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

arXiv: https://arxiv.org/abs/1806.09216 · HTML: https://mlsanity.com/paper/1806.09216/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2018.

## Built on by (most cited first, 1 of 1)

- [Supervised Learning for the (s,S) Inventory Model with General Interarrival Demands and General Lead Times](https://mlsanity.com/paper/2601.12900/) (2026)

## Abstract (arXiv)

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.