Approximation Algorithms For Rescheduling Problem On A Single Machine With Different Release Time

In recent years, rescheduling has attracted a amount of research attention.this paper considers scheduling problems where the processing of a set of jobs has been optimally scheduled by using some principle to minimize a classical cost objec-tive,however,the availability of a subset of the jobs is delayed to some time.Therefore, the decision maker needs to adjust the existing schedule to allow for the initial u-navailability of those jobs,but without causing excessive disruption to the optimal schedule to make the objective minimize.The objective function of the problem of this paper is classical sum of weighted completion times. Nicholas G.Hall and Chris N.Potts provides a dynamic program-ming algorithm TWCOA of which the complexity is pseudo polynomial time and its proof is given, then they give the approximation algorithms GAA, the worst-case performance ratio is 2. This paper improves the approximation algorithms GAA and get the approximation algorithms SR and the proof of its worst-case performance ratio less than GAA’s is given. At the same time,we expand the question to be more general,replacing common one release time of rescheduling jobs in the conditions of the problem with two different release time and give the problem an approximation algorithms SRT.