Lot-streaming flowshop scheduling under stochastic due dates
研究了随机交货期下批量流流水车间调度问题，推导了期望延迟的闭式表达式，提出了线性化方法和逻辑Benders分解算法，数值实验验证了考虑随机交货期的重要性及算法有效性。
The lot-streaming flowshop scheduling problem with stochastic due dates is addressed in this paper, aiming to minimise the sum of expected tardiness. Closed-form expressions for the expected tardiness of jobs are derived under various due date distributions. A mathematical model is then formulated for the problem. To tackle the highly nonlinear nature of the model, a linearisation method is proposed. Furthermore, based on the problem structure, a logic-based Benders decomposition methodology is designed, incorporating a branch-and-bound algorithm to solve its subproblem. A new tight lower bound is introduced based on the stochastic order property of the due dates. For due dates lacking stochastic order relationships, a valid lower bound can still be achieved by scaling and unifying the standard deviation of due dates. Moreover, three effective acceleration strategies are introduced to enhance the algorithm's efficiency. Numerical experiments demonstrate the importance of incorporating stochastic due dates and the effectiveness of the proposed algorithms.