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Abstract

One of the main results of "Order-Based Cost Optimization in Assemble-to-Order Systems" [1] by Y. Lu and J-S. Song, Operations Research, 53, 151-169 (2005) is Proposition 1 (c), which states that the cost function of an assemble-to-order inventory system satisfies a discrete convexity property called L♮-convexity. Based on this result, Lu and Song proposed two types of L♮-convex minimization algorithms for finding the optimum policy. We construct a simple assemble-to-order system for which the cost function fails to satisfy L♮-convexity. Using a similar system, we further show that the cost function may not enjoy a more general notion of discrete convexity property called D-convexity. Yet, because of some other properties of the cost function, one can still solve the cost optimization problem using other methods from the literature.