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

Jiankui Yang; David D. Yao; Hengqing Ye

doi:10.1145/3152042.3152044

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

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 language	English
Pages (from-to)	3-5
Number of pages	3
Journal	Performance Evaluation Review
Volume	45
Issue number	2
DOIs	https://doi.org/10.1145/3152042.3152044
Publication status	Published - 1 Sept 2017
Event	Workshop 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

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10.1145/3152042.3152044

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AU - Ye, Hengqing

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AB - 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.

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

Abstract

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