Abstract:
Human-machine collaboration (HMC) is a promising and important production model that combines the advantages of worker flexibility and machine efficiency. To obtain an optimal and exact solution, an integrated optimization framework based on mixed-integer linear programming (MILP) was established for the human-machine collaborative flexible flow shop scheduling problem (HMC-FFSP), which included three modeling ideas: adjacent sequence-based modeling idea, sequence-based modeling idea, and time-based modeling idea, with the sequence-based modelling idea further consisting of two variants. Firstly, the characteristics of the HMC-FFSP problem were analyzed, and then based on different modeling ideas, four MILP models were finally established through designing different discrete decision variables, continuous decision variables, and different constraint sets. In addition, small-scale and large-scale test instances were also designed, and those MILP models were compared from two aspects: size complexity and computational complexity, such as 0-1 Boolean decision variables, continuous decision variables, solution time, total number of constraints, and so on. Experimental results verified the feasibility and effectiveness of the four proposed MILP models in solving HMC-FFSP problems, and revealed that the sequence based modeling idea achieved the best performance, followed by the adjacent sequence-based modeling idea, while the time-based modeling idea performed the worst. Finally, statistical analyses, including the Wilcoxon signed-rank test and paired sample
t-test, were conducted on the experimental results, further enhancing the reliability of the conclusion.