Performance guarantees for flowshop heuristics to minimize makespan

This paper reviews the known worst-case ratios and absolute performance guarantees of various flowshop heuristics to minimize makespan. The absolute and worst-case performance ratio bounds are compared using probabilistic analysis. The best absolute performance bound is shown to outperform the tightest worst-case ratio bound with 99% probability when a certain minimum number of jobs is present. Thus, probabilistic analysis may provide a bridge between the absolute and worst-case performance guarantees of heuristic algorithms.