and setup carryover and crossover. The first is in line with other models from the literature, whereas the second considers a disaggregated setup variable, which tracks the starting and completion times of the setup operation. This innovative approach permits a more compact formulation. Computational results show that the proposed models have outperformed other state-of-the-art formulation.     

Stability and convergence of the spectral Lagrange-Galerkin method for mixed periodic/non-periodic convection-dominated diffusion problems

We present a convergence analysis of the spectral Lagrange-Galerkinmethod for mixed periodic/non-periodic convection-diffusionproblems. The scheme is unconditionally stable, independentof the diffusion coefficient, even in the case when numericalquadrature is used. The theoretical predictions are illustratedby a series of numerical experiments. For the periodic case,our results present a significant improvement on those givenby Süli & Ware (1991) SIAM J. Numer.Anal.28, 423-445).     

Investigating the potassium interactions with the palytoxin induced channels in Na+/K+ pump

K(+) has been appointed as the main physiological inhibitor of the palytoxin (PTX) effect on the Na(+)/K(+) pump. This toxin acts opening monovalent cationic channels through the Na(+)/K(+) pump. We investigate, by means of computational modeling, the kinetic mechanisms related with K(+) interacting with the complex PTX-Na(+)/K(+) pump. First, a reaction model, with structure similar to Albers-Post model, describing the functional cycle of the pump, was proposed for describing K(+) interference on the complex PTX-Na(+)/K(+) pump in the presence of intracellular ATP. A mathematic model was derived from the reaction model and it was possible to solve numerically the associated differential equations and to simulate experimental maneuvers about the PTX induced currents in the presence of K(+) in the intra- and extracellular space as well as ATP in the intracellular. After the model adjusting to the experimental data, a Monte Carlo method for sensitivity analysis was used to analyze how each reaction parameter acts during each experimental maneuver involving PTX. For ATP and K(+) concentrations conditions, the simulations suggest that the enzyme substate with ATP bound to its high-affinity sites is the main substate for the PTX binding. The activation rate of the induced current is limited by the K(+) deocclusion from the PTX-Na(+)/K(+) pump complex. The K(+) occlusion in the PTX induced channels in the enzymes with ATP bound to its low-affinity sites is the main mechanism responsible for the reduction of the enzyme affinity to PTX.