The hybrid flow shop group scheduling problem (HFGSP) with the delivery time windows has been widely studied owing to its better flexibility and suitability for the current just-in-time production mode. However, there are several unresolved challenges in problem modeling and algorithmic design tailored for HFGSP. In our study, we place emphasis on the constraint of timeliness. Therefore, this paper first constructs a mixed integer linear programming model of HFGSP with sequence-dependent setup time and delivery time windows to minimize the total weighted earliness and tardiness (TWET). Then a penalty groups-assisted iterated greedy integrating idle time insertion ( $\mathrm{P}\mathrm{G}\mathrm{\_}\mathrm{I}\mathrm{G}\mathrm{\_}\mathrm{I}\mathrm{T}\mathrm{I}$) is proposed to solve the above problem. In the $\mathrm{P}\mathrm{G}\mathrm{\_}\mathrm{I}\mathrm{G}\mathrm{\_}\mathrm{I}\mathrm{T}\mathrm{I}$, a double decoding strategy is proposed based on the earliest available machine rule and the idle time insertion rule to calculate the TWET value. Subsequently, to reduce the amount of computation, a skip-based destruction and reconstruction strategy is designed, and a penalty groups-assisted local search is proposed to further improve the quality of the solution by disturbing the penalized groups, i.e., early and tardy groups. Finally, through comprehensive statistical experiments on 270 test instances, the results prove that the proposed algorithm is effective compared to four state-of-the-art algorithms.

The distributed hybrid flow shop scheduling problem (DHFSP), which integrates distributed manufacturing models with parallel machines, has gained significant attention. However, in actual scheduling, some adjacent machines do not have buffers between them, resulting in blocking. This paper focuses on addressing the DHFSP with blocking constraints (DBHFSP) based on the actual production conditions. To solve DBHFSP, we construct a mixed integer linear programming (MILP) model for DBHFSP and validate its correctness using the Gurobi solver. Then, an advanced iterated greedy (AIG) algorithm is designed to minimize the makespan, in which we modify the Nawaz, Enscore, and Ham (NEH) heuristic to solve blocking constraints. To balance the global and local search capabilities of AIG, two effective inter-factory neighborhood search strategies and a swap-based local search strategy are designed. Additionally, each factory is mutually independent, and the movement within one factory does not affect the others. In view of this, we specifically designed a memory-based decoding method for insertion operations to reduce the computation time of the objective. Finally, two shaking strategies are incorporated into the algorithm to mitigate premature convergence. Five advanced algorithms are used to conduct comparative experiments with AIG on 80 test instances, and experimental results illustrate that the makespan and the relative percentage increase (RPI) obtained by AIG are 1.0% and 86.1%, respectively, better than the comparative algorithms.