In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series numbers. The mean, or Kolmogorov–Nagumo generalizes the classical mean and appears in many disciplines, from information theory to physics, economics traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introd...

The problem of scheduling jobs that arrive over time on a single machine is well-studied. We study the preemptive model and the model with restarts. We provide lower bounds for deterministic and randomized algorithms for several optimality criteria: weighted and unweighted total completion time, and weighted and unweighted total ow time. By using new techniques, we provide the rst lower bounds ...

This paper presents a review of single machine scheduling to minimize the weighted number of tardy jobs. The problem involves processing n jobs on a single machine, each having processing time pj and due date dj . The aim is to schedule the jobs to meet their due date. A job is tardy if the completion time of job j is Cj > dj and on-time otherwise. This paper assesses works done to minimize the...

We consider a stochastic online scheduling environment, where jobs with stochastic processing requirements arrive over time and the objective is to minimize the total weighted completion time. We show that any nondelay algorithm is asymptotically optimal for the stochastic online single machine, flow shop and uniform parallel machine problems under some mild assumptions.