An approximation algorithm for the m-machine permutation flow shop scheduling problem with controllable processing times

Abstract

The paper deals with the m-machine permutation flow shop scheduling problem in which job processing times, along with a processing order, are decision variables. It is assumed that the cost of processing a job on each machine is a linear function of its processing time and the overall schedule cost to be minimized is the total processing cost plus maximum completion time cost. A 4 3 - approximation algorithm for the problem with m = 2 is provided; the best approximation algorithm until now has a worst-case performance ratio equal to 3 2 . An extension to the m-machine ( m ≥2) permutation flow shop problem yields an approximation algorithm with a worst-case bound equal to 1 2 (ϱ + √ϱ(m −1) ) + 1 4 + O(1/ √ϱm) , where ϱ is the worst-case performance ratio of a procedure used, in the proposed algorithm, for solving the (pure) sequencing problem. Moreover, examples which achieve this bound for ϱ = 1 are also presented.