On the optimality of reflection control, with production-inventory applications

Jiankui Yang, David D. Yao, Hengqing Ye

Research output: Journal article publicationConference articleAcademic researchpeer-review


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.
Original languageEnglish
Pages (from-to)180-183
Number of pages4
JournalPerformance Evaluation Review
Issue number3
Publication statusPublished - 20 Mar 2018
Event35th IFIP International Symposium on Computer Performance, Modeling, Measurements and Evaluation, IFIP WG 7.3 Performance 2017 - Columbia University, New York, United States
Duration: 13 Nov 201717 Nov 2017

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications

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