English

Optimal periodic replenishment policies for spectrally positive L\'evy demand processes

Optimization and Control 2020-09-16 v2 Mathematical Finance

Abstract

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 show the optimality of a periodic barrier replenishment policy that restocks any shortage below a certain threshold at each replenishment opportunity. The optimal policies and value functions are concisely written in terms of the scale functions. Numerical results are also provided.

Keywords

Cite

@article{arxiv.1806.09216,
  title  = {Optimal periodic replenishment policies for spectrally positive L\'evy demand processes},
  author = {José-Luis Pérez and Kazutoshi Yamazaki and Alain Bensoussan},
  journal= {arXiv preprint arXiv:1806.09216},
  year   = {2020}
}

Comments

27 pages, 3 figures. Forthcoming in SIAM Journal on Control and Optimization