Solving Inventory Management Problems with Inventory-dynamics-informed Neural Networks

Abstract

A key challenge in inventory management is to identify policies that optimally replenish inventory from multiple suppliers. To solve such optimization problems, inventory managers need to decide what quantities to order from each supplier, given the on-hand inventory and outstanding orders, so that the expected backlogging, holding, and sourcing costs are jointly minimized. Inventory management problems have been studied extensively for over 60 years, and yet even basic dual sourcing problems, in which orders from an expensive supplier arrive faster than orders from a regular supplier, remain intractable in their general form.In this work, we approach dual sourcing from a neural-network-based optimization lens. By incorporating inventory dynamics into the design of neural networks, we are able to learn near-optimal policies of commonly used instances within a few minutes of CPU time on a regular personal computer. To demonstrate the versatility of inventory-dynamics-informed neural networks, we show that they are able to control inventory dynamics with empirical demand distributions that are challenging to tackle effectively using alternative, state-of-the-art approaches.

Near-optimal control of dynamical systems with neural ordinary differential equations

“…We use PMP to derive u * (t), which we will assume to be the OC associated with equations ( 14) and (15). We obtain…”

“…The optimal control (OC) of complex dynamical systems is relevant in many scientific disciplines [1], including biology [2][3][4][5][6][7], epidemiology [8,9], quantum engineering [10][11][12], power systems [13,14], and supply chains [15].…”