Development of lower bounds for the scheduling of setup tasks in serial production lines

Efficient production resettings are necessary to achieve production flexibility. For this reason, it is of primary importance to reduce the setup time required to switch the production from one product type to another, and more generally to minimise the loss of production during these resetting phases. In this paper, we investigate the problem of scheduling operations within a production resetting that arises at the ball bearing factories of the SKF group. In the case of full serial production lines, improving the setup times amount to minimising the time spent prior to restarting production. We show that the problem of scheduling operations within a production resetting can be modelled as an unrelated parallel machine scheduling problem, and we propose several lower bounds. The first one is an extension of the improved energetic reasoning to the unrelated parallel machine problem. The second one is based on a preemptive relaxation that includes valid inequalities. We report the results of computational experiments that were carried out on both industrial and generated instances and that provide evidence of the efficacy of the proposed lower bounds. [Received 1 June 2010; Revised 31 October 2010; Revised 9 June 2011; Revised 11 October 2011; Accepted 20 January 2012]