Robustness of the partitions in grouping multi-item inventories

A recent work obtained closed-form solutions to the.problem of optimally grouping a multi-item inventory into subgroups with a common order cycle per group, when the distribution by value of the inventory could be described by a Pareto function. This paper studies the sensitivity of the optimal subgroup boundaries so obtained. Closed-form expressions have been developed to find intervals for the subgroup boundaries for any given level of suboptimality. Graphs have been provided to aid the user in selecting a cost-effective level of aggregation and choosing appropriate subgroup boundaries for a whole range of inventory distributions. The results of sensitivity analyses demonstrate the availability of flexibility in the partition boundaries and the cost-effectiveness of any stock control system through three groups, and thus also provide a theoretical support to the intuitive ABC system of classifying the items.

EPR studies on donor doped BaTiO3 grain boundary layer ceramic dielectrics

Donor doped BaTiO3 ceramics become insulating5 under controlled conditions with effective dielectric constants >10. The changes in EPR signals indicate that a certain fraction of the donor doped BaTiO3 is cubic even at room temperature and that the cubic fraction increases with the donor content. X-ray powder diffraction data support the EPR results. The coexistence of both the phases over a range of temperature is characteristic of diffused phase transition. The effect of grain size variation on EPR signal intensities indicate that the boundary layers surrounding the grains may constitute the cubic phase as a result of higher Ba-vacancies and donor contents at the grain boundary layer than in the bulk. Since the acceptor states arising from the Ba-vacancies and the impurities are activated in the cubic phase, they capture electrons from the conduction band, rendering the cubic phase electrically more insulating than the semiconductive tetragonal grain interiors. Thus, the cubic grain boundary layers act as effective dielectric media where the field tends to concentrate.

A note on the effective medium theory of random resistive-reactive medium

The effective medium theory for a system with randomly distributed point conductivity and polarisability is reformulated, with attention to cross-terms involving the two disorder parameters. The treatment reveals a certain inconsistency of the conventional theory owing to the neglect of the Maxwell-Wagner effect. The results are significant for the critical resistivity and dielectric anomalies of a binary liquid mixture at the phase separation point.