Asymptotically Optimal Inventory Control for Assemble-to-Order Systems

TL;DR

This paper develops an asymptotically optimal inventory control policy for Assemble-to-Order systems with general Bill of Materials and lead times, minimizing long-term costs as lead times grow.

Contribution

It introduces a novel multi-stage stochastic programming approach and a non-traditional replenishment policy that achieves asymptotic optimality in complex ATO systems.

Findings

Policy is asymptotically optimal as lead times increase.

Provides a broad stochastic tracking model with convergence results.

Deviates from conventional constant base stock policies.

Abstract

We consider Assemble-to-Order (ATO) inventory systems with a general Bill of Materials and general deterministic lead times. Unsatisfied demands are always backlogged. We apply a four-step asymptotic framework to develop inventory policies for minimizing the long-run average expected total inventory cost. Our approach features a multi-stage Stochastic Program (SP) to establish a lower bound on the inventory cost and determine parameter values for inventory control. Our replenishment policy deviates from the conventional constant base stock policies to accommodate non-identical lead times. Our component allocation policy differentiates demands based on backlog costs, Bill of Materials, and component availabilities. We prove that our policy is asymptotically optimal on the diffusion scale, that is, as the longest lead time grows, the percentage difference between the average cost under our policy and its lower bound converges to zero. In developing these results, we formulate a broad Stochastic Tracking Model and prove general convergence results from which the asymptotic optimality of our policy follows as specialized corollaries.