A Worst-case Performance of the Shortest-processing-time Heuristic for Single Machine Scheduling

This paper analyses a worst-case performance of the shortest-processing-time (SPT) heuristic in minimizing a quadratic function of job lateness for single machine scheduling. A sufficient condition on processing-plus-wait due dates is found for the SPT sequence to be optimal. A worst-case lower bound to the optimal solution is derived from the SPT sequence. It is then shown that the SPT sequence is asymptotically optimal. Extensive computational experiments suggest that the SPT heuristic may be a good choice for just-in-time production.