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.

Health status of an elderly population in Sharpeville, South Africa

The objective of this cross-sectional study was a comprehensive nutrition and health assessment to provide a basis for future intervention strategies for an elderly population attending a day-care centre. Socio-demographic, health and 24-hour recall dietary intake questionnaires were administered and anthropometric and biochemical measurements taken. The results indicate that the majority of respondents had an income of between R501 and R1 000 (South African rand) per month and most of them reported an occasional lack of funds to meet basic household needs, confirming the presence of food insecurity. Daily dietary intakes (mean [+ or -] Standard Deviation [SD]) of the women were 5 395 [+ or -] 2 946 kJ energy, 47 [+ or -] 27 g protein, 28 [+ or -] 21 g fat and 196 [+ or -] 123 g carbohydrates compared to 8 641 [+ or -] 3 799 kJ, 86 [+ or -] 48 g, 49 [+ or -] 32 g and 301 [+ or -] 139 g of the men, respectively. The majority (83.6%) of the women were overweight (body mass index [BMI] [greater than or equal to] 25) or obese (BMI [greater than or equal to] 30) whilst 78% had a mid-upper arm circumference (MUAC) of [greater than or equal to] 21.7 cm. Mean intakes of micronutrients were low in comparison to reference standards and serum zinc levels were suboptimal. Obesity, hypertension and raised total serum cholesterol levels indicated an increased risk for coronary heart disease. It can be concluded that a low income, household food insecurity and risk factors associated with malnutrition and non-communicable diseases were prevalent in this elderly population. OPSOMMING Die doelwit van hierdie dwarssnitstudie was ‘n omvattende bepaling van voeding- en gesondheidstatus om as basis te dien vir toekomstige intervensiestrategieë vir ’n groep bejaardes wat ’n dagsentrum besoek. Sosiodemografiese, gesondheid- en 24-uur herroep-dieetinname vraelyste is voltooi en antropometriese en biochemiese metings is geneem. Die resultate het bevestig dat die meerderheid respondente ‘n maandelikse inkomste van tussen R501 en R1 000 (Suid-Afrikaanse rand) gehad het. Die meeste het ‘n geldtekort vir basiese huishoudelike behoeftes gerapporteer wat dui op huishoudelike voedselinsekuriteit. Daaglikse dieetinnames (gemiddeld±standaardafwyking [SA]) van die vroue was onderskeidelik 5 395±2 946 kJ energie, 47±27 g proteïen, 28±21 g vet en 196±123 g koolhidrate in vergelyking met 8 641±3 799 kJ, 86±48 g, 49±32 g en 301±139 g vir die mans. Die meerderheid (83.6%) van die vroue was oorgewig (liggaamsmassa-indeks [LMI] >25) of vetsugtig (LMI > 30) en 78% het ’n middel-bo-armomtrek (MUAC) van > 21.7 cm gehad. Gemiddelde mikronutriëntinnames was laag in vergelyking met die verwysingstandaarde en serumsink was suboptimaal. Vetsug, hipertensie en verhoogde totale serumcholesterolvlakke het op ‘n verhoogde risiko van kardiovaskulêre siekte gedui. Die resultate het dus bewys dat lae inkomste, huishoudelike voedselinsekuriteit en die risikofaktore wat met wanvoeding en leefstylsiektes geassosieer word, teenwoordig was.