Scheduling to minimize average completion time: off-line and on-line approximation algorithms
Mathematics of Operations Research
Online computation and competitive analysis
Online computation and competitive analysis
Approximation Techniques for Average Completion Time Scheduling
SIAM Journal on Computing
Information Processing Letters
Online Scheduling of a Single Machine to Minimize Total Weighted Completion Time
Mathematics of Operations Research
Minimizing the total completion time on-line on a single machine, using restarts
Journal of Algorithms
On-line scheduling of parallel machines to minimize total completion times
Computers and Operations Research
Approximation algorithms for scheduling problems with a modified total weighted tardiness objective
Operations Research Letters
A class of on-line scheduling algorithms to minimize total completion time
Operations Research Letters
On-line scheduling to minimize average completion time revisited
Operations Research Letters
| Hi-index | 5.23 |
We consider online scheduling problems to minimize modified total tardiness. The problems are online in the sense that jobs arrive over time. For each job J"j, its processing time p"j, due date d"j and weight w"j become known at its arrival time (or release time) r"j. Preemption is not allowed. We first show that there is no finite competitive ratio for problem 1|online,r"j,d"j|@?w"jT"j. So we focus on problem 1|online,r"j,d"j|@?w"j(T"j+d"j) and show that D-SWPT (Delayed Shortest Weighted Processing Time) algorithm is 3-competitive. We further study two problems 1|online,r"j,d"j,h(1),res|@?w"j(T"j+d"j) and 1|online,r"j,d"j,h(1),N-res|@?w"j(T"j+d"j), where res and N-res denote resumable and non-resumable models respectively, and h(1) denotes a non-available time interval [s,@as] with s0 and @a=1. We give a lower bound of 1+@a for both problems and prove that M-D-SWPT (Modified D-SWPT) is 3@a and 6@a-competitive in the resumable and non-resumable models, respectively. Moreover, we extend the upper bounds to the scenario of parallel machine scheduling with uniform job weight and an assumption that all machines have the same non-available time interval [s,@as]. A lower bound of min{@a,1+@am} is given as well for the scenario.