Mathematical Programming Approaches to Capacity-Constrained MRP Systems: Review, Formulation and Problem Reduction
针对MRP系统在容量约束下失效的问题，综述了多阶段生产调度问题的文献，提出了线性与混合整数线性规划模型，并介绍了一种在不损失最优性的前提下缩小问题规模的产品结构压缩方法。
This paper introduces a line of research on capacity-constrained multi-stage production scheduling problems. The first section introduces the problem area as it arises from a failure of MRP systems. Then a review of the literature and an analysis of the type of problems that exist are presented in §2. Section 3 outlines linear and mixed integer-linear programming formulations. These formulations compute the required production lead times according to the demands on available capacity, thereby reducing in-process inventory compared to the usual practice in MRP. A discussion of how to use the LP version is included. However, the size of the problems in practice implies that more efficient solution techniques must be found. The final topic of this paper, Product Structure Compression, is introduced as a method to reduce the size of the problem without losing optimality.