Weighted completion time minimization on a single-machine with a fixed non-availability interval: Differential approximability

This paper is the first successful attempt on differential approximability study for a scheduling problem. Such a study considers the weighted completion time minimization on a single machine with a fixed non-availability interval. The analysis shows that the Weighted Shortest Processing Time (WSPT) rule cannot yield a differential approximation for the problem under consideration in the general case. Nevertheless, a slight modification of this rule provides an approximation with a differential ratio of $\frac{3?\sqrt{5}}{2}\approx 0.38$.