A Solvable One-Dimensional Model of a Diffusion Inventory System

Agnès Sulem

96 citations0/0 files storedMathematics of Operations Research

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Supply Chain and Inventory Management Stochastic processes and financial applications Advanced Queuing Theory Analysis

Abstract

We analyse the optimal ordering policy for impulse control of a one-product inventory system subject to a demand modelised by a diffusion process. The purpose is to minimize the expected discounted cost that includes a fixed set-up cost and linear costs of purchase, storage and shortage. The optimal cost is explicitly obtained as the smoothest solution of a Quasi-Variational Inequality derived from the optimal principle of Dynamic Programming. The optimal (s, S) policy is determined as the unique solution of a system of algebraic equations.

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References

2005The Optimality of (S,s) Policies in the Dynamic Inventory Problem 1971Introduction to stochastic control 1983Impulse Control of Brownian Motion 1982Stochastic Control by Functional Analysis Methods 1978Existence of Optimal Simple Policies for Discounted-Cost Inventory and Cash Management in Continuous Time 1966A continuous time inventory model

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