Intl. Trans. in Op. Res. 00 (2017) 1–18 DOI: 10.1111/itor.12421 INTERNATIONAL TRANSACTIONS IN OPERATIONAL RESEARCH Enhanced lower bounds and exact procedures for total completion time minimization in a two-machine permutation flowshop with release dates Mehdi Mrad a , Sabrine Chalghoumi b , Talel Ladhari b,c,d and Anis Gharbi a a Industrial Engineering Department, King Saud University, Riyadh, Saudi Arabia b University of Tunis, BADEM, Bir El Kassaa, 2059 Tunis, Tunisia c Ecole Suprieure des Sciences Economiques et Commerciales de Tunis, Universit de Tunis, 1089 Montfleury, Tunis, Tunisia d Department of Business Administration, College of Business Management at Umm Al-Qura University, Mecca, Saudi Arabia E-mail: mmrad@ksu.edu.sa [Mrad]; chalghoumisabrine@yahoo.fr [Chalghoumi]; talel_ladhari2004@yahoo.fr [Ladhari]; a.gharbi@ksu.edu.sa [Gharbi] Received 31 August 2016; received in revised form 28 March 2017; accepted 30 March 2017 Abstract We consider the problem of minimizing the sum of completion times in a two-machine permutation flowshop subject to release dates. New procedures are proposed for effectively bounding the completion time of a given job that is processed at a given position. New assignment-based lower bounds are derived as well as an enhanced mathematical programming formulation. Our computational analysis shows a consistent tightness of the proposed lower bounds and a high outperformance of the enhanced mathematical formulation with respect to the classical one. Keywords: flowshop; total completion time; release date; lower bounds; mixed-integer linear programming 1. Introduction We consider minimizing the total completion time in a two-machine permutation flowshop schedul- ing problem with release dates. The studied problem can be described as follows: let J ={1, 2, ....n} be a set of n jobs to be processed on two machines M 1 and M 2 . Each job must be processed during p 1, j time units on machine M 1 , then during p 2, j time units on machine M 2 . Job j cannot start processing on machine M 1 before a release date r j . No more than one job can be processed on any machine at a time. Both machines are continuously available from time zero. The order by which the jobs are processed on any machine is identical (permutation) and is not known. The objective is to find a nonpreemptive schedule that minimizes the total completion time. According to the three-field notation of Pinedo (2012), this strongly NP-hard problem is denoted by F 2|r j , prmu| ∑ C j . C  2017 The Authors. International Transactions in Operational Research C  2017 International Federation of Operational Research Societies Published by John Wiley & Sons Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main St, Malden, MA02148, USA.