Mage Marmol, Anita Goyal, Pedro Jesus Copado-Mendez, Javier Panadero and Angel A. Juan
For any given customer, his/her profitability for a business enterprise can be estimated by the so-called customer lifetime value (CLV). One specific goal for many enterprises…
Abstract
Purpose
For any given customer, his/her profitability for a business enterprise can be estimated by the so-called customer lifetime value (CLV). One specific goal for many enterprises consists in maximizing the aggregated CLV associated with its set of customers. To achieve this goal, a company uses marketing resources (e.g. marketing campaigns), which are usually expensive.
Design/methodology/approach
This paper proposes a formal model of the Customer Life Value problem inspired by the uncapacitated facility location problem.
Findings
The computational experiments conducted by the authors illustrate the potential of the approach when compared with a standard (non-algorithm-supported) one.
Originality/value
The approach leads up to the economic trade-off between the volume of the employed resources and the aggregated CLV, i.e. the higher the number of resources utilized, but also the higher the cost of achieving this level of lifetime value. Hence, the number of resources to be “activated” has to be decided, and the effect of each of these resources on each CLV will depend upon how “close” the resource is from the corresponding customer (i.e. how large will the impact of the active resource on the customer).
Details
Keywords
Manuel Pineda-Sanchez, Angel Sapena-Baño, Juan Perez-Cruz, Javier Martinez-Roman, Ruben Puche-Panadero and Martin Riera-Guasp
Rectangular conductors play an important role in planar transmission line structures, multiconductor transmission lines, in power transmission and distribution systems, LCL…
Abstract
Purpose
Rectangular conductors play an important role in planar transmission line structures, multiconductor transmission lines, in power transmission and distribution systems, LCL filters, transformers, industrial busbars, MEMs devices, among many others. The precise determination of the inductance of such conductors is necessary for their design and optimization, but no explicit solution for the AC resistance and internal inductances per-unit length of a linear conductor with a rectangular cross-section has been found, so numerical methods must be used. The purpose of this paper is to introduce the use of a novel numerical technique, the proper generalized decomposition (PGD), for the calculation of DC and AC internal inductances of rectangular conductors.
Design/methodology/approach
The PGD approach is used to obtain numerically the internal inductance of a conductor with circular cross-section and with rectangular cross-section, both under DC and AC conditions, using a separated representation of the magnetic vector potential in a 2D domain. The results are compared with the analytical and approximate expressions available in the technical literature, with an excellent concordance.
Findings
The PGD uses simple one-dimensional meshes, one per dimension, so the use of computational resources is very low, and the simulation speed is very high. Besides, the application of the PGD to conductors with rectangular cross-section is particularly advantageous, because rectangular shapes can be represented with a very few number of independent terms, which makes the code very simple and compact. Finally, a key advantage of the PGD is that some parameters of the numerical model can be considered as additional dimensions. In this paper, the frequency has been considered as an additional dimension, and the internal inductance of a rectangular conductor has been computed for the whole range of frequencies desired using a single numerical simulation.
Research limitations/implications
The proposed approach may be applied to the optimization of electrical conductors used in power systems, to solve EMC problems, to the evaluation of partial inductances of wires, etc. Nevertheless, it cannot be applied, as presented in this work, to 3D complex shapes, as, for example, an arrangement of layers of helically stranded wires.
Originality/value
The PGD is a promising new numerical procedure that has been applied successfully in different fields. In this paper, this novel technique is applied to find the DC and AC internal inductance of a conductor with rectangular cross-section, using very dense and large one-dimensional meshes. The proposed method requires very limited memory resources, is very fast, can be programmed using a very simple code, and gives the value of the AC inductance for a complete range of frequencies in a single simulation. The proposed approach can be extended to arbitrary conductor shapes and complex multiconductor lines to further exploit the advantages of the PGD.