Joint Control of Component Production and Inventory Allocation in an Assemble-to-order System with Lost Sales

Abstract

This paper considers a joint control problem of combined component production and inventory allocation in an assemble-to-order system which consists of two components and three demand classes with lost sales. Each demand class arrives according to a Poisson process, and the production time of each component follows an exponential distribution. By formulating the system as a Markov decision process under the expected total discounted cost criterion, we obtain the optimality equation following the Lippman transformation, from which we derive the structural properties of the optimal control policy. Specially, the optimal production policy for each component is shown to be a base stock policy with the base-stock level non-decreasing in the inventory level of the other component, and the optimal inventory allocation for each component is a state-dependent threshold policy, where the threshold point for the demand for one kind of components is non-decreasing in the inventory level of the other component, while the threshold point for the demand for both components is non-increasing in the inventory level of the other component. Finally, we give some numerical examples to show how the optimal control policy changes with the system parameters, and we also provide some managerial insights.