{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:29:00Z","timestamp":1787322540191,"version":"build-2736575974"},"reference-count":22,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","funder":[{"DOI":"10.13039\/501100001700","name":"Ministry of Education, Culture, Sports, Science, and Technology","doi-asserted-by":"publisher","award":["17K05377"],"award-info":[{"award-number":["17K05377"]}],"id":[{"id":"10.13039\/501100001700","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001700","name":"Ministry of Education, Culture, Sports, Science, and Technology","doi-asserted-by":"publisher","award":["19H01791"],"award-info":[{"award-number":["19H01791"]}],"id":[{"id":"10.13039\/501100001700","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001700","name":"Ministry of Education, Culture, Sports, Science, and Technology","doi-asserted-by":"publisher","award":["20K03758"],"award-info":[{"award-number":["20K03758"]}],"id":[{"id":"10.13039\/501100001700","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000121","name":"Division of Mathematical Sciences","doi-asserted-by":"publisher","award":["1905449"],"award-info":[{"award-number":["1905449"]}],"id":[{"id":"10.13039\/100000121","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2020,1]]},"abstract":"<jats:p>We consider a version of the stochastic inventory control problem for a spectrally positive L\u00e9vy demand process, in which the inventory can only be replenished at independent exponential times. We show the optimality of a periodic barrier replenishment policy that restocks any shortage below a certain threshold at each replenishment opportunity. The optimal policies and value functions are concisely written in terms of the scale functions. Numerical results are also provided.<\/jats:p>","DOI":"10.1137\/18m1196406","type":"journal-article","created":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T10:25:18Z","timestamp":1605608718000},"page":"3428-3456","source":"Crossref","is-referenced-by-count":10,"title":["Optimal Periodic Replenishment Policies for Spectrally Positive L\u00e9vy Demand Processes"],"prefix":"10.1137","volume":"58","author":[{"given":"Jos\u00e9-Luis","family":"P\u00e9rez","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7401-2157","authenticated-orcid":true,"given":"Kazutoshi","family":"Yamazaki","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alain","family":"Bensoussan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2020,11,17]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.3150\/15-BEJ695"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2014.01.005"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1214\/105051606000000709"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2017.04.013"},{"key":"atypb5","unstructured":"R. G. Bartle,\n                      The Elements of Integration\n                      , John Wiley & Sons, New York, 1966."},{"key":"atypb6","unstructured":"A. Bensoussan,\n                      Dynamic Programming and Inventory Control\n                      , IOS Press, Amsterdam, 2011."},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012904443737"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2013.12.044"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1093\/rfs\/11.3.597"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-010-0289-4"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1137\/15M1051208"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"A. Kuznetsov, A. E, Kyprianou, and V. Rivero,\n                      The Theory of Scale Functions for Spectrally Negative L\u00e9vy Processes\n                      , L\u00e9vy Matters II, Lecture Notes in Math., Springer, Berlin, 2013.","DOI":"10.1007\/978-3-642-31407-0_2"},{"key":"atypb13","doi-asserted-by":"crossref","unstructured":"A. E. Kyprianou,\n                      Introductory Lectures on Fluctuations of L\u00e9vy Processes with Applications\n                      , Springer, Berlin, 2006.","DOI":"10.1007\/978-3-540-31343-4"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2009.03.002"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2013.11.005"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2018.02.004"},{"key":"atypb17","doi-asserted-by":"publisher","DOI":"10.1016\/j.insmatheco.2017.08.001"},{"key":"atypb18","doi-asserted-by":"publisher","DOI":"10.3390\/risks6020033"},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-018-9494-9"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1142\/S0219024915500326"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2016.0801"},{"key":"atypb22","doi-asserted-by":"crossref","unstructured":"P. Protter,\n                      Stochastic Integration and Differential Equations\n                      , 2nd ed., Springer, Berlin, 2005.","DOI":"10.1007\/978-3-662-10061-5"}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1196406","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:22:55Z","timestamp":1787318575000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1196406"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1]]},"references-count":22,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2020,1]]}},"alternative-id":["10.1137\/18M1196406"],"URL":"https:\/\/doi.org\/10.1137\/18m1196406","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1]]}}}