Verifying the inverse Laplace transform of total expected stock-outs when demand is Poisson

Ettore Settanni

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arXiv · 2311.12629

Verifying the inverse Laplace transform of total expected stock-outs when demand is Poisson

Ettore Settanni

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Abstract

This note aims to verify a Laplace transform pair, previously published without proof, concerning the expected stock-out that may occur in a production-inventory systems when demand is Poisson, and the time horizon is finite. Stock-out, or "backlog", is understood as the non-negative difference between cumulative demand, a stochastic variable, and production over a finite time interval. The hoped for outcome is greater clarity on how the Laplace transform pair of interest might be arrived at, and a possible improvement in terms of accuracy on the original result.

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Ettore Settanni. 2023-11-21. Verifying the inverse Laplace transform of total expected stock-outs when demand is Poisson. https://arxiv.org/abs/2311.12629

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