Bi-criteria SDST hybrid flow shop scheduling with learning effect of setup times: water flow-like algorithm approach

In studies on automatic scheduling problems, processing times do not differ according to repetition of job or process sequences so it may also be necessary to consider processing times independent from setup times. While considering setup times, the human factor has an important effect on setup, so by the processing of similar tasks frequently worker skills improve and they are able to perform setup at a greater pace. This fact is known as the 'learning effect' in the literature. This paper deals with sequence-dependent setup times (SDSTs) hybrid flow shop scheduling with learning effect of setup times for minimising weighted sum of makespan and total tardiness. A mathematical programming model that incorporates these aspects of the problem is developed which belongs to the NP-hard class. Thus, because of the intensive computation, we propose a novel meta-heuristic approach called water flow-like algorithm (WFA) which has the feature of multiple and dynamic numbers of solution agents. Various parameters of the problem and the WFA are reviewed by means of Taguchi experimental design. For the evaluation of the proposed WFA, problem data was generated to compare it against a random key genetic algorithm (RKGA). The results demonstrate the high performance of the WFA with respect to the RKGA.