Keywords: Assemble-to-order (ATO) Inventory Stochastic program Optimal policy Multi-dimensional newsvendor model a b s t r a c t In this paper we introduce a multi-stage stochastic program that provides a lower bound on the long-run average inventory cost of a general class of assemble-to-order (ATO) inventory systems. The stochastic program also motivates a replenishment policy for these syste...

We consider an assemble-to-order (ATO) system with multiple products, multiple components which may be demanded in different quantities by different products, possible batch ordering of components, random lead times, and lost sales. We model the system as an infinite-horizon Markov decision process under the average cost criterion. A control policy specifies when a batch of components should be...

The last years have displayed an impressive e-commerce boom. To protect the customer stricter policies have been imposed to e-tailers, most important of which is the return policy. Companies have to deal now with more complicated management of inventories due to uncertainty in the reverse flow of materials. Moreover, returns do not re-enter the supply chain immediately after leaving the custome...

We consider component allocation in Assemble-to-Order production–inventory systems. We prove that asymptotic optimality on the diffusion scale can be achieved under a continuous-review policy. We also show that in many systems, meeting this optimality criterion requires component reservation.

We first prove that if y * optimizes (16), then |y * j | ≤ M, 1 ≤ j ≤ n. (EC.1) Suppose that in (16), given y and D, z * (y; D) optimizes ϕ(y; D). Then the objective function is C(y) = h · E[y − Az * (y; D)] + b · E[D − z * (y; D)]. i:a ji >0 a ji b i a ji E[D i − z * i ] ≥ ζ j A j · E[D − z * ] ≥ ζ j (A j · E[D] − y j), and C(y) ≥ h · E[y − Az * ] ≥ h j (y j − A j · E[z * ]) ≥ h j (y j − A j ·...

We study multi-product and multi-item assemble-to-order systems under general assumptions on demand patterns and replenish leadtime distributions. We only assume that the demand process of each product being a renewal process, and the replenish leadtimes follow general distributions. Based upon techniques from renewal theory, we developed procedures for approximating key performance measures of...