An improved approximation algorithm for the two-machine flow shop scheduling problem with an interstage transporter

We study the two-machine flow shop problem with an uncapacitated interstage transporter. The jobs have to be split into batches, and upon completion on the first machine, each batch has to be shipped to the second machine by a transporter. The best known heuristic for the problem is a –approximation algorithm that outputs a two-shipment schedule. We design a –approximation algorithm that finds schedules with at most three shipments, and this ratio cannot be improved, unless schedules with more shipments are created. This improvement is achieved due to a thorough analysis of schedules with two and three shipments by means of linear programming. We formulate problems of finding an optimal schedule with two or three shipments as integer linear programs and develop strongly polynomial algorithms that find solutions to their continuous relaxations with a small number of fractional variables

BSHM meetings: BMS History of Mathematics Splinter Group

Introduction to abstracts from papers given at BMS History of Mathematics Splinter Group, held 17 April 2007, in Swansea.

BSHM meetings [Photographs]

Report on Research in Progress, held The Queen’s College, Oxford, 24 February 2007. Photos by Tony Mann. Figure 1. Raymond Flood presenting the BSHM prize for 2007 to Tony Gould. Figure 2. Speakers and helpers at Research in Progress 2007. From left to right: Craig Stephenson, Raymond Flood, Benjamin Wardhaugh, David Parks, Mel Bayley, Eleanor Sheppard, Judith Grabiner, Jackie Stedall, Nicola Boyle, Amirouche Moktefi.

Reviews [Book review]

Review of John Dee: interdisciplinary studies in English renaissance thought, Stephen Clucas (editor), Springer International Archives of the History of Ideas 193, 2006, 383pp, £ 111, ISBN 1-4020-4245-0.

[Book review] Reviews

Review of biography of Leonhard Euler - Andreas K Heyne and Alice P Heyne (text) and Elena S Pini (illustrations), Leonhard Euler: a man to be reckoned with, translated from the German by Alice P Heyne and Tahu Matheson, Birkhauser, 2007, 45 pp, £14.50, ISBN 3-7643-8332-9.

BSHM meetings: British Mathematics Colloquium

Report on the British Mathematics Colloquium, which took place in York, 25-28 March 2008. Also includes abstracts of the individual talks.

[BSHM meetings] Topics in the history of financial mathematics: early commerce to chaos in modern stock markets

This account provides an overview of the study day, entitled 'Topics in the History of Financial Mathematics: Early commerce to chaos in modern stock markets,' held by the British Society for the History of Mathematics jointly with Gresham College, at Gresham College, London on 25th April 2008. The series of talks explored the development of mathematics and mathematical techniques in a commercial and financial context.

Does culture affect a brand's personality?

Global branding brings with it exposure to an increasingly culturally-diverse audience. Examples of Islamic finance products being consumed by non-Muslims, and designer labels being adopted, by those outside of their intended target audience; seem to suggest that brands are being shaped more and more by consumers. Within current literature on branding, and cross-cultural consumer behaviour; there appears to have emerged a difference of opinion - as to whether a consumer’s culture has any bearing on their decision making; or subsequent influence brand personalities. The purpose of this paper is to present existing evidence; as a basis for undertaking future research.

Constructive notice and independent legal advice: a study of lending institution practice

Cases on when lending institutions will be put on inquiry as to circumstances giving rise to presumption of undue influence, and results of research on lending practice of residential mortgage lenders in light of case law. [From Legal Journals Index]