On optimal intervention for customer lifetime value

The potential value of a customer to a commercial organisation can be a core ingredient in decision-making. There is a growing literature on the topic, much of it presented in rather general terms. In this paper, we examine a particular aspect, namely the expected income to the firm from a customer over his ‘lifetime’ (period of tenure with the firm). To derive quantitative results, we adopt a type of model in which there are underlying income and cost processes for a customer that evolve over time. In addition, we include a customer-specific effect that reflects the fact that some customers give rise to more income than others. These two stochastic elements are monitored by the firm for each new customer over an initial probationary period. Depending on the result of this assessment the firm might decide to offer a continuation of the account, perhaps on modified terms. The problem for the firm, which is the case addressed here, is to determine the length of the probationary period and the criterion for continuation. We set out a framework in which these two aspects may be optimised.     

Two-dimensional phased arrays for surgery: Movement of a single focus

Numerical simulation and comparative analysis of acoustic fields generated by two-dimensional phased arrays designed for ultrasonic surgery is conducted. The case of movement of a single focus by an array with the surface shaped as a part of a spherical shell with the curvature radius 120 mm is considered. The influence of the number of elements (varying from 64 to 1024), their diameter (from 2.5 to 10 mm), frequency (from 1 to 2 MHz), and the degree of sparseness of the elements at the array surface on the field characteristics is studied. The calculations are performed for arrays with elements positioned at the surface both regularly (in square, annular, or hexagonal patterns) and randomly. Criteria for the evaluation of the “quality” of intensity distributions in the field generated by an array in the case of movement of a single focus are suggested. Of all arrays studied, the best quality of distributions is obtained for an array containing 256 elements of diameter 5 mm randomly positioned at the array surface. The quality of the intensity distributions for arrays consisting of 255, 256, and 1024 elements positioned regularly (in square, annular, and hexagonal patterns) is inferior to the corresponding quality for arrays with randomly positioned elements. The irregularity in elements’ positioning considerably improves the distribution quality by suppressing the secondary intensity peaks in the field generated by the array; or, alternatively, it provides an opportunity to obtain the same distribution quality with a fraction of the number of elements in the array. The effects of the number and shape of elements, errors in phase setting, frequency modulation of signals, and non-uniform distribution of amplitudes over the array surface on the distribution quality are analyzed.     

Analysis of a Y-junction optical waveguide interleaver

A Y-junction optical planar lightwave circuit (PLC) interleaver is analyzed and a polymeric interleaver is fabricated. This interleaver is composed of two identical but reversed Y-junction components. The formula for channel spacing of this device is generated and influence factor of channel spacing is analyzed. The fabrication tolerance of this device is provided. Our analysis shows that there is a less than 2% deviation from the design value of 1.6 nm when the core width varies by 10%.     

Direct versus indirect credit scoring classifications

We introduce a new approach to assigning bank account holders to ‘good’ or ‘bad’ classes based on their future behaviour. Traditional methods simply treat the classes as qualitatively distinct, and seek to predict them directly, using statistical techniques such as logistic regression or discriminant analysis based on application data or observations of previous behaviour. We note, however, that the ‘good’ and ‘bad’ classes are defined in terms of variables such as the amount overdrawn at the time at which the classification is required. This permits an alternative, ‘indirect’, form of classification model in which, first, the variables defining the classes are predicted, for example using regression, and then the class membership is derived deterministically from these predicted values. We compare traditional direct methods with these new indirect methods using both real bank data and simulated data. The new methods appear to perform very similarly to the traditional methods, and we discuss why this might be. Finally, we note that the indirect methods also have certain other advantages over the traditional direct methods.     

Models in solar water heating—a critical comparison

A problem is discussed concerning the stochastic modelling of a system for collecting and storing solar energy. Three models are compared. These are: (i) a trivial, zero-order model; (ii) a linear (first-order) approximation to the system controls; and (iii) a full computer simulation. The Law of Diminishing Returns is demonstrated by this comparison, for although the computer simulation, involving great computational and programming effort is not matched by the linear models, considerable information is available, for little effort, from the linear approximation. Further it is shown that the use of this linear approximation can greatly assist a computer simulation since its use as a control variate can drastically reduce the variance.