Sequencing in just-in-time flow shop with time windows considering target completion: performance comparison of mathematical models

This work investigates mathematical formulations for the just-in-time sequencing problem in permutation flow shop with time windows, incorporating weighted penalties of earliness and tardiness, an endogenous completion target time, and a scaling parameter for balancing the objective function. Four models of mixed integer linear programming were proposed and evaluated: positional, precedence, immediate precedence and time-indexed. The computational experiments were performed in classes of instances with different combinations of tasks and machines, and different deadline scenarios. The results show that the positional and precedence formulations were the only ones capable of finding viable solutions for all the classes tested. Among them, the positional formulation showed more robust performance, with lower average optimality gaps and more stable behavior as the size of the instances increased. These results indicate that more compact formulations tend to offer better computational tractability for the problem studied