Polynomial-time approximation schemes for scheduling problems with time lags

We identify two classes of machine scheduling problems with time lags that possess Polynomial-Time Approximation Schemes (PTASs). These classes together, one for minimizing makespan and one for minimizing total completion time, include many well-studied time lag scheduling problems. The running times of these approximation schemes are polynomial in the number of jobs, but exponential in the number of machines and the ratio between the largest time lag and the smallest positive operation time. These classes constitute the first PTAS results for scheduling problems with time lags

Sports coaching and the law of negligence: implications for coaching practice

The ordinary principles of the law of negligence are applicable in the context of sport, including claims brought against volunteer and professional coaches. Adopting the perspective of the coach, this article intends to raise awareness of the emerging intersection between the law of negligence and sports coaching, by utilising an interdisciplinary analysis designed to better safeguard and reassure coaches mindful of legal liability. Detailed scrutiny of two cases concerning alleged negligent coaching, with complementary discussion of some of the ethical dilemmas facing modern coaches, reinforces the legal duty and obligation of all coaches to adopt objectively reasonable and justifiable coaching practices when interacting with athletes. Problematically, since research suggests that some coaching practice may be underpinned by ‘entrenched legitimacy’ and ‘uncritical inertia’, it is argued that coach education and training should place a greater emphasis on developing a coach’s awareness and understanding of the evolving legal context in which they discharge the duty of care incumbent upon them

Sequencing n Jobs on Two Machines with Arbitrary Time Lags

Each of n jobs must be run first on machine I and then on machine I. Running times for each job on each machine are given. Also specified are arbitrary time lags which prescribe that a job may not be started (completed) on machine II until at least a certain time has elapsed since starting (completing) the job on machine I. A rule is given for determining the sequence in which jobs are to be run on the machines--using the same sequence for both machines--in order to minimize the time between the start of production of the first job on machine I and the completion of production of the last job on machine II.

Sequencing Operations to Minimize In-Process Inventory Costs

A solution is presented for the problem of determining the sequence in which a set of manufacturing operations should be carried out in order to minimize in-process inventory costs while meeting a variety of technological constraints. Both strict precedence constraints and contiguity constraints are considered, the latter dealing with the requirement that certain sets of operations be performed contiguously (but without specification of any order).

The influence of low-density granite bodies on extensional basins

The Carboniferous North Pennine Basin remains the type locality for the ‘block and basin’ tectonic framework model. It has been widely believed that during periods of tectonic extension, large low-density bodies within the basement permit buoyant blocks to resist isostatic subsidence. However, lithosphere-scale structural and geodynamic modelling experiments dispute this; suggesting instead that the formation of intra-basinal highs occurs prior to lithospheric extension. In northern England, this poorly understood tectonic framework is controlled by a combination of tectonic stress, the buoyancy forces of low-density granite, lithospheric flexure and, importantly, the inherited structural framework. It is hoped that further study can lead to a greater appreciation of the interplay of structural and geodynamic process that control the ‘block and basin’ framework