{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,12]],"date-time":"2024-09-12T20:36:42Z","timestamp":1726173402321},"reference-count":0,"publisher":"Institute for Operations Research and the Management Sciences (INFORMS)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics of OR"],"published-print":{"date-parts":[[1983,8]]},"abstract":" A controller continuously monitors a storage system, such as an inventory or bank account, whose content Z = {Zt<\/jats:sub>,t\u22650} fluctuates as a (\u03bc, \u03c32<\/jats:sup>) Brownian motion in the absence of control. Holding costs are incurred continuously at rate h(Zt<\/jats:sub>). At any time, the controller may instantaneously increase the content of the system, incurring a proportional cost of r times the size of the increase, or decrease the content at a cost of l times the size of the decrease. We consider the case where h is convex on a finite interval [\u03b1, \u03b2] and h = \u221e outside this interval. The objective is to minimize the expected discounted sum of holding costs and control costs over an infinite planning horizon. <\/jats:p> It is shown that there exists an optimal control limit policy, characterized by two parameters a and b (\u03b1 \u2264 a < b \u2264 \u03b2). Roughly speaking, this policy exerts the minimum amounts of control sufficient to keep Zt<\/jats:sub> \u2208 [a, b] for all t \u2265 0. Put another way, the optimal control limit policy imposes on Z a lower reflecting barrier at a and an upper reflecting barrier at b. The optimality of a particular control limit policy is proved directly, with heavy reliance on the change of variable formula for semimartingales. We do not give a full-blown algorithm for construction of the optimal control limits, but a computational scheme could easily be developed from our constructive proof of existence. <\/jats:p>","DOI":"10.1287\/moor.8.3.439","type":"journal-article","created":{"date-parts":[[2008,10,31]],"date-time":"2008-10-31T22:43:38Z","timestamp":1225493018000},"page":"439-453","source":"Crossref","is-referenced-by-count":176,"title":["Instantaneous Control of Brownian Motion"],"prefix":"10.1287","volume":"8","author":[{"given":"J. Michael","family":"Harrison","sequence":"first","affiliation":[{"name":"Graduate School of Business, Department of Operations Research, Stanford University, Stanford, California 94305"}]},{"given":"Michael I.","family":"Taksar","sequence":"additional","affiliation":[{"name":"Graduate School of Business, Department of Operations Research, Stanford University, Stanford, California 94305"}]}],"member":"109","container-title":["Mathematics of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubsonline.informs.org\/doi\/pdf\/10.1287\/moor.8.3.439","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,2]],"date-time":"2023-04-02T11:00:11Z","timestamp":1680433211000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubsonline.informs.org\/doi\/10.1287\/moor.8.3.439"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,8]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1983,8]]}},"alternative-id":["10.1287\/moor.8.3.439"],"URL":"https:\/\/doi.org\/10.1287\/moor.8.3.439","relation":{},"ISSN":["0364-765X","1526-5471"],"issn-type":[{"value":"0364-765X","type":"print"},{"value":"1526-5471","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,8]]}}}