A polynomial algorithm for the three-machine open shop with a bottleneck machine

The paper considers the three‐machine open shop scheduling problem to minimize themakespan. It is assumed that each job consists of at most two operations, one of which is tobe processed on the bottleneck machine, the same for all jobs. A new lower bound on theoptimal makespan is derived, and a linear‐time algorithm for finding an optimalnon‐preemptive schedule is presented.

Heuristics for the two-stage job shop scheduling problem with a bottleneck machine

The paper considers the job shop scheduling problem to minimize the makespan. It is assumed that each job consists of at most two operations, one of which is to be processed on one of m⩾2 machines, while the other operation must be performed on a single bottleneck machine, the same for all jobs. For this strongly NP-hard problem we present two heuristics with improved worst-case performance. One of them guarantees a worst-case performance ratio of 3/2. The other algorithm creates a schedule with the makespan that exceeds the largest machine workload by at most the length of the largest operation.

An open shop scheduling problem with a non-bottleneck machine

This paper considers the problem of processing n jobs in a two-machine non-preemptive open shop to minimize the makespan, i.e., the maximum completion time. One of the machines is assumed to be non-bottleneck. It is shown that, unlike its flow shop counterpart, the problem is NP-hard in the ordinary sense. On the other hand, the problem is shown to be solvable by a dynamic programming algorithm that requires pseudopolynomial time. The latter algorithm can be converted into a fully polynomial approximation scheme that runs in time. An O(n log n) approximation algorithm is also designed whi finds a schedule with makespan at most 5/4 times the optimal value, and this bound is tight.

Two-stage open shop scheduling with a bottleneck machine

It is known that for the open shop scheduling problem to minimize the makespan there exists no polynomial-time heuristic algorithm that guarantees a worst-case performance ratio better than 5/4, unless P6≠NP. However, this result holds only if the instance of the problem contains jobs consisting of at least three operations. This paper considers the open shop scheduling problem, provided that each job consists of at most two operations, one of which is to be processed on one of the m⩾2 machines, while the other operation must be performed on the bottleneck machine, the same for all jobs. For this NP-hard problem we present a heuristic algorithm and show that its worst-case performance ratio is 5/4.

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.