{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:50:08Z","timestamp":1750308608300,"version":"3.41.0"},"reference-count":19,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2018,3,20]],"date-time":"2018-03-20T00:00:00Z","timestamp":1521504000000},"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":[[2018,3,20]]},"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 ? 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.<\/jats:p>","DOI":"10.1145\/3199524.3199554","type":"journal-article","created":{"date-parts":[[2018,3,22]],"date-time":"2018-03-22T15:17:48Z","timestamp":1521731868000},"page":"180-183","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":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"David D.","family":"Yao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Heng-Qing","family":"Ye","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2018,3,20]]},"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":"publisher","DOI":"10.1287\/moor.1080.0353"},{"volume-title":"Springer-Verlag","year":"2001","author":"Chen H.","key":"e_1_2_1_3_1"},{"volume-title":"Academic Press","year":"1981","author":"Cs\u00f6rgo M.","key":"e_1_2_1_4_1"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/9.471210"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1287\/11-SSY041"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1287\/11-SSY046"},{"volume-title":"Fourth Edition","year":"2010","author":"Durrett R.","key":"e_1_2_1_8_1"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1214\/105051605000000638"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.8.3.439"},{"key":"e_1_2_1_11_1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.8.3.454"},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.5555\/1550713"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1060.0380"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.9.3.441"},{"key":"e_1_2_1_15_1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.10.1.63"},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2013.0603"},{"key":"e_1_2_1_17_1","doi-asserted-by":"publisher","DOI":"10.1239\/jap\/1450802743"},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.5555\/3219383.3219384"},{"key":"e_1_2_1_19_1","unstructured":"Ye H.Q. and D.D. Yao Justifying diffusion approximations for stochastic processing networks under a moment condition under review.  Ye H.Q. and D.D. Yao Justifying diffusion approximations for stochastic processing networks under a moment condition under review."}],"container-title":["ACM SIGMETRICS Performance Evaluation Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3199524.3199554","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3199524.3199554","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T19:07:17Z","timestamp":1750273637000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3199524.3199554"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,20]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,3,20]]}},"alternative-id":["10.1145\/3199524.3199554"],"URL":"https:\/\/doi.org\/10.1145\/3199524.3199554","relation":{},"ISSN":["0163-5999"],"issn-type":[{"type":"print","value":"0163-5999"}],"subject":[],"published":{"date-parts":[[2018,3,20]]},"assertion":[{"value":"2018-03-20","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}