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).     

A new family of ionic liquids based on N,N-dialkyl-3-azabicyclo[3.2.2]nonanium cations: organic plastic crystal behaviour and highly reversible lithium metal electrodeposition

A new family of ionic liquids based on N,N-dialkyl-3-azabicyclo[3.2.2]nonanium cations exhibits wide electrochemical windows, excellent lithium deposition-stripping behaviour and plastic crystal properties and therefore these cation structures, which are extensions from pyrrolidinium- and piperidinium-based cations, complement a set of related structures for a systematic study on the physicochemical properties of ionic liquids.     

Predicting properties of new ionic liquids: density functional theory and experimental studies of tetra-alkylammonium salts of (thio)carboxylate anions, RCO2⁻, RCOS⁻ and RCS2⁻

Density functional theory calculations of alkyl-carboxylate anions and their sulfur substituted variants are presented here as an aid for the development of new ionic liquids. Electron transfer both within the anion, and between the anion and cation of an ion pair, are described using natural bond order analysis, using tetraethylammonium as a common cation. The overall stabilising effect of this electron transfer is quantified for the series of anions, and is found to correlate with clear trends in ion-pair binding energy. These and other electronic properties determine which compounds are synthesised, and experimental results validate the computational results. In combination with tetraethylammonium, a carboxylate with an unsaturated alkyl chain produces an ionic liquid at room temperature. However, computations suggest that sulfur substituted anions will produce a lower melting point and perhaps more fluid ionic liquid, but one which would be less stable against oxidation.     

Optimising organic ionic plastic crystal electrolyte for all solid-state and higher than ambient temperature lithium batteries

Organic ionic plastic crystal (OIPC) electrolytes are among the key enabling materials for solid-state and higher than ambient temperature lithium batteries. This work overviews some of the parameter studies on the Li|OIPC interface using lithium symmetrical cells as well as the optimisation and performance of Li|OIPC|LiFePO₄ cells. The effects of temperature and electrolyte thickness on the cycle performance of the lithium symmetrical cell, particularly with respect to the interfacial and bulk resistances, are demonstrated. Whilst temperature change substantially alters both the interfacial and bulk resistance, changing the electrolyte thickness predominantly changes the bulk resistance only. In addition, an upper limit of the current density is demonstrated, above which irreversible processes related to electrolyte decomposition take place. Here, we demonstrate an excellent discharge capacity attained on LiFePO₄|10 mol% LiNTf₂-doped [C₂mpyr][NTf₂]|Li cell, reaching 126 mAh g^-1 at 50 °C (when the electrolyte is in its solid form) and 153 mAh g^-1 at 80 °C (when the electrolyte is in its liquid form). Most remarkably, at high temperature operation, the capacity retention at long cycles and high current is excellent with only a slight (3%) drop in discharge capacity upon increasing the current from 0.2 C to 0.5 C. These results highlight the real prospects for developing a lithium battery with high temperature performance that easily surpasses that achievable with even the best contemporary lithium-ion technology.