Optimization of Continuous Flow-Shop Scheduling Considering Due Dates

Abstract

For a no-wait flow shop with continuous-flow characteristics, this study simultaneously considers machine setup times and rated processing speed constraints, aiming to minimize the sum of the maximum completion time and the maximum tardiness. First, lower bounds for the maximum completion time, the maximum tardiness, and the total objective function are developed. Second, a mixed-integer programming (MIP) model is formulated for the problem, and nonlinear elements are subsequently linearized via time discretization. Due to the computational complexity of the problem, two algorithms are proposed: a heuristic algorithm with fixed machine links and greedy rules (HAFG) and a genetic algorithm based on altering machine combinations (GAAM) for solving large-scale instances. The Earliest Due Date (EDD) rule is used as baselines for algorithmic comparison. To better understand the behaviors of the two algorithms, we observe the two components of the objective function separately. The results show that, compared with the EDD rule and GAAM, the HAFG algorithm tends to focus more on optimizing the maximum completion time. The performance of both algorithms is evaluated using their relative deviations from the developed lower bounds and is compared against the EDD rule. Numerical experiments demonstrate that both HAFG and GAAM significantly outperform the EDD rule. In large-scale instances, the HAFG algorithm achieves a gap of about 4%, while GAAM reaches a gap of about 3%, which is very close to the lower bound. In contrast, the EDD rule shows a deviation of about 10%. Combined with a sensitivity analysis on the number of machines, the proposed framework provides meaningful managerial insights for continuous-flow production environments.