Group technology approach to the open shop scheduling problem with batch setup times

This paper studies the problem of scheduling jobs in a two-machine open shop to minimize the makespan. Jobs are grouped into batches and are processed without preemption. A batch setup time on each machine is required before the first job is processed, and when a machine switches from processing a job in some batch to a job of another batch. For this NP-hard problem, we propose a linear-time heuristic algorithm that creates a group technology schedule, in which no batch is split into sub-batches. We demonstrate that our heuristic is a -approximation algorithm. Moreover, we show that no group technology algorithm can guarantee a worst-case performance ratio less than 5/4.

The recovery mechanism of platinum group metals from catalytic converters in spent automotive exhaust systems

The recovery of platinum group metals (PGMs) from catalytic converters of spent exhaust systems is considered in this paper. To be cost-effective, recovery processes must be well over 90% efficient and so the optimisation of their operation is vital. Effective optimisation requires a sound understanding of the operation and the underlying process mechanisms. This paper focuses on pyrometallurgical recovery operations used and typified by the Johnson–Matthey process. Analysis of this process reveals that it cannot be simply explained by the gravity model that is normally assumed. The analysis reveals that the affinity of PGM particles for the melted collector metal is a key factor in the behaviour of the process. A rational explanation of the key issues that govern the process behaviour is proposed and shown to be consistent with available operational data. The results generated would be applicable to other similar processes.

Collector-metal behaviour in the recovery of platinum-group metals from catalytic converters

A commercial pyrometallurgical process for the extraction of platinum-group metals (PGM) from a feedstock slag was analysed with the use of a model based on computational fluid dynamics. The results of the modelling indicate that recovery depends on the behaviour of the collector phase. A possible method is proposed for estimation of the rate at which PGM particles in slag are absorbed into an iron collector droplet that falls through it. Nanoscale modelling techniques (for particle migration or capture) are combined with a diffusion-controlled mass-transfer model to determine the iron collector droplet size needed for >95% PGM recovery in a typical process bath (70 mm deep) in a realistic time-scale (<1 h). The results show that an iron droplet having a diameter in the range 0.1–0.3 mm gives good recovery (>90%) within a reasonable time. This finding is compatible with published experimental data. Pyrometallurgical processes similar to that investigated should be applicable to other types of waste that contain low levels of potentially valuable metals.

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.

Horsham Properties Group Ltd v Clark: possession - mortgagee's right or discretionary remedy?

Comments on the Chancery Division decision in Horsham Properties Group Ltd v Clark on whether a mortgagee's exercise of its contractual right, on the mortgagor falling into arrears, to appoint receivers such that the property could be sold and possession obtained without triggering the court's discretionary powers pursuant to the Administration of Justice Act 1970 s.36 infringed the mortgagor's rights under the European Convention on Human Rights 1950 Protocol 1 art.1. Considers the implications of proposed reforms recasting the mortgagee's right to possession as a discretionary remedy. [From Legal Journals Index]