We show that certain twisting deformations of a family of supersolvable groups are simple as Hopf algebras. These groups are direct products of two generalized dihedral groups. Examples of this construction arise in dimensions 60 and pq, for prime numbers p, q with q|p − 1. We also show that certain twisting deformation of the symmetric group is simple as a Hopf algebra. On the other hand, we p...

The Vehicle Routing Problem (VRP) is one of the most studied topics in Operations Research. Among numerous variants VRP, this research addresses VRP with relaxed priority rules (VRP-RPR) which customers are assigned to several groups and highest priorities typically need be served before lower ones. Additional used control trade-off between cost efficiency. We propose a Mixed Integer Linear Pro...