Matching Supply and Demand in Production-Inventory Systems: Asymptotics and Optimization

TL;DR

This paper analyzes high-volume production-inventory systems using asymptotic methods to understand performance measures and optimize supply strategies, providing simple near-optimal solutions and linking lost-sales and backorder models.

Contribution

It introduces a novel asymptotic analysis of a power drift random walk and derives approximations for supply strategy optimization in production-inventory systems.

Findings

Asymptotic behavior of key performance measures is characterized.

Simple near-optimal supply strategies are derived.

Equivalence between lost-sales and backorder models is established.

Abstract

We consider a general class of high-volume, fast-moving production-inventory systems based on both lost-sales and backorder inventory models. Such systems require a fundamental understanding of the asymptotic behavior of key performance measures under various supply strategies, as well as the pre-planning of these strategies. Our analysis relies on a thorough study of the asymptotic behavior of a random walk with power drift, which is of independent interest. In addition to providing key insights, our analysis leads to approximations of the corresponding optimization problem that yield simple solutions which are close to optimal. We also establish an equivalence between the lost-sales and backorder models when both have the same penalty cost that becomes large.