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.

Probabilistic approach in weighted Markov branching processes

This note provides a new probabilistic approach in discussing the weighted Markov branching process (WMBP) which is a natural generalisation of the ordinary Markov branching process. Using this approach, some important characteristics regarding the hitting times of such processes can be easily obtained. In particular, the closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the process is investigated and the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained. The close link between these newly developed processes and the well-known compound Poisson processes is investigated. It is revealed that any weighted Markov branching process (WMBP) is a random time change of a compound Poisson process.

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.

We could make a meal out of nothing: contested explanations of inequalities in health

This paper reports on the qualitative findings from a comparative study of public health and lifestyles in South East England and Northern France, regions with similar geographic and economic characteristics. Data from health surveys showed that both countries had an increasing BMI with age, particularly in Northern France. This was despite the finding that the percentage eating fresh fruit and vegetable at least five days a week in Northern France increased with age (from well over 50% to over 90%) compared to around 50% to around 75% in South East England. Qualitative data on health inequalities and how they could be addressed were gathered by focus groups sampling from five tiers using the Townsend Index for comparability (14 in England with 106 participants overall; 13 in France with 143 participants). Both had about two thirds women participants, with a preponderance of middle aged and older people. There was a striking difference in the salience of diet between the two countries; in the French data it was raised only 14 times, whereas in England there were 165 occurrences, and these were often distinguished by their use of narrative. Older respondents contrasted the pressures on families today and the expense of fresh fruit and vegetables with their own childhood or childrearing, when cheap meals could be created using skills which have now been lost. These data therefore provide further evidence that providing food is a moral activity.