Replenishment Cost of a Storage System Modelled through a Defective Renewal Equation

TL;DR

This paper models the replenishment cost of a storage system with Poisson demand, showing it satisfies a defective renewal equation and providing an asymptotic expression for its expected present value.

Contribution

It introduces a novel mathematical model linking storage replenishment costs to defective renewal equations with asymptotic analysis.

Findings

Replenishment cost function satisfies a defective renewal equation.

An asymptotic expression for the expected present value is derived.

The model applies to systems with instant replacement and Poisson demand.

Abstract

A storage system where a k units stock is replaced instantaneously, when required,is presented in this work. It is also supposed a Poisson demand. It is proved that the storage system replenishment cost expected present value function fulfills a defective renewal equation, being proposed for it an asymptotic expression.