Total Late Work Research Articles

Approximation algorithms for scheduling a single machine to minimize total late work

In the problem of scheduling a single machine to minimize total late work, there are n jobs to be processed, each of which has an integer processing time and an integer due date. The objective is to find a sequence of jobs which minimizes the total late work, where the late work for a job is the amount of processing of this job that is performed after its due date. Three families of approximation algorithms { E k }, { A ε } and { B ε } are presented. Contained in the first family is a (1 + 1/ k)-approximation algorithm E k , for any positive integer k ≤ n, which uses truncated enumeration; E k requires O( n k + 1 ) time and O( n) space. The two other families { A ε } and B ε } are fully polynomial approximation schemes which are based on the rounding of state variables in dynamic programming formulations. In the superior scheme, for 0 ⩽ ε ⩽ 1, B ε si a (1 + ε)-approximation algorithm which has a time requirement of O( n 2 / ε) and a space requirement of O( n / ε).