{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T04:36:06Z","timestamp":1750221366338,"version":"3.41.0"},"reference-count":11,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2017,10,11]],"date-time":"2017-10-11T00:00:00Z","timestamp":1507680000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["SIGMETRICS Perform. Eval. Rev."],"published-print":{"date-parts":[[2017,10,11]]},"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.1145\/3152042.3152044","type":"journal-article","created":{"date-parts":[[2017,10,12]],"date-time":"2017-10-12T12:52:50Z","timestamp":1507812770000},"page":"3-5","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Optimality of Reflection Control, with Production--Inventory Applications"],"prefix":"10.1145","volume":"45","author":[{"given":"Jiankui","family":"Yang","sequence":"first","affiliation":[{"name":"Beijing University of Posts and Telemmunications, Beijing"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David D.","family":"Yao","sequence":"additional","affiliation":[{"name":"Columbia University, New York"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heng-Qing","family":"Ye","sequence":"additional","affiliation":[{"name":"Hong Kong Polytechnic University, Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,10,11]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012904443737"},{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-5301-1","volume-title":"Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization","author":"Chen H.","year":"2001","unstructured":"Chen , H. and D.D. Yao , Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization . Springer-Verlag , New York , 2001 . Chen, H. and D.D. Yao, Fundamentals of Queueing Networks: Performance, Asymptotics, and Optimization. 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