A New Improvement of the NEH Heuristic to Either Minimise Total Tardiness or Makespan for a Hybrid Flow Shop with Assembly Operations

Abstract

This paper proposes a new improvement of the NEH heuristic named I-NEH to solve a hybrid flow shop scheduling problem with assembly operations and unrelated parallel machines. The objective was to either minimise total tardiness or makespan. The novelty of I-NEH was to integrate two features into the original NEH heuristic, by applying four rules to break a tie in the machine selection process, and applying either total tardiness or makespan, to break a tie in a job insertion process. There were three main steps for I-NEH. The first step was to schedule jobs by a dispatching rule. The second step was to apply the job insertion and the machine selection processes iteratively. The last step was to apply the forward heuristic in order to reduce the earliness and flow time, whereas the total tardiness obtained from the first two steps must be maintained. Exhaustive experiments were conducted to evaluate the efficiency of I-NEH through the average relative percentage deviation index (ARPD). For the case studies, the results showed that I-NEH outperformed the dispatching rules that have been proven previously to obtain good solutions, with ARPD values of 34.46% for total tardiness and 17.43% for makespan. In addition, the proposed I-NEH heuristic reduced the maximum tardiness with the ARPD value of 19.84% when the objective was to minimise total tardiness, and the computational time of I-NEH was within a reasonable range.