We consider the classical online scheduling problem over single and parallel machines with the objective of minimizing total weighted flow time. We employ an intuitive and systematic analysis method and show that the weighted shortest processing time (WSPT) is an optimal online algorithm with the competitive ratio of +1 for the case of single machine, and it is ( +(3/2)−(1/2 ))-competitive for the case of parallel machines ( > 1), where P is the ratio of the longest to the shortest processing time.
Tao et al. REF showed that Weighted shortest processing time is ∆ + 1 and ∆ + -competitive for sum of weighted flow time on single and parallel machines, respectively.
WSPT's Competitive Performance for Minimizing the Total Weighted Flow Time: From Single to Parallel Machines
Mathematical Problems in Engineering
Computer Science