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