Bin Packing Problems with Variable Pattern Processing Times: A Proof-of-concept

In several real-world applications the time required to accomplish a job generally depends on the number of tasks that compose it. Although the same also holds for packing (or cutting) problems when the processing time of a bin depends by the number of its items, the approaches proposed in the literature usually do not consider variable bin processing times and therefore become inaccurate when time costs are worth more than raw material costs. In this paper we discuss this issue by considering a variant of the one-dimensional bin packing problem in which items are due by given dates and a convex combination of number of used bins and maximum lateness has to be minimized. An integer linear program that takes into account variable pattern processing times is proposed and used as proof-of-concept

Assessment of the bone quality of black male athletes using calcaneal ultrasound: a cross-sectional study

<p>Abstract</p> <p>Background</p> <p>Lifestyle, genetics and environmental factors are established determinants of bone density. We aimed to describe the bone characteristics of competitive top-ranked Nigerian male athletes using calcaneal ultrasound and to assess whether intensive training promotes higher bone density in an environment with reportedly low calcium intake; to compare the bone characteristics of footballers with runners and other sportsmen; and to assess the correlation of stiffness index (SI) with activity level, since energy expenditure correlates with length of training and by extension, magnitude of skeletal loading.</p> <p>Methods</p> <p>We recruited 102 male athletes: these included football (n = 68), running (n = 15), handball (n = 7), taekwando (n = 6), cycling (n = 2), judo (1), badminton (1) and high jump (1). Anthropometric data were first recorded on a structured form and energy expenditure was indirectly estimated with a validated questionnaire. Bone density was assessed using the Lunar Achilles+ calcaneal ultrasonometer.</p> <p>Results</p> <p>The mean age of athletes was 25 ± 6 years. The means of BMI and energy expenditure were 21.9 ± 2.0 kg/m²and 35.0 ± 13.7 kcal/kg/day, respectively. Footballers were younger (p < 0.001) and heavier (p < 0.001) than runners. Football was a significant determinant of BUA independent of age, BMI and energy expenditure (p = 0.001). Football was also a significant determinant of SOS independent of age, height, weight and BMI (p < 0.001). The mean SI was 127 ± 16 and the median T-score was 0.82 (-1.88, 3.35). The mean SI of footballers (130 ± 15), runners (130 ± 12) and other sportsmen (115 ± 18) differed significantly (p = 0.001). Multivariate analyses revealed that football (p < 0.001) and running (p < 0.001) were significant determinants of SI independent of age and BMI. Footballers when compared with other sportsmen had a higher mean SI independent of age and BMI (p < 0.001). Age was not correlated with SI. The median T-score of footballers, 0.94 (-1.0, 3.35) was higher than that of other sportsmen.</p> <p>Conclusion</p> <p>Repetitive skeletal loading at the heel has the potential to improve bone density in black male athletes. The magnitude of increase may be higher in medium impact sports such as soccer and running compared with low or non-impact sports such as judo or taekwando, and is independent of age and BMI. However, future longitudinal data will be required to support our observations.</p