Abstract: In this paper,we consider the delays problems in single resource scheduling with compressible processing time.A heuristic algorithm is provided on the basis of reverse critical path and a set of tasks needing compression is picked up,when a delay task occurs in the process of scheduling tasks,with the objective of minimum length of delay time,and minimum number of compressed tasks.At the end,the validity of the heuristic is proved and an experimental result is showed.

Key words: compressible processing time, single resource scheduling, delays, critical procedure