In this paper a single machine time-dependent scheduling problem with total completion time criterion is considered. There are given n jobs J1,…,Jn and the processing time pi of the ith job is given by pi=a+bisi, where si is the starting time of the ith job (i=1,…,n),bi is its deterioration rate and a is the common base processing time. If all jobs have deterioration rates different and not smaller than a certain constant u>0,...

A problem of scheduling deteriorating jobs on a single processor is considered. The processing time of a job is given by a function pi=ai+bisi, where si is the starting time of the job, ai>=0, bi>=0, for i=1,...,n. Jobs are non-preemptive and independent and there are neither ready times nor deadlines. The goal is to minimize the total weighted completion time. We show how to employ the concept of non-dominated schedules to construct...

The Clairvoyant algorithm proposed in “A novel MPI reduction algorithm resilient to imbalances in process arrival times” was analyzed, commented and improved. The comments concern handling certain edge cases in the original pseudocode and description, i.e., adding another state of a process, improved cache friendliness more precise complexity estimations and some other issues improving the robustness of the algorithm implementation....