Flow shop scheduling with flexible processing times

In numerous flow shop variants, the processing times of the operations are not fixed in advance, but may be distributed with some flexibility among the machines. In this paper, we introduce a general model which is expressive enough to cover several models from the literature. While in most cases it is NP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {NP}$$\end{document}-hard to find a job permutation and a corresponding distribution of processing times minimizing the makespan, we show that for a fixed job permutation a best processing time distribution can be calculated in polynomial time by linear programming. Based on this, we propose a tabu search procedure using the set of all job permutations as search space. In a computational study, we show the power of the new model. Besides the classical permutation flow shop environment, we study variants with blocking, no-wait and synchronous movement constraints.