A Simple Forward Algorithm to Solve General Dynamic Lot Sizing Models with n Periods in 0(n log n) or 0(n) Time
提出一个简单前向算法，将一般动态批量模型（Wagner-Whitin模型）的计算时间从传统的O(n²)降至O(n log n)，并在两种重要特例下实现线性时间O(n)，对库存与生产计划研究者有参考价值。
This paper is concerned with the general dynamic lot size model, or (generalized) Wagner-Whitin model. Let n denote the number of periods into which the planning horizon is divided. We describe a simple forward algorithm which solves the general model in 0(n log n) time and 0(n) space, as opposed to the well-known shortest path algorithm advocated over the last 30 years with 0(n 2 ) time. A linear, i.e., 0(n)-time and space algorithm is obtained for two important special cases: (a) models without speculative motives for carrying stock, i.e., where in each interval of time the per unit order cost increases by less than the cost of carrying a unit in stock; (b) models with nondecreasing setup costs. We also derive conditions for the existence of monotone optimal policies and relate these to known (planning horizon and other) results from the literature.