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Previous article Next article Bounds on the Solution of the Lagged Optimal Inventory Equation with No Demand Backlogging and Proportional CostsThomas E. MortonThomas E. Mortonhttps://doi.org/10.1137/1011090PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Kenneth J. Arrow, , Theodore Harris and , Jacob Marschak, Optimal inventory policy, Econometrica, 19 (1951), 250–272 MR0044094 0045.23205 CrossrefISIGoogle Scholar[2] Kenneth J. Arrow, , Samuel Karlin and , Herbert Scarf, Studies in the mathematical theory of inventory and production, Stanford Mathematical Studies in the Social Sciences, I, Stanford University Press, Stanford, Calif., 1958xi+340 MR0094248 0079.36003 Google Scholar[3] R. Bellman, , I. Glicksberg and , O. Gross, On the optimal inventory equation, Management Sci., 2 (1955), 83–104 MR0074761 0995.90501 CrossrefGoogle Scholar[4] A. Dvoretzky, , J. Kiefer and , J. Wolfowitz, The inventory problem. I. Case of known distributions of demand, Econometrica, 20 (1952), 187–222 MR0047304 0046.37603 CrossrefISIGoogle Scholar[5] Herbert E. Scarf, A survey of analytic techniques in inventory theoryMultistage Inventory Models and Techniques, Stanford Univ. Press, Stanford, Calif., 1963, 185–225 MR0186412 0126.16101 Google Scholar[6] Arthur F. Veinott, Jr., The status of mathematical inventory theory, Management Sci., 12 (1966), 745–777 MR0195593 0143.21801 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Can Deep Reinforcement Learning Improve Inventory Management? 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Cross Ref Joint Inventory and Revenue Management with Removal DecisionsSSRN Electronic Journal | 1 Jan 2017 Cross Ref Optimality Gap of Constant-Order Policies Decays Exponentially in the Lead Time for Lost Sales ModelsOperations Research, Vol. 64, No. 6 | 1 Dec 2016 Cross Ref Inventory TheoryDecision Sciences | 1 December 2016 Cross Ref Order quantities for perishable inventory control with non-stationary demand and a fill rate constraintInternational Journal of Production Economics, Vol. 181 | 1 Nov 2016 Cross Ref Asymptotic Optimality of Constant-Order Policies for Lost Sales Inventory Models with Large Lead TimesMathematics of Operations Research, Vol. 41, No. 3 | 1 Aug 2016 Cross Ref Structural properties of the optimal policy for dual-sourcing systems with general lead timesIIE Transactions, Vol. 47, No. 8 | 8 December 2014 Cross Ref Parametric replenishment policies for inventory systems with lost sales and fixed order costEuropean Journal of Operational Research, Vol. 241, No. 2 | 1 Mar 2015 Cross Ref Optimal Policies and Bounds for Stochastic Inventory Systems with Lost SalesJournal of Optimization Theory and Applications, Vol. 164, No. 1 | 25 March 2014 Cross Ref Demand seasonality in retail inventory managementEuropean Journal of Operational Research, Vol. 238, No. 2 | 1 Oct 2014 Cross Ref Robustness of Order-Up-to Policies in Lost-Sales Inventory SystemsOperations Research, Vol. 62, No. 5 | 1 Oct 2014 Cross Ref Integrality in Stochastic Inventory ModelsProduction and Operations Management, Vol. 23, No. 9 | 17 January 2014 Cross Ref Fixed-Dimensional Stochastic Dynamic Programs: An Approximation Scheme and an Inventory ApplicationOperations Research, Vol. 62, No. 1 | 1 Feb 2014 Cross Ref OPTIMAL CONTROL OF A FINITE-CAPACITY INVENTORY SYSTEM WITH SETUP COST AND LOST SALESJournal of Applied Analysis & Computation, Vol. 4, No. 2 | 1 Jan 2014 Cross Ref Determination of safety stocks in a lost sales inventory system with periodic review, positive lead-time, 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No. 4 | 1 Jan 2008 Cross Ref A Comparison of the Optimal Costs of Two Canonical Inventory SystemsOperations Research, Vol. 55, No. 5 | 1 Oct 2007 Cross Ref Relaxing channel separation: Integrating a virtual store into the supply chain via transshipmentsIIE Transactions, Vol. 38, No. 11 | 1 Nov 2006 Cross Ref Integrating direct and indirect sales channels under decentralized decision-makingInternational Journal of Production Economics, Vol. 103, No. 1 | 1 Sep 2006 Cross Ref Lost-Sales Problems with Stochastic Lead Times: Convexity Results for Base-Stock PoliciesOperations Research, Vol. 52, No. 5 | 1 Oct 2004 Cross Ref RETAIL INVENTORY CONTROL WITH LOST SALES, SERVICE CONSTRAINTS, AND FRACTIONAL LEAD TIMESProduction and Operations Management, Vol. 8, No. 4 | 5 January 2009 Cross Ref A perishable inventory model with positive order lead timesEuropean Journal of Operational Research, Vol. 116, No. 2 | 1 Jul 1999 Cross Ref Chapter 1 Single-Product, single-Location modelsLogistics of Production and Inventory | 1 Jan 1993 Cross Ref The dynamics of hedging the master scheduleInternational Journal of Production Research, Vol. 24, No. 6 | 1 Nov 1986 Cross Ref Approximation techniques for several stochastic inventory modelsComputers & Operations Research, Vol. 8, No. 3 | 1 Jan 1981 Cross Ref Volume 11, Issue 4| 1969SIAM Review429-672 History Submitted:28 May 1968Published online:18 July 2006 InformationCopyright © 1969 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1011090Article page range:pp. 572-596ISSN (print):0036-1445ISSN (online):1095-7200Publisher:Society for Industrial and Applied Mathematics

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