Classical inventory theory considers that stockouts generate penalty costs to the firm, often assumed to be proportional to the excess of demand over supply. While such a concept is sometimes appropriate, it does not correctly reflect the effect of loss of goodwill. The latter is characterized by the fact that a disappointed customer reacts in the future to change his purchasing habits. Thus the nature of the effect is that subsequent demand is perturbed, a phenomenon quite different from having an immediate penalty cost imposed. Models with this property are termed perturbed demand, abbreviated PD. In this paper, this concept is defined precisely, and some of its properties are developed. Some typical cases are solved to determine optimal policies when PD prevails.

Objective In this study, we determined efficient head model sizes relative to predicted current densities in transcranial direct current stimulation (tDCS). Approach Efficiency measures were defined based on a finite element (FE) simulations performed using nine human head models derived from a single MRI data set, having extents varying from 60-100% of the original axial range. Eleven tissue types, including anisotropic white matter, and three electrode montages (T7-T8, F3-right supraorbital, Cz-Oz) were used in the models. Main results Reducing head volume extent from 100% to 60%, that is, varying the model’s axial range from between the apex and C3 vertebra to one encompassing only apex to the superior cerebellum, was found to decrease the total modeling time by up to half. Differences between current density predictions in each model were quantified by using a relative difference measure (RDM). Our simulation results showed that RDM was the least affected (a maximum of 10% error) for head volumes modeled from the apex to the base of the skull (60-75% volume). Significance This finding suggested that the bone could act as a bioelectricity boundary and thus performing FE simulations of tDCS on the human head with models extending beyond the inferior skull may not be necessary in most cases to obtain reasonable precision in current density results.

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Investigation is continued of inventory models in which customer good will is lost when stockout occurs. Several models are formulated and optimal policies for the firm are derived conceptually (i.e., algebraic equations satisfied by the optimal parameter values are determined). Both constant and distributed demand are considered, and it is shown that the same formulation applies to both.

This paper presents a new class of queuing models. There are n distinct types of customers and n distinct types of service facilities. Some customers can be processed at any service facility, but other customer types can only use selected ones among the service-facility types. This class of model is named “lane selection,” abbreviated LS, since the arriving customers with some freedom of choice must select the queue, or lane, in which they are to be processed through the system. It is shown by example that many physical situations are represented more accurately by this model than by more conventional ones. However, in analysis, the LS concept raises many theoretical difficulties. For a number of special cases, this paper obtains in explicit form as functions of the model parameters the mean queue lengths and waiting times for the different classes of customers.

The mechanical properties of the lung are embodied in its mechanical input impedance, which it is interpreted in physiological terms by being fit with a mathematical model. The normal lung is extremely well described by a model consisting of a single uniformly ventilated compartment comprised of tissue having a constant-phase impedance, but to describe the abnormal lung it frequently becomes necessary to invoke additional compartments. To date, all evidence of regional mechanical heterogeneity in the mouse lung has been assumed to be of the parallel variety. We therefore investigated the use of a serial heterogeneity model, relative to parallel heterogeneity and homogeneous models, for describing impedance spectra in mice subjected to a variety of interventions designed to make their lungs heterogeneous. We found that functional evidence of the finite stiffness of the airway wall in mice with airways obstruction can sometimes be apparent in lung impedance below 20 Hz. The model estimates of airway stiffness were smaller than direct estimates obtained from micro-CT images of the lung in vivo, suggesting that the conducting airways alone are likely not the precise anatomical correlate of proximal functional stiffness in the lung. Nevertheless, we conclude that central airway shunting in mice can sometimes be an important physiological phenomenon.

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