Improved Approximation Guarantees for Joint Replenishment in Continuous Time

TL;DR

This paper advances the understanding of the continuous-time joint replenishment problem by providing improved approximation guarantees, surpassing the long-standing power-of-2 policy benchmarks established since the 1980s.

Contribution

It offers the first quantitative improvements over traditional power-of-2 policies in the continuous-time joint replenishment model, addressing long-standing open questions.

Findings

First quantitative improvements over power-of-2 policies.

Resolved several long-standing open questions.

Enhanced performance guarantees in inventory management.

Abstract

The primary objective of this work is to revisit and revitalize one of the most fundamental models in deterministic inventory management, the continuous-time joint replenishment problem. Our main contribution consists of resolving several long-standing open questions in this context. For most of these questions, we obtain the first quantitative improvement over power-of-$2$ policies and their nearby derivatives, which have been state-of-the-art in terms of provable performance guarantees since the mid-80's.