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

Jiankui Yang; David D. Yao; Hengqing Ye

doi:10.1145/3199524.3199554

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

Jiankui Yang, David D. Yao, Hengqing Ye

Research output: Journal article publication › Conference article › Academic research › peer-review

Abstract

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 language	English
Pages (from-to)	180-183
Number of pages	4
Journal	Performance Evaluation Review
Volume	45
Issue number	3
DOIs	https://doi.org/10.1145/3199524.3199554
Publication status	Published - 20 Mar 2018
Event	35th 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 2017 → 17 Nov 2017

ASJC Scopus subject areas

Software
Hardware and Architecture
Computer Networks and Communications

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10.1145/3199524.3199554

http://hdl.handle.net/10397/98319

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

Abstract

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