On the stochastic inventory problem under order capacity constraints
研究了有固定订货成本和订单容量约束的随机库存系统，发现最优策略并非简单的单区间订货，而是修正的多(s,S)策略，并通过数值反例和大量实证验证了其近优性。
• We consider the stochastic lot sizing problem under order capacity constraints. • A policy with a single continuous interval over which one orders is not optimal. • A modified multi-(s,S) policy is optimal under the “continuous order property”. • The continuous order property is never violated in a large-scale empirical study. • A modified (s,S) policy also performs well in this empirical setting. We consider the single-item single-stocking location stochastic inventory system under a fixed ordering cost component. A long-standing problem is that of determining the structure of the optimal control policy when this system is subject to order quantity capacity constraints; to date, only partial characterisations of the optimal policy have been discussed. An open question is whether a policy with a single continuous interval over which ordering is prescribed is optimal for this problem. Under the so-called “continuous order property” conjecture, we show that the optimal policy takes the modified multi- ( s , S ) form. Moreover, we provide a numerical counterexample in which the continuous order property is violated, and hence show that a modified multi- ( s , S ) policy is not optimal in general. However, in an extensive computational study, we show that instances violating the continuous order property do not surface, and that the plans generated by a modified multi- ( s , S ) policy can therefore be considered, from a practical standpoint, near-optimal. Finally, we show that a modified ( s , S ) policy also performs well in this empirical setting.