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

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.

No-Holdback Allocation Rules for Continuous-Time Assemble-to-Order Systems

“…For such a system, we establish the optimality of the NHB rules assuming certain replenishment policies. Dogru et al (2010) proved results on the joint optimal replenishment and allocation policy for their model, but these results do not carry over to the general system considered here. Interestingly, both studies identify similar cost structures to guarantee optimality, even though the approaches taken are very different.…”

“…They show that under Markovian assumptions on demand and production, the optimal replenishment policy is a statedependent base-stock policy, and the optimal allocation rule is a multilevel rationing policy that depends on the inventory levels of all other components. Dogru et al (2010) considered a special case of the W system in which all components have identical constant lead times. They show that when a symmetric cost condition or a "balanced capacity" condition is satisfied, the optimal replenishment policy is a state-independent base-stock policy and the optimal allocation policy is an NHB policy (which they call myopic policies).…”

“…Also, these authors only studied performance evaluation of the fill rates and did not consider backorders and optimality conditions. Second, Dogru et al (2010) incidentally noticed the general class of the NHB rules. In particular, they considered a priority-based backlog clearing policy as well as a reservation policy.…”

“…Interestingly, both studies identify similar cost structures to guarantee optimality, even though the approaches taken are very different. The analysis of Dogru et al (2010) is based on a stochastic programming (SP) formulation and a lower bound approach, whereas we use a sample path approach, supplemented with a system reduction technique that reduces the original ATO systems to a single-item inventory system.…”

Technical Note—Optimal Structural Results for Assemble-to-Order Generalized M-Systems

“…Several authors have managed to partially or fully characterize optimal policies for specific ATO systems: Dogru et al (2010) consider a W -system with backordering and identical component lead times. They establish the optimality of a base-stock replenishment policy and a priority-based backorder clearing rule (without reservation) when the "balanced capacity" condition holds, or when both products have the same unit inventory costs.…”