On-line algorithms for single machine scheduling with family setup times

The paper considers an on-line single machine scheduling problem where the goal is to minimize the makespan. The jobs are partitioned into families and a setup is performed every time the machine starts processing a batch of jobs of the same family. The scheduler is aware of the number of families and knows the setup time of each family, although information about a job only becomes available when that job is released. We give a lower bound on the competitive ratio of any on-line algorithm. Moreover, for the case of two families, we provide an algorithm with a competitive ratio that achieves this lower bound. As the number of families increases, the lower bound approaches 2, and we give a simple algorithm with a competitive ratio of 2.

The Richit-Richards family of distributions and its use in forestry

Johnson's SB and the logit-logistic are four-parameter distribution models that may be obtained from the standard normal and logistic distributions by a four-parameter transformation. For relatively small data sets, such as diameter at breast height measurements obtained from typical sample plots, distribution models with four or less parameters have been found to be empirically adequate. However, in situations in which the distributions are complex, for example in mixed stands or when the stand has been thinned or when working with aggregated data, then distribution models with more shape parameters may prove to be necessary. By replacing the symmetric standard logistic distribution of the logit-logistic with a one-parameter “standard Richards” distribution and transforming by a five-parameter Richards function, we obtain a new six-parameter distribution model, the “Richit-Richards”. The Richit-Richards includes the “logit-Richards”, the “Richit-logistic”, and the logit-logistic as submodels. Maximum likelihood estimation is used to fit the model, and some problems in the maximum likelihood estimation of bounding parameters are discussed. An empirical case study of the Richit-Richards and its submodels is conducted on pooled diameter at breast height data from 107 sample plots of Chinese fir (Cunninghamia lanceolata (Lamb.) Hook.). It is found that the new models provide significantly better fits than the four-parameter logit-logistic for large data sets.

An improved approximation algorithm for the two-machine open shop scheduling problem with family setup times

We consider the problem of scheduling families of jobs in a two-machine open shop so as to minimize the makespan. The jobs of each family can be partitioned into batches and a family setup time on each machine is required before the first job is processed, and when a machine switches from processing a job of some family to a job of another family. For this NP-hard problem the literature contains (5/4)-approximation algorithms that cannot be improved on using the class of group technology algorithms in which each family is kept as a single batch. We demonstrate that there is no advantage in splitting a family more than once. We present an algorithm that splits one family at most once on a machine and delivers a worst-case performance ratio of 6/5.

Family, community and politics: the fertile legacy of Michael Young

The Institute of Community Studies was set up by Michael Young in order to carry out research on politically relevant social issues, in a context free from direct political control. A research method was devised for it whereby researchers made their own values and objectives very explicit, while staying as close as possible in their reports to the concerns and language of respondents themselves. This method has often been criticized by professional sociologists: but it reflects quite well the nature of social knowledge. It has produced reports which help to increase public understanding of social processes, and provide useful guidance to policy makers. Professional sociology on the other hand has tried to develop a rigorously value-free method. As a result, though, it often seems to be tied implicitly to values shared among researchers but not more universally. Arguably this makes it harder for the general public to understand, and accept, its findings.

Insolvency: ordering a sale of the family home

Comments on the Chancery Division ruling in Nicholls v Lan on whether the interests of a bankrupt husband's creditors prevailed over those of the wife, despite her circumstances being exceptional within the meaning of the Insolvency Act 1986 s.335A on account of her suffering from chronic schizophrenia, where the wife was the joint owner of another property which could be realised to buy out the trustee in bankruptcy's half share in the equity of the matrimonial home.

Showing interest

Comments on the Chancery Division judgment in Jones v Kernott on the beneficial interests of former cohabiting partners in their family home. Considers whether the partners must have intended to vary their shares when the man stopped paying the mortgage, bought a house in his own name and went to live there. Discusses whether the court could take into account what was considered fair between the partners based on the whole course of dealing, including non-payment of maintenance for children.

Socrates and Plato on asking ‘what is x?’

The Socratic elenchus is a method of philosophical enquiry attributed by Plato, in his dialogues, to his teacher Socrates. It is a method that uses a dialectic technique of questioning and answering to try to discover the truth of the issue under investigation. For Plato’s Socrates, the fundamental question for human beings is that of how to live, thus the enquiries he initiates concern our understanding of what it is to act ethically. In order to begin to enquire into how to act in a virtuous manner, however, Socrates claimed that we must first know what virtue is. We must, that is, first understand the meaning of virtue before we can consider its application it to any particular kind of action; we must first be able to answer the question “what is x?” before considering whether a particular action or kind of action is an instance of x. This requirement leads to what is known as the ‘Socratic Paradox’: if we have to first establish what x means before we confirm or discount cases of it, then how can our enquiry ever commence; how can we begin in asking questions about x if we don’t yet know what x is? Philosophy has continued to grapple with the Socratic paradox since Plato’s formulation of it. This presentation will explain how the paradox is produced out of the elenchus and consider the ways in which Wittgenstein’s account of family resemblance sheds new light upon this age-old issue. [From the Author]