Minimizing the Total Completion Time of Jobs for a Permutation Flow-Shop System

The paper considers the problem of minimizing the sum of completion times in a permutation flow-shop system. It is known that the problem under consideration cannot be approximated in polynomial within arbitrarily good precision (the problem belongs to the APX-hard class). The problem is common in some manufacturing environments and for information processing systems. The proposed approach is based on the concept of solvable class of systems, for which an optimal scheduling algorithm of polynomial complexity exists. The paper presents the results of a computational experiment using Taylard's tests for pipeline-type systems and for systems defined by an acyclic graph.