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 benefits of a health impact assessment in relation to fuel poverty: assessing Luton's affordable warmth strategy and the need for a national strategy

The links between fuel poverty and poor health are well documented, yet there is no statutory requirement on local authorities to develop fuel poverty strategies, which tend to be patchy nationally and differ substantially in quality. Fuel poverty starts from the perspective of income, even though interventions can improve health. The current public health agenda calls for more partnership-based, cost-effective strategies based on sound evidence. Fuel poverty represents a key area where there is currently little local evidence quantifying and qualifying health gain arising from strategic interventions. As a result, this initial study sought to apply the principles of a health impact assessment to Luton’s Affordable Warmth Strategy, exploring the potential to identify health impact arising – as a baseline for future research – in the context of the public health agenda. A national strategy would help ensure the promotion of targeted fuel poverty strategies.