Optimal and Asymptotically Optimal Policies for Assemble-to-Order N- and W-Systems

Abstract

We consider two specially structured assemble-to-order (ATO) systems -- the N- and W-systems -- under continuous review, stochastic demand, and non-identical component replenishment leadtimes. Using a hybrid approach that combines sample-path analysis, linear programming, and the tower property of conditional expectation, we characterize the optimal component replenishment policy and common-component allocation rule, present comparative statics of the optimal policy parameters, and show that some commonly used heuristic policies can lead to significant optimality loss. The optimality results require a certain symmetry in the cost parameters. In the absence of this symmetry, we show that, for systems with high demand volume, the asymptotically optimal policy has essentially the same structure; otherwise, the optimal policies have no clear structure. For these latter systems, we develop heuristic policies and show their effectiveness.

Keywords: Inventory Control, Assemble-to-order system, asymptotical analysis