{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:33:11Z","timestamp":1740123191505,"version":"3.37.3"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,6,17]],"date-time":"2017-06-17T00:00:00Z","timestamp":1497657600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2017,6,17]],"date-time":"2017-06-17T00:00:00Z","timestamp":1497657600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000147","name":"Division of Civil, Mechanical and Manufacturing Innovation","doi-asserted-by":"publisher","award":["CMMI-1335296","CMMI-1636193"],"award-info":[{"award-number":["CMMI-1335296","CMMI-1636193"]}],"id":[{"id":"10.13039\/100000147","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Ann Oper Res"],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s10479-017-2548-6","type":"journal-article","created":{"date-parts":[[2017,6,17]],"date-time":"2017-06-17T04:55:57Z","timestamp":1497675357000},"page":"29-45","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Structure of optimal policies to periodic-review inventory models with convex costs and backorders for all values of discount factors"],"prefix":"10.1007","volume":"317","author":[{"given":"Eugene A.","family":"Feinberg","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Liang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,6,17]]},"reference":[{"issue":"3","key":"2548_CR1","doi-asserted-by":"publisher","first-page":"250","DOI":"10.2307\/1906813","volume":"19","author":"KJ Arrow","year":"1951","unstructured":"Arrow, K. J., Harris, T., & Marschak, J. (1951). Optimal inventory policy. Econometrica, 19(3), 250\u2013272.","journal-title":"Econometrica"},{"key":"2548_CR2","volume-title":"Dynamic programming and inventory control","author":"A Bensoussan","year":"2011","unstructured":"Bensoussan, A. (2011). Dynamic programming and inventory control. Amsterdam: IOS Press."},{"key":"2548_CR3","volume-title":"Dynamic programming and optimal control","author":"DP Bertsekas","year":"2000","unstructured":"Bertsekas, D. P. (2000). Dynamic programming and optimal control (2nd ed., Vol. 1). Belmont, MA: Athena Scientific.","edition":"2"},{"key":"2548_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-71604-6","volume-title":"Markovian demand inventory models","author":"D Beyer","year":"2010","unstructured":"Beyer, D., Cheng, F., Sethi, S. P., & Taksar, M. (2010). Markovian demand inventory models. New York: Springer."},{"issue":"3","key":"2548_CR5","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1023\/A:1021734003033","volume":"101","author":"D Beyer","year":"1999","unstructured":"Beyer, D., & Sethi, S. P. (1999). The classical average-cost inventory models of Iglehart and Veinott\u2013Wagner revisited. Journal of Optimization Theory and Applications, 101(3), 523\u2013555.","journal-title":"Journal of Optimization Theory and Applications"},{"issue":"6","key":"2548_CR6","doi-asserted-by":"publisher","first-page":"887","DOI":"10.1287\/opre.1040.0127","volume":"52","author":"X Chen","year":"2004","unstructured":"Chen, X., & Simchi-Levi, D. (2004a). Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The finite horizon case. Operations Research, 52(6), 887\u2013896.","journal-title":"Operations Research"},{"issue":"3","key":"2548_CR7","doi-asserted-by":"publisher","first-page":"698","DOI":"10.1287\/moor.1040.0093","volume":"29","author":"X Chen","year":"2004","unstructured":"Chen, X., & Simchi-Levi, D. (2004b). Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: The infinite horizon case. Mathematics of Operations Research, 29(3), 698\u2013723.","journal-title":"Mathematics of Operations Research"},{"issue":"4","key":"2548_CR8","doi-asserted-by":"publisher","first-page":"586","DOI":"10.2307\/1907924","volume":"21","author":"A Dvoretzky","year":"1953","unstructured":"Dvoretzky, A., Kiefer, J., & Wolfowitz, J. (1953). On the optimal character of the (s, S) policy in inventory theory. Econometrica, 21(4), 586\u2013596.","journal-title":"Econometrica"},{"key":"2548_CR9","doi-asserted-by":"crossref","unstructured":"Feinberg, E. A. (2016). Optimality conditions for inventory control. In A. Gupta & A. Capponi (Eds.), Tutorials in Operations Research. Optimization challenges in complex, networked, and risky systems (pp. \u00a014\u201344). Cantonsville, MD: INFORMS.","DOI":"10.1287\/educ.2016.0145"},{"issue":"3","key":"2548_CR10","doi-asserted-by":"publisher","first-page":"485","DOI":"10.1007\/s11228-015-0318-7","volume":"23","author":"EA Feinberg","year":"2015","unstructured":"Feinberg, E. A., & Kasyanov, P. O. (2015). Continuity of minima: Local results. Set-Valued and Variational Analysis, 23(3), 485\u2013499.","journal-title":"Set-Valued and Variational Analysis"},{"issue":"2","key":"2548_CR11","doi-asserted-by":"publisher","first-page":"1040","DOI":"10.1016\/j.jmaa.2013.12.011","volume":"413","author":"EA Feinberg","year":"2014","unstructured":"Feinberg, E. A., Kasyanov, P. O., & Voorneveld, M. (2014). Berges maximum theorem for noncompact image sets. Journal of Mathematical Analysis and Applications, 413(2), 1040\u20131046.","journal-title":"Journal of Mathematical Analysis and Applications"},{"issue":"4","key":"2548_CR12","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1287\/moor.1120.0555","volume":"37","author":"EA Feinberg","year":"2012","unstructured":"Feinberg, E. A., Kasyanov, P. O., & Zadoianchuk, N. V. (2012). Average cost Markov decision processes with weakly continuous transition probabilities. Mathematics of Operations Research, 37(4), 591\u2013607.","journal-title":"Mathematics of Operations Research"},{"issue":"1","key":"2548_CR13","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/j.jmaa.2012.07.051","volume":"397","author":"EA Feinberg","year":"2013","unstructured":"Feinberg, E. A., Kasyanov, P. O., & Zadoianchuk, N. V. (2013). Berge\u2019s theorem for noncompact image sets. Journal of Mathematical Analysis and Applications, 397(1), 255\u2013259.","journal-title":"Journal of Mathematical Analysis and Applications"},{"key":"2548_CR14","unstructured":"Feinberg, E. A., & Lewis, M. E. (2015). On the convergence of optimal actions for Markov decision processes and the optimality of $$(s, S)$$ policies for inventory control. arXiv:1507.05125."},{"key":"2548_CR15","volume-title":"Stochastic models in operations research","author":"DP Heyman","year":"1984","unstructured":"Heyman, D. P., & Sobel, M. J. (1984). Stochastic models in operations research (Vol. II). New York: McGraw-Hill."},{"key":"2548_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-02796-7","volume-title":"Convex analysis and minimization algorithms I","author":"J-B Hiriart-Urruty","year":"1993","unstructured":"Hiriart-Urruty, J.-B., & Lemar\u00e9chal, C. (1993). Convex analysis and minimization algorithms I. Berlin: Springer."},{"issue":"3","key":"2548_CR17","doi-asserted-by":"publisher","first-page":"783","DOI":"10.1287\/opre.1070.0462","volume":"56","author":"WT Huh","year":"2008","unstructured":"Huh, W. T., & Janakiraman, G. (2008). $$(s, S)$$ Optimality in joint inventory-pricing control: An alternate approach. Operations Research, 56(3), 783\u2013790.","journal-title":"Operations Research"},{"issue":"1","key":"2548_CR18","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1287\/opre.1100.0845","volume":"59","author":"WT Huh","year":"2011","unstructured":"Huh, W. T., Janakiraman, G., & Nagarajan, M. (2011). Average cost single-stage inventory models: An analysis using a vanishing discount approach. Operations Research, 59(1), 143\u2013155.","journal-title":"Operations Research"},{"key":"2548_CR19","first-page":"1","volume-title":"Multistage inventory control models and techniques","author":"DL Iglehart","year":"1963","unstructured":"Iglehart, D. L. (1963). Dynamic programming and stationary analysis of inventory roblems. In H. Scarf, D. Gilford, & M. Shelly (Eds.), Multistage inventory control models and techniques (pp. 1\u201331). Stanford, CA: Stanford University Press."},{"key":"2548_CR20","doi-asserted-by":"publisher","DOI":"10.1007\/s10479-015-1998-y","author":"MN Katehakis","year":"2016","unstructured":"Katehakis, M. N., Melamed, B., & Shi, J. (2016). Optimal replenishment rate for inventory systems with compound Poisson demands and lost-sales: A direct treatment of time average cost. Annals of Operations Research,. doi:10.1007\/s10479-015-1998-y.","journal-title":"Annals of Operations Research"},{"key":"2548_CR21","volume-title":"Convex structures and economic theory, mathematics in science and engineering","author":"H Nikaido","year":"1968","unstructured":"Nikaido, H. (1968). Convex structures and economic theory, mathematics in science and engineering (Vol. 51). New York: Academic Press."},{"key":"2548_CR22","doi-asserted-by":"publisher","DOI":"10.1515\/9781503619883","volume-title":"Foundations of stochastic inventory theory","author":"E Porteus","year":"2002","unstructured":"Porteus, E. (2002). Foundations of stochastic inventory theory. Stanford, CA: Stanford University Press."},{"key":"2548_CR23","first-page":"196","volume-title":"Mathematical methods in the social sciences","author":"H Scarf","year":"1960","unstructured":"Scarf, H. (1960). The optimality of (S, s) policies in the dynamic inventory problem. In K. Arrow, S. Karlin, & P. Suppes (Eds.), Mathematical methods in the social sciences (pp. 196\u2013202). Stanford, CA: Stanford University Press."},{"issue":"3","key":"2548_CR24","doi-asserted-by":"publisher","first-page":"528","DOI":"10.1137\/0130048","volume":"30","author":"M Sch\u00e4l","year":"1976","unstructured":"Sch\u00e4l, M. (1976). On the optimality of $$(s, S)$$-policies in dynamic inventory models with finite horizon. SIAM Journal on Applied Mathematics, 30(3),528\u2013537.","journal-title":"SIAM Journal on Applied Mathematics"},{"issue":"1","key":"2548_CR25","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"},{"key":"2548_CR26","volume-title":"The logic of logistics: Theory, algorithms, and applications for logistics management","author":"D Simchi-Levi","year":"2004","unstructured":"Simchi-Levi, D., Chen, X., & Bramel, J. (2004). The logic of logistics: Theory, algorithms, and applications for logistics management (2nd ed.). New York: Springer.","edition":"2"},{"issue":"5","key":"2548_CR27","doi-asserted-by":"publisher","first-page":"525","DOI":"10.1287\/mnsc.11.5.525","volume":"11","author":"AF Veinott","year":"1965","unstructured":"Veinott, A. F., & Wagner, H. M. (1965). Computing optimal $$(s, S)$$ policies. Management Science, 11(5), 525\u2013552.","journal-title":"Management Science"},{"issue":"1","key":"2548_CR28","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1287\/mnsc.9.1.123","volume":"9","author":"E Zabel","year":"1962","unstructured":"Zabel, E. (1962). A note on the optimality of $$(s, S)$$ policies in inventory theory. Management Science, 9(1), 123\u2013125.","journal-title":"Management Science"},{"issue":"4","key":"2548_CR29","doi-asserted-by":"publisher","first-page":"802","DOI":"10.2307\/3214683","volume":"28","author":"Y Zheng","year":"1991","unstructured":"Zheng, Y. (1991). A simple proof for the optimality of $$(s, S)$$ policies in infinite horizon inventory systems. Journal of Applied Probability, 28(4), 802\u2013810.","journal-title":"Journal of Applied Probability"},{"key":"2548_CR30","volume-title":"Foundations of inventory management","author":"PH Zipkin","year":"2000","unstructured":"Zipkin, P. H. (2000). Foundations of inventory management. New York: McGraw-Hill."}],"container-title":["Annals of Operations Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-017-2548-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10479-017-2548-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10479-017-2548-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,18]],"date-time":"2022-10-18T18:20:53Z","timestamp":1666117253000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10479-017-2548-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,6,17]]},"references-count":30,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["2548"],"URL":"https:\/\/doi.org\/10.1007\/s10479-017-2548-6","relation":{},"ISSN":["0254-5330","1572-9338"],"issn-type":[{"type":"print","value":"0254-5330"},{"type":"electronic","value":"1572-9338"}],"subject":[],"published":{"date-parts":[[2017,6,17]]},"assertion":[{"value":"17 June 2017","order":1,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}