Minimizing total weighted completion time in a proportionate flow shop

We study the special case of the m machine flow shop problem in which the processing time of each operation of job j is equal to pj; this variant of the flow shop problem is known as the proportionate flow shop problem. We show that for any number of machines and for any regular performance criterion we can restrict our search for an optimal schedule to permutation schedules. Moreover, we show that the problem of minimizing total weighted completion time is solvable in O(n2) time. © 1998 John Wiley & Sons, Ltd.

A fully polynomial approximation scheme for the single machine weighted total tardiness problem with a common due date

We develop a fully polynomial-time approximation scheme (FPTAS) for minimizing the weighted total tardiness on a single machine, provided that all due dates are equal. The FPTAS is obtained by converting an especially designed pseudopolynomial dynamic programming algorithm.

An algorithm for total variation inpainting based on nonlinear multi-grid methods

Image inpainting refers to restoring a damaged image with missing information. The total variation (TV) inpainting model is one such method that simultaneously fills in the regions with available information from their surroundings and eliminates noises. The method works well with small narrow inpainting domains. However there remains an urgent need to develop fast iterative solvers, as the underlying problem sizes are large. In addition one needs to tackle the imbalance of results between inpainting and denoising. When the inpainting regions are thick and large, the procedure of inpainting works quite slowly and usually requires a significant number of iterations and leads inevitably to oversmoothing in the outside of the inpainting domain. To overcome these difficulties, we propose a solution for TV inpainting method based on the nonlinear multi-grid algorithm.

Two simple constant ratio approximation algorithms for minimizing the total weighted completion time on a single machine with a fixed non-availability interval

In this note, we consider the scheduling problem of minimizing the sum of the weighted completion times on a single machine with one non-availability interval on the machine under the non-resumable scenario. Together with a recent 2-approximation algorithm designed by Kacem [I. Kacem, Approximation algorithm for the weighted flow-time minimization on a single machine with a fixed non-availability interval, Computers & Industrial Engineering 54 (2008) 401–410], this paper is the first successful attempt to develop a constant ratio approximation algorithm for this problem. We present two approaches to designing such an algorithm. Our best algorithm guarantees a worst-case performance ratio of 2+ε. © 2008 Elsevier B.V. All rights reserved.

The reporting behaviours of student nurses who have experienced verbal abuse

Background: There is evidence that student nurses are vulnerable to experiencing verbal abuse from a variety of sources and under-reporting of verbal abuse is prevalent throughout the nursing profession. The objective of the study is to explore the reporting behaviours of student nurses who have experienced verbal abuse. Method: For this study a definition of verbal abuse was adopted from current Department of Health (England) guidelines. Questionnaires were distributed in 2005 to a convenience sample of 156 third year nursing students from one pre-registration nursing programme in England. A total of 114 questionnaires were returned, giving an overall response rate of 73.0%. Results: Fifty one students (44.7% of responses) reported verbal abuse; all of these completed the section exploring reporting behaviours. The incidents involved patients in thirty three cases (64.7%); eight cases (15.7%) involved visitors or relatives and ten cases (19.6%) involved other healthcare workers. Thirty two students (62.7%) stated that they did report the incident of verbal abuse they experienced and nineteen (37.3%) of respondents reported that they did not. Only four incidents developed from an oral report to being formally documented. There was a statistically significant association (P = 0.003) between the focus of verbal abuse (patient/visitor or colleague) and the respondents reporting practices with respondents experiencing verbal abuse from colleagues less likely to report incidents. Most frequent feelings following experiences of verbal abuse from colleagues were feelings of embarrassment and hurt/shock. Most frequent consequences of experiencing verbal abuse from patients or relatives were feeling embarrassed and feeling sorry for the abuser. When comparing non reporters with reporters, the most frequent feelings of non reporters were embarrassment and hurt and reporters, embarrassment and feeling sorry for the abuser. When considering levels of support after the incident the mean rating score of respondents who reported the incident was 5.40 (standard deviation 2.89) and of those that did not, 4.36 (standard deviation 2.87) which was not statistically significant (p = 0.220). Conclusions: 1. Not documenting experiences of verbal abuse formally in writing is a prevalent phenomenon within the sample studied and reporting practices are inconsistent. 2. Both Higher Education Institutions and health care providers should consider emphasising formal reporting and documenting of incidents of verbal abuse during student nurse training and access to formal supportive services should be promoted. 3. Effective incident reporting processes and analysis of these reports can lead to an increased awareness of how to avoid negative interactions in the workplace and how to deal with incidents effectively.