Results of the worst-case analysis for some scheduling problem

The paper deals with the permutation flow-shop problem with the mean flow time criterion. This problem has obtained considerable attention, chiefly due to its industrial applications. Since the problem is NP-hard for two and more than two machines, a lot of approximation algorithms have been developed to provide a good solution in a quick time. Performance of each of these algorithms can be examined analytically (worst-case analysis, probabilistic analysis) or experimentally (computer tests on random instances). Most of the known approximation algorithms recommended for this problem have the worst-case performance ratio equal the number of jobs n. The best such the ratio, equal the number of machines m, have been found for an extension of the well-known SPT rule to m-machine flow-shop. We propose a new algorithm with the worst-case performance ratio upper bound [m/2]ρ, where ρ is the worst-case performance ratio of an algorithm which solves the auxiliary two-machine problem