Optim Lett DOI 10.1007/s11590-014-0741-y ORIGINAL PAPER Exact resolution of the two-stage hybrid flow shop with dedicated machines Hatem Hadda · Najoua Dridi · Sonia Hajri-Gabouj Received: 7 May 2013 / Accepted: 20 March 2014 © Springer-Verlag Berlin Heidelberg 2014 Abstract In this paper we introduce a branch and bound algorithm for the two- stage hybrid flow shop problem with dedicated machines. An elimination rule is used to enhance the algorithm’s performances. Experimental results show that big size instances are solved and that the elimination rule contributed to discard up to 50 % of the nodes. We also propose an empirical analysis of the makespan distribution for small sizes instances. Keywords Scheduling · Hybrid flow shop · Dedicated machines · Branch and bound · Elimination rule 1 Introduction This paper, considers a two-stage hybrid flow shop problem composed by a single machine M 0 on the first stage and m dedicated machines M k , k ∈{1,..., m}, on the second stage. The problem consists on scheduling n jobs belonging to m disjoint types T k , k ∈{1,..., m}. Each job consists of a sequence of two operations. The first operation of all jobs must be performed on machine M 0 . The second operation must be processed on M k if the job is of type T k (k ∈{1,..., m}). Each machine processes only one job at a time, and each job is processed by at most one machine at a time. The objective is to minimize the maximum completion time, i.e. makespan (noted C max ). H. Hadda (B ) · S. Hajri-Gabouj LISI, INSAT-Tunis, Centre Urbain Nord B.P. N676, 1080 Tunis Cedex, Tunisia e-mail: hatem.hadda@esti.rnu.tn S. Hajri-Gabouj e-mail: sonia.gabouj@insat.rnu.tn N. Dridi Unité de Recherche OASIS, ENIT, BP. 37, Le belvédère, 1002 Tunis, Tunisia e-mail: najoua.dridi@enit.rnu.tn 123