A recursion-free functional approximation for the dynamic inventory problem

TL;DR

This paper introduces a simple, recursion-free approximation method for the dynamic inventory problem with non-stationary demands, enabling efficient heuristic computation of policy parameters that outperform previous heuristics.

Contribution

The authors develop a novel recursion-free approximation for the cost function, facilitating easier and more effective heuristic policy parameter computation in non-stationary inventory management.

Findings

Heuristic outperforms earlier methods in simulations

Method is based on convex minimization and shortest paths

Provides an easy-to-use alternative to dynamic programming

Abstract

We consider the dynamic inventory problem with non-stationary demands. It has long been known that non-stationary (s, S) policies are optimal for this problem. However, finding optimal policy parameters remains a computational challenge as it requires solving a large-scale stochastic dynamic program. To address this, we devise a recursion-free approximation for the optimal cost function of the problem. This enables us to compute policy parameters heuristically, without resorting to a stochastic dynamic program. The heuristic is easy-to-understand and -use since it follows by elementary methods of convex minimization and shortest paths, yet it is very effective and outperforms earlier heuristics.