Heuristics for the mixed no-idle flowshop with sequence-dependent setup times and total flowtime criterion

Abstract

This paper addresses the mixed no-idle flowshop scheduling problem with sequence-dependent setup times and total flowtime minimisation. In the mixed no-idle flowshop problem, machines that allow idleness coexist with stages that require uninterrupted processing. We studied an extension of this problem, which considers sequence-dependent setup times in machines where idleness is allowed. We present a mixed integer linear programming (MILP) model for the new problem. We also provide a method to evaluate the total flowtime of a permutation sequence. Furthermore, an acceleration method to calculate the total flowtime in an insertion neighbourhood is proposed. A new set of efficient heuristics were developed. In order to evaluate the proposed methods we adapted the best known heuristics available from related problems. The adapted heuristics, as well as the methods proposed here, were tested and compared through statistical and computational experimentation in an extensive benchmark with 4500 instances. We also compared the proposed heuristics with the optimal solutions found by the MILP formulation for small sized problems instances. The results demonstrate that the proposed heuristics perform extremely well in terms of solution quality and computational efficiency.