Two new approaches for a two-stage hybrid flowshop problem with a single batch processing machine under waiting time constraint

This paper investigates a two-stage hybrid flowshop problem with a single batch processing machine in the first stage and a single machine in the second stage. In this problem, each job has an individual release time and they are grouped into several batches. The batch processing machine can process a batch (limited number) of jobs simultaneously. To be more practical, the waiting time between the batch processing machine and the single machine is restricted in the two-stage hybrid flowshop problem. The objective is to minimize the makespan. To the best of our knowledge, few study researches the problem which is common in many real-life applications. Two immunoglobulin-based artificial immune system (IAIS) algorithms are developed to solve the problem which is NP-hard. The proposed IAIS algorithms provide different encoding and decoding ways to solve the problem. To verify proposed IAISs, comparisons with existing algorithms are made. Two lower bounds are also proposed to test solution quality. Computational results have shown that the proposed IAIS algorithms for the two-stage hybrid flowshop problem are quite stable and efficient.