Journal of Intelligent Manufacturing manuscript No. (will be inserted by the editor) A variable neighborhood descent heuristic for the problem of makespan minimisation on unrelated parallel machines with setup times Krzysztof Fleszar · Christoforos Charalambous · Khalil S. Hindi Received: date / Accepted: date Abstract The NP-hard problem of scheduling jobs on unrelated parallel machines, in the presence of machine-dependent and sequence-dependent setup times, with the objective of minimizing the makespan, is considered. A variable neighborhood descent search algorithm, hybridized with mathematical programming elements, is presented and its performance is evaluated on a large set of benchmark problem instances. The extensive computational experiments show that the proposed algorithm outperforms previously proposed methods in terms of solution quality as well as computation time. Keywords parallel machine scheduling, hybrid optimization, neighborhood search, makespan minimization, mixed-integer programming This research has been supported by the Cyprus Research Promotion Foundation (Project TEXNO/0603/08 - NETEXNOPRO). Krzysztof Fleszar American University of Beirut (AUB) Olayan School of Business P.O. Box 11-0236, Riad El Solh Beirut 1107 2020, Lebanon E-mail: kfleszar@gmail.com E-mail: kf09@aub.edu.lb Christoforos Charalambous Frederick University Department of Computer Science and Engineering P.O. Box 24729 1303 Nicosia, Cyprus Tel.: +357 22431355 ext. 116 Fax: +357 22438234 E-mail: c.charalambous@frederick.ac.cy Khalil S. Hindi American University of Beirut (AUB) Olayan School of Business P.O. Box 11-0236, Riad El Solh Beirut 1107 2020, Lebanon E-mail: khalil.hindi@aub.edu.lb