Most deterministic machine scheduling models assume that the processing time of a job on a machine is fixed externally and known in advance of scheduling. However, in most realistic situations, apart from the machines, it requires additional resources to process jobs, and the processing time of a job is determined internally by the amount of the resources allocated. In these situations, both th...

Harrington and Soare introduced the notion of an n-tardy set. They showed that there is a nonempty E property Q(A) such that if Q(A) then A is 2tardy. Since they also showed no 2-tardy set is complete, Harrington and Soare showed that there exists an orbit of computably enumerable sets such that every set in that orbit is incomplete. Our study of n-tardy sets takes off from where Harrington and...

We consider the solution of some NP-hard parallel machine scheduling problems involving minimization weighted or unweighted number tardy jobs. first show that these cannot be approximated in polynomial time. Then we propose exponential-time approximation algorithms and fixed parameter tractable exact to solve them.

Background. In setting a problem of minimizing total weighted tardiness by the heuristic based on remaining available and processing periods, there are two opposite ways to input data: job release dates given in either ascending or descending order. It was recently ascertained that scheduling few equal-length jobs is expectedly faster order, whereas 30 70 1.5 % 2.5 For number between roughly 90...