On the Optimality of Reflection Control, with Production-Inventory Applications

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Original languageEnglish
Pages (from-to)3-5
Journal / PublicationPerformance Evaluation Review
Issue number2
Publication statusPublished - Sep 2017
Externally publishedYes


Title19th Workshop on MAthematical performance Modeling and Analysis (MAMA 2017)
PlaceUnited States
Period5 June 2017


We study the control of a Brownian motion (BM) with a negative drift, so as to minimize a long-run average cost objective. We show the optimality of a class of reflection controls that prevent the BM from dropping below some negative level r, by cancelling out from time to time part of the negative drift; and this optimality is established for any holding cost function h(x) that is increasing in |x|. Furthermore, we show the optimal reflection level can be derived as the fixed point that equates the long-run average cost to the holding cost. We also show the asymptotic optimality of this reflection control when it is applied to production-inventory systems driven by discrete counting processes.