Optimal Periodic Replenishment Policies for Spectrally Positive Lévy Demand Processes

Optimal Periodic Replenishment Policies for Spectrally Positive Lévy Demand Processes
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DOI：
10.1137/18m1196406
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发表时间：
2018-06
期刊：
SIAM J. Control. Optim.
影响因子：
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通讯作者：
José-Luis Pérez;K. Yamazaki;A. Bensoussan
José-Luis Pérez;K. Yamazaki;A. Bensoussan
中科院分区：
其他
文献类型：
--
作者：
José-Luis Pérez;K. Yamazaki;A. Bensoussan

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我们考虑了一个谱正L\'evy需求过程的随机库存控制问题，其中库存只能在独立的指数时间补充。我们将展示周期性壁垒补充政策的最优性，即在每次补充机会中补充低于一定壁垒的任何短缺。最优策略和价值函数用尺度函数简明地表示。并给出了数值结果。
We consider a version of the stochastic inventory control problem for a spectrally positive L\'evy demand process, in which the inventory can only be replenished at independent exponential times. We will show the optimality of a periodic barrier replenishment policy that replenishes any shortage below a certain barrier at each replenishment opportunity. The optimal policies and value functions are concisely written in terms of the scale functions. Numerical results are also provided.