Bounds for the position of the smallest job in completion time variance minimization

The problem of scheduling jobs on a single machine so as to minimize the variance of job completion times is considered. We develop bounds on the position of the smallest job in an optimal sequence, which is vital due to the fact that an optimal sequence is necessarily a V-shaped sequence. Results of numerical experimentation indicate that the bounds are very effective if the job processing times are homogeneous. Using these bounds, we develop a new heuristic method to solve the problem. Based on numerical investigation, it is shown that performance of this heuristic compares favorably with existing but older heuristics.