A stochastic programming based inventory policy for assemble-to-order systems with application to the W model. (English) Zbl 1231.90026

Doğru, Mustafa K.; Reiman, Martin I.; Wang, Qiong

Oper. Res. 58, No. 4, Part 1, 849-864 (2010).

Summary: 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.

MSC:

90B05	Inventory, storage, reservoirs
90C15	Stochastic programming

Keywords:

multi-item inventory; assemble-to-order; component commonality; stochastic programming; approximations; heuristics