{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:10:43Z","timestamp":1750306243099,"version":"3.41.0"},"reference-count":17,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2016,9,29]],"date-time":"2016-09-29T00:00:00Z","timestamp":1475107200000},"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":[[2016,9,29]]},"abstract":"<jats:p>This paper describes the structure of optimal policies for discounted periodic-review single-commodity total-cost inventory control problems with fixed ordering costs for finite and infinite horizons. There are known conditions in the literature for optimality of (st, St) policies for finite-horizon problems and the optimality of (s, S) policies for infinitehorizon problems. The results of this paper cover the situation, when such assumptions may not hold. This paper describes a parameter, which, together with the value of the discount factor and the horizon length, defines the structure of an optimal policy. For the infinite horizon, depending on the values of this parameter and the discount factor, an optimal policy either is an (s, S) policy or never orders inventory. For a finite horizon, depending on the values of this parameter, the discount factor, and the horizon length, there are three possible structures of an optimal policy: (i) it is an (st, St) policy, (ii) it is an (st, St) policy at earlier stages and then does not order inventory, or (iii) it never orders inventory. The paper also establishes continuity of the optimal value function and describes the optimal actions at states st and s.<\/jats:p>","DOI":"10.1145\/3003977.3003985","type":"journal-article","created":{"date-parts":[[2016,10,3]],"date-time":"2016-10-03T13:40:48Z","timestamp":1475502048000},"page":"21-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Structure of Optimal Solutions to Periodic-Review Total-Cost Stochastic Inventory Control Problems"],"prefix":"10.1145","volume":"44","author":[{"given":"Eugene A.","family":"Feinberg","sequence":"first","affiliation":[{"name":"Stony Brook University, Stony Brook, NY"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yan","family":"Liang","sequence":"additional","affiliation":[{"name":"Stony Brook University, Stony Brook, NY"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2016,9,29]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_2_1_1_1","DOI":"10.2307\/1906813"},{"volume-title":"IOS Press","year":"2011","author":"Bensoussan A.","key":"e_1_2_1_2_1"},{"unstructured":"D. P. Bertsekas. Dynamic Programming and Optimal Control 2nd ed vol. 1 Athena Scientific MA 2000.   D. P. Bertsekas. Dynamic Programming and Optimal Control 2nd ed vol. 1 Athena Scientific MA 2000.","key":"e_1_2_1_3_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_4_1","DOI":"10.1023\/A:1021734003033"},{"doi-asserted-by":"publisher","key":"e_1_2_1_5_1","DOI":"10.1287\/opre.1040.0127"},{"doi-asserted-by":"publisher","key":"e_1_2_1_6_1","DOI":"10.1287\/moor.1040.0093"},{"issue":"4","key":"e_1_2_1_7_1","first-page":"586","article-title":"On the Optimal Character of the (s,S) Policy","volume":"21","author":"Dvoretzky A.","year":"1953","journal-title":"Inventory Theory. Econometrica"},{"volume-title":"INFORMS","year":"2016","author":"Feinberg E. A.","key":"e_1_2_1_8_1"},{"doi-asserted-by":"publisher","key":"e_1_2_1_9_1","DOI":"10.1287\/moor.1120.0555"},{"unstructured":"E. A. Feinberg and M. E. Lewis. On the Convergence of Optimal Actions for Markov Decision Processes and the Optimality of (s S) Policies for Inventory Control http:\/\/arxiv.org\/abs\/1507.05125 2015.  E. A. Feinberg and M. E. Lewis. On the Convergence of Optimal Actions for Markov Decision Processes and the Optimality of (s S) Policies for Inventory Control http:\/\/arxiv.org\/abs\/1507.05125 2015.","key":"e_1_2_1_10_1"},{"unstructured":"D. P. Heyman and M. J. Sobel. Stochastic Models in Operations Research vol. II McGraw-Hill NY 1984.  D. P. Heyman and M. J. Sobel. Stochastic Models in Operations Research vol. II McGraw-Hill NY 1984.","key":"e_1_2_1_11_1"},{"unstructured":"D. L. Iglehart. Dynamic Programming and Stationary Analysis of Inventory Problems. Office of Naval Research Monographs on Mathematical Methods in Logistics ch. 1 pp. 1--31 Stanford University Press CA 1963.  D. L. Iglehart. Dynamic Programming and Stationary Analysis of Inventory Problems. 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