{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T19:35:55Z","timestamp":1765827355833},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,9,25]],"date-time":"2015-09-25T00:00:00Z","timestamp":1443139200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2015,9,25]],"date-time":"2015-09-25T00:00:00Z","timestamp":1443139200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s10479-015-1998-y","type":"journal-article","created":{"date-parts":[[2015,9,25]],"date-time":"2015-09-25T15:30:26Z","timestamp":1443195026000},"page":"665-691","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Optimal replenishment rate for inventory systems with compound Poisson demands and lost sales: a direct treatment of time-average cost"],"prefix":"10.1007","volume":"317","author":[{"given":"Michael N.","family":"Katehakis","sequence":"first","affiliation":[]},{"given":"Benjamin","family":"Melamed","sequence":"additional","affiliation":[]},{"given":"Jim Junmin","family":"Shi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,9,25]]},"reference":[{"issue":"3","key":"1998_CR1","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1007\/s00186-005-0032-6","volume":"62","author":"I Adan","year":"2005","unstructured":"Adan, I., Boxma, O., & Perry, D. (2005). The G\/M\/1 queue revisited. Mathematical Methods of Operations Research, 62(3), 437\u2013452.","journal-title":"Mathematical Methods of Operations Research"},{"key":"1998_CR2","doi-asserted-by":"publisher","first-page":"899","DOI":"10.1287\/mnsc.24.9.899","volume":"24","author":"B Archibald","year":"1978","unstructured":"Archibald, B., & Silver, E. (1978). ($$s$$, $$S$$) policy under continuous review and discrete compound Poisson demands. Management Science, 24, 899\u2013909.","journal-title":"Management Science"},{"key":"1998_CR3","doi-asserted-by":"crossref","unstructured":"Beyer, D., Cheng, F., Sethi, S. P., & Taksar, M. I. (2010). Markovian demand inventory models. International series in operations research and management science. New York, NY: Springer.","DOI":"10.1007\/978-0-387-71604-6"},{"issue":"5","key":"1998_CR4","doi-asserted-by":"publisher","first-page":"957","DOI":"10.1287\/opre.31.5.957","volume":"31","author":"A Federgruen","year":"1983","unstructured":"Federgruen, A., & Schechner, Z. (1983). Cost formulas for continuous review inventory models with fixed delivery lags. Operations Research, 31(5), 957\u2013965.","journal-title":"Operations Research"},{"key":"1998_CR5","doi-asserted-by":"publisher","first-page":"654","DOI":"10.2307\/3213131","volume":"15","author":"R Feldman","year":"1978","unstructured":"Feldman, R. (1978). A continuous review ($$s$$, $$S$$) inventory system in a random environment. Journal of Applied Probability, 15, 654\u2013659.","journal-title":"Journal of Applied Probability"},{"key":"1998_CR6","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1287\/mnsc.28.4.400","volume":"28","author":"SC Graves","year":"1982","unstructured":"Graves, S. C. (1982). The application of queueing theory to continuous perishable inventory systems. Management Science, 28, 400\u2013406.","journal-title":"Management Science"},{"key":"1998_CR7","doi-asserted-by":"publisher","first-page":"246","DOI":"10.1287\/moor.6.2.246","volume":"6","author":"SC Graves","year":"1981","unstructured":"Graves, S. C., & Keilson, J. (1981). The compensation method applied to a one-product production inventory model. Mathematics of Operations Research, 6, 246\u2013262.","journal-title":"Mathematics of Operations Research"},{"key":"1998_CR8","unstructured":"Gullu, R., Jackson, P. L. (1993). On the continuous time capacitated production\/inventory problem with no set up costs. ORIE technical reports."},{"key":"1998_CR9","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0891-4","volume-title":"Probability","author":"AF Karr","year":"1993","unstructured":"Karr, A. F. (1993). Probability. New York: Springer."},{"issue":"1","key":"1998_CR10","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1007\/s10479-012-1071-z","volume":"200","author":"MN Katehakis","year":"2012","unstructured":"Katehakis, M. N., & Smit, L. C. (2012). On computing optimal ($$Q$$, $$r$$) replenishment policies under quantity discounts. Annals of Operations Research, 200(1), 279\u2013298.","journal-title":"Annals of Operations Research"},{"issue":"3","key":"1998_CR11","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1002\/nav.20395","volume":"57","author":"D Li","year":"2010","unstructured":"Li, D., & Glazebrook, K. D. (2010). An approximate dynamic programming approach to the development of heuristics for the scheduling of impatient jobs in a clearing system. Naval Research Logistics, 57(3), 225\u2013236.","journal-title":"Naval Research Logistics"},{"issue":"1","key":"1998_CR12","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1016\/j.ijpe.2006.12.028","volume":"108","author":"S Minner","year":"2007","unstructured":"Minner, S., & Silver, E. A. (2007). Replenishment policies for multiple products with compound-Poisson demand that share a common warehouse. International Journal of Production Economics, 108(1), 388\u2013398.","journal-title":"International Journal of Production Economics"},{"issue":"1","key":"1998_CR13","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1017\/S026996480216102X","volume":"16","author":"D Perry","year":"2002","unstructured":"Perry, D., & Stadje, W. (2002). Exact distributions in a jump-diffusion storage model. Probability in the Engineering and Informational Sciences, 16(1), 19\u201327.","journal-title":"Probability in the Engineering and Informational Sciences"},{"key":"1998_CR14","doi-asserted-by":"publisher","first-page":"451","DOI":"10.1016\/S0167-6377(03)00032-4","volume":"31","author":"D Perry","year":"2003","unstructured":"Perry, D., & Stadje, W. (2003). Duality of dams via mountain processes. Operations Research Letters, 31, 451\u2013458.","journal-title":"Operations Research Letters"},{"key":"1998_CR15","volume-title":"Queues and inventories: a study of their basic stochastic processes","author":"NU Prabhu","year":"1965","unstructured":"Prabhu, N. U. (1965). Queues and inventories: a study of their basic stochastic processes. New York: Wiley."},{"issue":"2","key":"1998_CR16","doi-asserted-by":"publisher","first-page":"279","DOI":"10.1111\/j.1937-5956.2006.tb00245.x","volume":"15","author":"E Presman","year":"2006","unstructured":"Presman, E., & Sethi, S. P. (2006). Inventory models with continuous and Poisson demands and discounted and average costs. Production and Operations Management, 15(2), 279\u2013293.","journal-title":"Production and Operations Management"},{"key":"1998_CR17","doi-asserted-by":"publisher","first-page":"366","DOI":"10.1287\/opre.23.2.366","volume":"23","author":"FR Richards","year":"1975","unstructured":"Richards, F. R. (1975). Comments on the distribution of inventory position in a continuous-review ($$s$$, $$S$$) inventory system. Operations Research, 23, 366\u2013371.","journal-title":"Operations Research"},{"key":"1998_CR18","unstructured":"Ross, S. M. (1996). Stochastic processes (Vol. 2). New York: Wiley."},{"key":"1998_CR19","doi-asserted-by":"publisher","first-page":"717","DOI":"10.1287\/opre.27.4.717","volume":"27","author":"I Sahin","year":"1979","unstructured":"Sahin, I. (1979). On the stationary analysis of continuous review ($$s$$, $$S$$) inventory systems with constant lead times. Operation Research, 27, 717\u2013730.","journal-title":"Operation Research"},{"key":"1998_CR20","doi-asserted-by":"publisher","first-page":"213","DOI":"10.2307\/3213739","volume":"20","author":"I Sahin","year":"1983","unstructured":"Sahin, I. (1983). On the continuous review ($$s$$, $$S$$) inventory model under compound renewal demand and random lead times. Journal of Applied Probability, 20, 213\u2013219.","journal-title":"Journal of Applied Probability"},{"issue":"1","key":"1998_CR21","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1007\/s10479-012-1130-5","volume":"208","author":"J Shi","year":"2013","unstructured":"Shi, J., Katehakis, M. N., & Melamed, B. (2013). Martingale methods for pricing inventory penalties under continuous replenishment and compound renewal demands. Annals of Operations Research, 208(1), 593\u2013612.","journal-title":"Annals of Operations Research"},{"issue":"5","key":"1998_CR22","doi-asserted-by":"publisher","first-page":"1048","DOI":"10.1287\/opre.2014.1299","volume":"6","author":"J Shi","year":"2014","unstructured":"Shi, J., Katehakis, M. N., Melamed, B., & Xia, Y. (2014). Optimal continuous replenishment for a production-inventory system with compound Poisson demands and lost-sales. Operations Research, 6(5), 1048\u20131063.","journal-title":"Operations Research"},{"key":"1998_CR23","unstructured":"Simchi-Levi, D., Kaminsky, P., & Simchi-Levi, E. (2008). Designing and managing the supply chain (3rd\u00a0ed.). New York: McGraw-Hill\/Irwin."},{"key":"1998_CR24","unstructured":"Springael, J., Nieuwenhuyse, I. V. (2005). A lost sales inventory model with a compound Poisson demand pattern. Working papers, University of Antwerp."},{"key":"1998_CR25","doi-asserted-by":"publisher","first-page":"581","DOI":"10.1080\/00207547508943030","volume":"13","author":"R Thompstone","year":"1975","unstructured":"Thompstone, R., & Silver, E. (1975). A coordinated inventory control system for compound Poisson demand and zero lead time. International Journal of Production Research, 13, 581\u2013602.","journal-title":"International Journal of Production Research"},{"key":"1998_CR26","unstructured":"Tijms, H. C. (1972). Analysis of ($$s$$) inventory models. Amsterdam: Mathematich Centrum."},{"key":"1998_CR27","volume-title":"The Laplace transform","author":"DV Widder","year":"1959","unstructured":"Widder, D. V. (1959). The Laplace transform. New Jersey: Princeton University Press."}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-015-1998-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-015-1998-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-015-1998-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-015-1998-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,1]],"date-time":"2022-11-01T13:42:07Z","timestamp":1667310127000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-015-1998-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,25]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["1998"],"URL":"https:\/\/doi.org\/10.1007\/s10479-015-1998-y","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"value":"0254-5330","type":"print"},{"value":"1572-9338","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9,25]]},"assertion":[{"value":"25 September 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}