A multi-depot travelling salesman problem and its iterative and integrated approaches

This paper formulates a logistics distribution problem as the multi-depot travelling salesman problem (MDTSP). The decision makers not only have to determine the travelling sequence of the salesman for delivering finished products from a warehouse or depot to a customer, but also need to determine which depot stores which type of products so that the total travelling distance is minimised. The MDTSP is similar to the combination of the travelling salesman and quadratic assignment problems. In this paper, the two individual hard problems or models are formulated first. Then, the problems are integrated together, that is, the MDTSP. The MDTSP is constructed as both integer nonlinear and linear programming models. After formulating the models, we verify the integrated models using commercial packages, and most importantly, investigate whether an iterative approach, that is, solving the individual models repeatedly, can generate an optimal solution to the MDTSP. Copyright © 2006 Inderscience Enterprises Ltd.

Solitons: permanent waves

Communications engineers are learning to create an electromagnet wave at will, to transmit information. This wave, the optical soliton, is the subject of astounding recent developments in nonlinear optics and lasers. The author describes the principles behind the use of solitons in optical communications and shows that in the context of such communications the most important property of solitons is that they are extremely stable. Not only do they not disperse, but an encounter with a perturbation (e.g. a joint in optical fibre) will usually leave the soliton unaltered.

Surface wave techniques for the study of engineering structures and materials

A wire drive pulse echo method of measuring the spectrum of solid bodies described. Using an 's' plane representation, a general analysis of the transient response of such solids has been carried out. This was used for the study of the stepped amplitude transient of high order modes of disks and for the case where there are two adjacent resonant frequencies. The techniques developed have been applied to the measurenent of the elasticities of refractory materials at high temperatures. In the experimental study of the high order in-plane resonances of thin disks it was found that the energy travelled at the edge of the disk and this initiated the work on one dimensional Rayleigh waves.Their properties were established for the straight edge condition by following an analysis similar to that of the two dimensional case. Experiments were then carried out on the velocity dispersion of various circuits including the disk and a hole in a large plate - the negative curvature condition.Theoretical analysis established the phase and group velocities for these cases and experimental tests on aluminium and glass gave good agreement with theory. At high frequencies all velocities approach that of the one dimensional Rayleigh waves. When applied to crack detection it was observed that a signal burst travelling round a disk showed an anomalous amplitude effect. In certain cases the signal which travelled the greater distance had the greater amplitude.An experiment was designed to investigate the phenanenon and it was established that the energy travelled in two nodes with different velocities.It was found by analysis that as well as the Rayleigh surface wave on the edge, a seoond node travelling at about the shear velocity was excited and the calculated results gave reasonable agreement with the experiments.

A study of magnetic non-linearity and finite length effects in solid iron subjected to a travelling MMF wave

This thesis describes an experimental and analytic study of the effects of magnetic non-linearity and finite length on the loss and field distribution in solid iron due to a travelling mmf wave. In the first half of the thesis, a two-dimensional solution is developed which accounts for the effects of both magnetic non-linearity and eddy-current reaction; this solution is extended, in the second half, to a three-dimensional model. In the two-dimensional solution, new equations for loss and flux/pole are given; these equations contain the primary excitation, the machine parameters and factors describing the shape of the normal B-H curve. The solution applies to machines of any air-gap length. The conditions for maximum loss are defined, and generalised torque/frequency curves are obtained. A relationship between the peripheral component of magnetic field on the surface of the iron and the primary excitation is given. The effects of magnetic non-linearity and finite length are combined analytically by introducing an equivalent constant permeability into a linear three-dimensional analysis. The equivalent constant permeability is defined from the non-linear solution for the two-dimensional magnetic field at the axial centre of the machine to avoid iterative solutions. In the linear three-dimensional analysis, the primary excitation in the passive end-regions of the machine is set equal to zero and the secondary end faces are developed onto the air-gap surface. The analyses, and the assumptions on which they are based, were verified on an experimental machine which consists of a three-phase rotor and alternative solid iron stators, one with copper end rings, and one without copper end rings j the main dimensions of the two stators are identical. Measurements of torque, flux /pole, surface current density and radial power flow were obtained for both stators over a range of frequencies and excitations. Comparison of the measurements on the two stators enabled the individual effects of finite length and saturation to be identified, and the definition of constant equivalent permeability to be verified. The penetration of the peripheral flux into the stator with copper end rings was measured and compared with theoretical penetration curves. Agreement between measured and theoretical results was generally good.

Fundamental characteristics of space-charge waves in photorefractive sillenite crystals

We investigate experimentally the fundamental characteristics of space-charge waves excited in a photorefractive crystal of Bi12SiO20. Features such as their transient rise and decay as well as their steady-state frequency response are investigated. Based on this, we find the dependence of the space-charge waves' quality factor on spatial frequency and electric-field biasing. The experimental findings are compared with the linear space-charge wave theory developed previously by Sturman et al. [J. Opt. Sec. Am. B 10, 1919 (1993)].

Business cycles, long waves, and company langevity in Birmingham area metal industries 1780-1980

This doctoral thesis originates from an observational incongruence between the perennial aims and aspirations of economic endeavour and actually recorded outcomes, which frequently seem contrary to those intended and of a recurrent, cyclical type. The research hypothesizes parallel movement between unstable business environments through time, as expressed by periodically fluctuating levels of economic activity, and the precipitation rates of industrial production companies. A major problem arose from the need to provide theoretical and empirical cohesion from the conflicting, partial and fragmented interpretations of several hundred historians and economists, without which the research question would remain unanswerable. An attempt to discover a master cycle, or superimposition theorem, failed, but was replaced by minute analysis of both the concept of cycles and their underlying data-bases. A novel technique of congregational analysis emerged, resulting in an integrated matrix of numerical history. Two centuries of industrial revolution history in England and Wales was then explored and recomposed for the first time in a single account of change, thereby providing a factual basis for the matrix. The accompanying history of the Birmingham area provided the context of research into the failure rates and longevities of firms in the city's staple metal industries. Sample specific results are obtained for company longevities in the Birmingham area. Some novel presentational forms are deployed for results of a postal questionnaire to surviving firms. Practical demonstration of the new index of national economic activity (INEA) in relation to company insolvencies leads to conclusions and suggestions for further applications of research into the tempo of change, substantial Appendices support the thesis and provide a compendium of information covering immediately contiguous domains.

Fundamental characteristics of space-charge waves in photorefractive sillenite crystals

We investigate experimentally the fundamental characteristics of space-charge waves excited in a photorefractive crystal of Bi12SiO20. Features such as their transient rise and decay as well as their steady-state frequency response are investigated. Based on this, we find the dependence of the space-charge waves' quality factor on spatial frequency and electric-field biasing. The experimental findings are compared with the linear space-charge wave theory developed previously by Sturman et al. [J. Opt. Sec. Am. B 10, 1919 (1993)].