Ergodic inventory control with diffusion demand and general ordering costs

TL;DR

This paper establishes the global optimality of an $(s,S)$ inventory policy in a continuous-time setting with diffusion demand and complex ordering costs, broadening the scope of ergodic inventory control models.

Contribution

It introduces a novel approach combining lower bound techniques and comparison theorems to prove optimality under general, possibly discontinuous, ordering cost functions.

Findings

Proves the optimality of $(s,S)$ policies in a broad class of inventory models.

Handles non-monotone, discontinuous ordering costs.

Extends ergodic inventory control theory to diffusion demand processes.

Abstract

In this work, we consider a continuous-time inventory system where the demand process follows an inventory-dependent diffusion process. The ordering cost of each order depends on the order quantity and is given by a general function, which is not even necessarily continuous and monotone. By applying a lower bound approach together with a comparison theorem, we show the global optimality of an $(s,S)$ policy for this ergodic inventory control problem.