On-line algorithms for single machine scheduling with family setup times

The paper considers an on-line single machine scheduling problem where the goal is to minimize the makespan. The jobs are partitioned into families and a setup is performed every time the machine starts processing a batch of jobs of the same family. The scheduler is aware of the number of families and knows the setup time of each family, although information about a job only becomes available when that job is released. We give a lower bound on the competitive ratio of any on-line algorithm. Moreover, for the case of two families, we provide an algorithm with a competitive ratio that achieves this lower bound. As the number of families increases, the lower bound approaches 2, and we give a simple algorithm with a competitive ratio of 2.

Study of the thermal stress in a Pb-free half-bump solder joint under current stressing

The thermal stress in a Sn3.5Ag1Cu half-bump solder joint under a 3.82×108 A/m2 current stressing was analyzed using a coupled-field simulation. Substantial thermal stress accumulated around the Al-to-solder interface, especially in the Ni+(Ni,Cu)3Sn4 layer, where a maximal stress of 138 MPa was identified. The stress gradient in the Ni layer was about 1.67×1013 Pa/m, resulting in a stress migration force of 1.82×10-16 N, which is comparable to the electromigration force, 2.82×10-16 N. Dissolution of the Ni+(Ni,Cu)3Sn4 layer, void formation with cracks at the anode side, and extrusions at the cathode side were observed