Improved bounds for hybrid flow shop scheduling with multiprocessor tasks

• We investigate the problem of minimizing makespan in a hybrid flow shop with multiprocessor tasks.
• We propose a new discrepancy search method that is based on adjacent discrepancies.
• We describe a new lower bound that is based on the concept of dual feasible functions.
• The proposed lower and the upper bounds consistently outperform the best existing ones.

In this paper, we investigate the problem of minimizing makespan in a multistage hybrid flow-shop scheduling with multiprocessor tasks. To generate high-quality approximate solutions to this challenging NP-hard problem, we propose a discrepancy search heuristic that is based on the new concept of adjacent discrepancies. Moreover, we describe a new lower bound based on the concept of dual feasible functions. The proposed lower and upper bounds are assessed through computational experiments conducted on 300 benchmark instances with up to 100 jobs and 8 stages. For these instances, we provide evidence that the proposed bounds consistently outperform the best existing ones. In particular, the proposed heuristic successfully improved the best known solution of 75 benchmark instances.