Effective heuristics and metaheuristics to minimise total tardiness for the distributed permutation flowshop scheduling problem

During recent years, the distributed permutation flowshop scheduling problem (DPFSP) has become a very active area of research. However, minimising total tardiness in DPFSP, a very essential and relevant objective for today's customer-orientated market, has not been studied much. In this paper, we address the DPFSP with the total tardiness criterion. We present a mixed-integer linear programming model, two heuristics, hybrid discrete Harris hawks optimisation and an enhanced variant of iterated greedy algorithm to solve the considered problem. Problem-specific knowledge is explored and effective technologies, such as path relinking and random sub-sequence/single-point local search, are employed to improve the presented algorithms. The operators and parameters of the algorithms are analysed and calibrated using the design of experiments. To evaluate the performance, the well-known benchmark problem set of Naderi and Ruiz for DPFSP is extended with due dates. We compare the presented algorithms against seven other well-known meta-heuristics from the literature. Statistically sound results demonstrate the effectiveness of the presented algorithms for the considered problem.