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


is held by author/owner(s). 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.
Original languageEnglish
Pages (from-to)3-5
Number of pages3
JournalPerformance Evaluation Review
Issue number2
Publication statusPublished - 1 Sept 2017
EventWorkshop on MAthematical Performance Modeling and Analysis, MAMA 2017, 2017 Greenmetrics Workshop and Workshop on Critical Infrastructure Network Security, CINS 2017 - Urbana-Champaign, United States
Duration: 1 Sept 2017 → …

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications


Dive into the research topics of 'On the optimality of reflection control, with production-inventory applications'. Together they form a unique fingerprint.

Cite this