A Stochastic Programming Based Inventory Policy for Assemble-to-Order Systems with Application to the W Model

TLDR

The study focuses on assemble‑to‑order inventory systems with identical component lead times. The authors aim to develop an inventory strategy via a stochastic program that enables preferential component allocation to minimize total inventory cost. They formulate a stochastic program for the W system, devise efficient solution procedures for both the full and relaxed models, and propose a priority allocation policy that sets base‑stock levels based on the first‑stage solution. The policy attains the lower bound and is optimal under symmetry or balanced‑capacity conditions, and in other cases it performs well and outperforms alternative approaches.

Abstract

We consider assemble-to-order inventory systems with identical component lead times. We use a stochastic program (SP) to develop an inventory strategy that allows preferential component allocation for minimizing total inventory cost. We prove that the solution of a relaxation of this SP provides a lower bound on total inventory cost for all feasible policies. We demonstrate and test our approach on the W system, which involves three components used to produce two products. (There are two unique parts and a common part. Each product uses the common part and its own unique part.) For the W system, we develop efficient solution procedures for the SP as well as the relaxed SP. We define a simple priority allocation policy that mimics the second-stage SP recourse solution and set base-stock levels according to the first-stage SP solution. We show that our policy achieves the lower bound and is, thus, optimal in two situations: when a certain symmetry condition in the cost parameters holds and when the SP solution satisfies a “balanced capacity” condition. For other cases, numerical results demonstrate that our policy works well and outperforms alternative approaches in many circumstances.