Online Inventory Problems: Beyond the i.i.d. Setting with Online Convex Optimization

TL;DR

This paper introduces MaxCOSD, an online algorithm for multi-product inventory control that handles non-i.i.d. demands and complex dynamics, extending beyond traditional models with fixed assumptions.

Contribution

The paper presents MaxCOSD, a novel online algorithm capable of managing non-i.i.d. demands and stateful dynamics in inventory control, with theoretical guarantees.

Findings

MaxCOSD performs well under non-i.i.d. demand conditions.

The algorithm provides provable guarantees for complex inventory dynamics.

Non-degeneracy assumptions are necessary for effective learning.

Abstract

We study multi-product inventory control problems where a manager makes sequential replenishment decisions based on partial historical information in order to minimize its cumulative losses. Our motivation is to consider general demands, losses and dynamics to go beyond standard models which usually rely on newsvendor-type losses, fixed dynamics, and unrealistic i.i.d. demand assumptions. We propose MaxCOSD, an online algorithm that has provable guarantees even for problems with non-i.i.d. demands and stateful dynamics, including for instance perishability. We consider what we call non-degeneracy assumptions on the demand process, and argue that they are necessary to allow learning.