Mixed-integer linear programming and composed heuristics for three-stage remanufacturing system scheduling problem

The three-stage remanufacturing system scheduling problem (3T-RSSP) has been a hot research topic recently. The remanufacturing system in this paper is equipped with a novel configuration of unrelated parallel disassembly/reassembly workstations and parallel dedicated flow-shop-type reprocessing lines. To this end, a mixedinteger linear programming (MILP) model based on the adjacent sequence-based modeling idea is first proposed to address the 3T-RSSP for a makespan minimization. Compared with other ideas, the adjacent sequence-based modeling idea is effective in deciding precedence relationship between two adjacent operations, especially for the investigated 3T-RSSP. The 3T-RSSP is NP (non-deterministic polynomial)-hard, we also design 18 composed heuristics for large-sized problems to gain a better performance, compared to traditional isolated heuristics. Simulation experiments are carried out on a publicly available dataset to test the performance the MILP model and composed heuristics. Results imply that the MILP model solved by CPLEX can seek optimum solutions within a short time when the problem size is small. It is found that when problem size becomes 2.0, 4.0, 8.0 times large, performance indicators NCs (number of constraints) and NBVs (number of binary variables) of the model become 3.29, 11.81, 44.60 and 3.43, 12.57, 48.00 times large. Besides, compared with other composed heuristics, LTRTF (longest total reprocessing time-first available machine) gains the best performance. Instance P5-C3-D2/A2 is selected to quantitatively analyze the MILP model by presenting the detailed 0-1 binary variable values. Finally, by comparing with position-based MILP model, the adjacent sequence-based MILP model has better performance in characterizing the investigated 3T-RSSP.