Inventory and total completion time minimization for assembly job-shop scheduling considering material integrity and assembly sequential constraint

Assembly job-shop scheduling problems (AJSSP), considering material integrity and assembly sequential constraint (AJSSP-IS), exist widely in rolling stock industries. Production efficiency and inventory levels are the key concerns for this type of industry. Thus, this paper investigates an AJSSP-IS via a lexicographical mixed-integer linear programming (MILP) model and an enhanced simulated annealing algorithm (ESA) to minimize a regular primary objective, the total completion time and an unregular secondary objective, the total inventory time. The lexicographical MILP model is formulated to determine the processing sequence and assembly sequence, and a lexicographical optimization method is applied to obtain the best scheme of a secondary objective from the optimal schemes of a primary objective. Further, an ESA is developed to solve the problem efficiently. In ESA, an assembly-driven initialization is designed to create high-quality solutions by considering assembly relationships; a two-stage decoding is developed in which a semi-active schedule achieves the minimization of the total completion time and a right-shift schedule reduces the total inventory time without extending the total completion time; an improved neighborhood search is proposed by introducing a critical block-oriented selection and a filter selection to increase search efficiency. Experimental results indicate that the lexicographical MILP model can find the lower bound of small-scale problems, and the ESA significantly outperforms six state-of-the-art algorithms in fixing the considered problem.