We study the parallel machine scheduling problem with release dates and we consider several “min-sum” objective functions including total weighted tardiness, total tardiness, total weighted completion time and total completion time. We describe several lower bounds for these problems, most of them being original ones. We provide experimental results to compare these lower bounds according to th...

We consider a general class of multiprocessor shop scheduling problems, preemptive or nonpreemptive, with precedence constraints between operations, with job or operation release dates, and with a class of objective functions including weighted sums of job, operations and stage completion times. We present a general approximation method combining a linear programming relaxation in the operation...

This paper is devoted to the investigation of weighted mean topological dimension in dynamical systems. We show that not larger than metric dimension, which generalizes classical result Lindenstrauss and Weiss [16] . also establish relationship between entropy systems, indicates each system with finite or small boundary property has zero dimension.