Optimal Assignment of Total-work-content Due-dates and Sequencing in a Single-machine Shop

This paper considers the problem of optimal assignment of total-work-content due-dates to n jobs and of sequencing them on a single machine to minimize an objective function depending on the assigned due-date multiple value and maximum tardiness penalty. It is shown that both the earliest due-date and shortest processing time orders yield an optimal sequence. A simple analytical solution method is presented to find the optimal due-dates. After the theoretical treatment an illustrative example is presented for discussion.     

Fractal landscapes in biological systems: long-range correlations in DNA and interbeat heart intervals

Here we discuss recent advances in applying ideas of fractals and disordered systems to two topics of biological interest, both topics having common the appearance of scale-free phenomena, i.e., correlations that have no characteristic length scale, typically exhibited by physical systems near a critical point and dynamical systems far from equilibrium. (i) DNA nucleotide sequences have traditionally been analyzed using models which incorporate the possibility of short-range nucleotide correlations. We found, instead, a remarkably long-range power law correlation. We found such long-range correlations in intron-containing genes and in non-transcribed regulatory DNA sequences as well as intragenomic DNA, but not in cDNA sequences or intron-less genes. We also found that the myosin heavy chain family gene evolution increases the fractal complexity of the DNA landscapes, consistent with the intron-late hypothesis of gene evolution. (ii) The healthy heartbeat is traditionally thought to be regulated according to the classical principle of homeostasis, whereby physiologic systems operate to reduce variability and achieve an equilibrium-like state. We found, however, that under normal conditions, beat-to-beat fluctuations in heart rate display long-range power law correlations.