A heuristic for the two-machine open-shop scheduling problem with transportation times

The paper considers a problem of scheduling n jobs in a two-machine open shop to minimize the makespan, provided that preemption is not allowed and the interstage transportation times are involved. This problem is known to be unary NP-hard. We present an algorithm that requires O (n log n) time and provides a worst-case performance ratio of 3/2.

Proportionate flow shop with controllable processing times

This paper considers a special class of flow-shop problems, known as the proportionate flow shop. In such a shop, each job flows through the machines in the same order and has equal processing times on the machines. The processing times of different jobs may be different. It is assumed that all operations of a job may be compressed by the same amount which will incur an additional cost. The objective is to minimize the makespan of the schedule together with a compression cost function which is non-decreasing with respect to the amount of compression. For a bicriterion problem of minimizing the makespan and a linear cost function, an O(n log n) algorithm is developed to construct the Pareto optimal set. For a single criterion problem, an O(n2) algorithm is developed to minimize the sum of the makespan and compression cost. Copyright © 1999 John Wiley & Sons, Ltd.

The collection and analysis of pre-evacuation times derived from evacuation trials and their application to evacuation modelling

This paper presents data relating to occupant pre-evacuation times from university and hospital outpatient facilities. Although the two occupancies are entirely different, they do employ relatively similar procedures: members of staff sweep areas to encourage individuals to evacuate.However the manner in which the dependent population reacts to these procedures is quite different. In the hospital case, the patients only evacuated once a member of the nursing staff had instructed them to do so, while in the university evacuation, the students were less dependent upon the actions of the staff, with over 50% of them evacuating with no prior prompting. In addition, the student pre-evacuation time was found to be dependent on their level of engagement in various activities.

The collection of pre-evacuation times from evacuation trials involving a Hospital Outpatient area and a University Library facility

This paper presents data relating to occupant pre-evacuation times from a university and a hospital outpatient facility. Although the two structures are entirely different they do employ relatively similar procedures: members of staff sweeping areas of the structure to encourage individuals to evacuate. However, the manner in which the dependent population reacts to these procedures is quite different. In the hospital case the patients only evacuated once a member of the nursing staff had instructed them to do so while in the university evacuation the students were less dependent upon the actions of the staff with over 50% of them evacuating with no prior prompting. Although this data may be useful in a variety of areas, it was collected primarily for use within evacuation models.

Pre-emptive scheduling problems with controllable processing times

We consider a range of single machine and identical parallel machine pre-emptive scheduling models with controllable processing times. For each model we study a single criterion problem to minimize the compression cost of the processing times subject to the constraint that all due dates should be met. We demonstrate that each single criterion problem can be formulated in terms of minimizing a linear function over a polymatroid, and this justifies the greedy approach to its solution. A unified technique allows us to develop fast algorithms for solving both single criterion problems and bicriteria counterparts.

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.

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.

Fast divide-and-conquer algorithms for preemptive scheduling problems with controllable processing times - a polymatroid optimization approach

We consider a variety of preemptive scheduling problems with controllable processing times on a single machine and on identical/uniform parallel machines, where the objective is to minimize the total compression cost. In this paper, we propose fast divide-and-conquer algorithms for these scheduling problems. Our approach is based on the observation that each scheduling problem we discuss can be formulated as a polymatroid optimization problem. We develop a novel divide-and-conquer technique for the polymatroid optimization problem and then apply it to each scheduling problem. We show that each scheduling problem can be solved in $ \O({\rm T}_{\rm feas}(n) \times\log n)$ time by using our divide-and-conquer technique, where n is the number of jobs and Tfeas(n) denotes the time complexity of the corresponding feasible scheduling problem with n jobs. This approach yields faster algorithms for most of the scheduling problems discussed in this paper.

Schedules with due-date assignment and position-dependent processing times

Single machine scheduling problems are considered, in which the processing of jobs depend on positions of the jobs in a schedule and the due-dates are assigned either according to the CON rule (a due-date common to all jobs is chosen) or according to the SLK rule (the due-dates are computed by increasing the actual processing times of each job by a slack, common to all jobs). Polynomial-time dynamic programming algorithms are proposed for the problems with the objective functions that include the cost of assigning the due-dates, the total cost of disgarded jobs (which are not scheduled) and, possibly, the total earliness of the scheduled jobs.

[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.

The UK WTC 9/11 evacuation study: an overview of the methodologies employed and some analysis relating to fatigue, stair travel speeds and occupant response times

This paper briefly describes the methodologies employed in the collection and storage of first-hand accounts of evacuation experiences derived from face-to-face interviews with evacuees from the World Trade Center (WTC) Twin Towers complex on 11 September 2001 and the development of the High-rise Evacuation Evaluation Database (HEED). The main focus of the paper is to present an overview of preliminary analysis of data derived from the evacuation of the North Tower.

Single machine scheduling and due date assignment with positionally dependent processing times

We consider single machine scheduling and due date assignment problems in which the processing time of a job depends on its position in a processing sequence. The objective functions include the cost of changing the due dates, the total cost of discarded jobs that cannot be completed by their due dates and, possibly, the total earliness of the scheduled jobs. We present polynomial-time dynamic programming algorithms in the case of two popular due date assignment methods: CON and SLK. The considered problems are related to mathematical models of cooperation between the manufacturer and the customer in supply chain scheduling.

Preemptive scheduling on uniform parallel machines with controllable job processing times

In this paper, we provide a unified approach to solving preemptive scheduling problems with uniform parallel machines and controllable processing times. We demonstrate that a single criterion problem of minimizing total compression cost subject to the constraint that all due dates should be met can be formulated in terms of maximizing a linear function over a generalized polymatroid. This justifies applicability of the greedy approach and allows us to develop fast algorithms for solving the problem with arbitrary release and due dates as well as its special case with zero release dates and a common due date. For the bicriteria counterpart of the latter problem we develop an efficient algorithm that constructs the trade-off curve for minimizing the compression cost and the makespan.

Metaphors and metamorphoses: narratives of identity during times of crisis

The narrative of transformative crisis appears in both autobiographical and fictional accounts of individual lives; it typically involves a difficult or traumatic episode and a period of self-questioning out of which a person emerges more able and more emotionally mature than before (Booker, 2005; Erikson, 1968; Tedeschi and Calhoun, 1995). The present study used interviews to elicit 22 narratives about crises experienced between the ages of 25 and 40, and about any developmental transformation and change that surrounded these crises. Analysis revealed a common four-phase process to the crisis episodes, common metaphors and recurrent descriptions of identity metamorphosis, ie. of ‘becoming a new person’. Comparison of these findings with theory on fictional plots shows a clear parallel between the four-phase process of crisis found in the current study and the ‘rebirth’ plot described by Booker (2005). The theoretical significance of these findings and interpretations is discussed.