New efficient lower bound for the Hybrid Flow Shop Scheduling Problem with Multiprocessor Tasks

Abstract

In this paper, we address the hybrid flow shop scheduling problem with multiprocessor tasks. The objective is to minimize the maximum completion time. This problem is encountered in manufacturing, parallel and distributed computing, and real-time machine vision systems. This problem is strongly NP-hard, and consequently, several heuristics and meta heuristics were proposed in the literature in order to provide a near optimal solution. Assessing the performance of these heuristics requires efficient lower bounds. Surprisingly, few lower bounds with moderate performance were proposed. Because of this reason, we propose in this paper a new efficient destructive lower bound. This lower bound is based on the concept of revisited energetic reasoning, which is basically a feasible test with window time adjustments. The efficiency of the proposed lower bound is assessed throughout an extensive computational experiments conducted on a benchmark of 2,100 instances with up to ten centers. The numerical results provide evidence that the proposed lower bound consistently improves the best existing ones.