Continuity of discounted values and the structure of optimal policies for periodic‐review inventory systems with setup costs
研究了带固定订货成本、库存容量和订货量约束的定期盘点库存控制问题，证明了有限和无限时域下折扣价值函数的连续性，并给出了最优策略的存在性和结构特征。
Abstract This paper proves continuity of value functions in discounted periodic‐review single‐commodity total‐cost inventory control problems with continuous inventory levels, fixed ordering costs, possibly bounded inventory storage capacity, and possibly bounded order sizes for finite and infinite horizons. In each of these constrained models, the finite and infinite‐horizon value functions are continuous, there exist deterministic Markov optimal finite‐horizon policies, and there exist stationary deterministic Markov optimal infinite‐horizon policies. For models with bounded inventory storage and unbounded order sizes, this paper also characterizes the conditions under which policies are optimal in the finite horizon and an policy is optimal in the infinite horizon.