Network flow-based deterministic and stochastic models for the integrated lot-sizing and scheduling problem with sequence-dependent set-up costs
针对单设施多产品多周期的集成批量与调度问题，提出网络流模型和有效不等式，并扩展至随机需求情形，用Benders分解求解，计算表明优于CPLEX直接求解。
In this paper we address an uncapacitated integrated lot-sizing and scheduling problem with sequence-dependent set-up costs in which several products with associated demand are produced across multiple periods in a single facility. We develop a network-flow-based model formulation for the problem and propose facet-defining inequalities that make the formulation even tighter. We extend the model to include backordering, lost sales, and constraints for capacitated problems; these formulations with corresponding examples are provided in an appendix. In addition, we present a stochastic linear programming model and a two-stage stochastic model with a recourse policy to incorporate demand uncertainty. A Benders decomposition-based scheme is deployed to solve the models. A computational investigation is carried out that reveals the proposed method to outperform the direct solution of the model formulations by CPLEX. Few interesting managerial insights are also provided. Lastly, we summarise our work and suggest potential directions for future research.