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

Research output: Journal Publications and Reviews (RGC: 21, 22, 62)21_Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)180-183
Journal / PublicationPerformance Evaluation Review
Issue number3
Publication statusPublished - Dec 2017
Externally publishedYes


Title35th International Symposium on Computer Performance, Modeling, Measurements and Evaluation, IFIP WG 7.3 Performance 2017
LocationColumbia University
PlaceUnited States
CityNew York
Period13 - 17 November 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 ≥ 0 and decreasing in x ≤ 0. 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.