Technical Note—Error Noted in “Order-Based Cost Optimization in Assemble-to-Order Systems” by Lu and Song (2005)

Mohammadreza Bolandnazar (), Woonghee Tim Huh (), S. Thomas McCormick () and Kazuo Murota ()
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Mohammadreza Bolandnazar: Columbia Business School, Columbia University, New York, New York 10027
Woonghee Tim Huh: Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
S. Thomas McCormick: Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
Kazuo Murota: School of Business Administration, Tokyo Metropolitan University, Tokyo 192-0397, Japan

Operations Research, 2019, vol. 67, issue 1, 163-166

Abstract: One of the main results of “Order-Based Cost Optimization in Assemble-to-Order Systems” [ Lu Y, Song J-S (2005) Order-based cost optimization in assemble-to-order systems. Oper. Res. 53(1):151–169] 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. We construct a counterexample showing that this result is incorrect, and hence their proposed steepest decent algorithm may not work.

Keywords: inventory/production: stochastic; multi-item; assemble-to-order; optimization: submodularity; discrete convexity (search for similar items in EconPapers)
Date: 2019
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