A note of using effective immune based approach for the flow shop scheduling with buffers

This note considers flow shop scheduling with buffers. The objective is to minimize the makespan. As we know, such a problem has several applications in manufacturing and has gained wide attention both in academic and engineering fields. In this note, we propose an immune based approach (IA) to solve this NP-hard problem. Numerical results of 29 benchmark problems from the OR-Library are reported and compared with those of a hybrid genetic algorithm (HGA). As shown, the proposed IA is effective and robust. The solutions by proposed IA are superior to those of HGA reported in the literature. In addition, the average of the relative errors of the proposed IA is only 0.85% for 29 instances with infinite buffers. Limited numerical results show that, as expected, buffer size has a great impact on the scheduling objective especially for larger-scale instances, and there are also significant differences with or without buffers for all instances. But the effect of increasing buffer size from 1 up to 2, 4 or ∞ decreases drastically for all instances.