Asymptotic Optimality of Semi-Open-Loop Policies in Markov Decision Processes with Large Lead Times

Published Online:https://doi.org/10.1287/opre.2021.0088

References

  • Abouee-Mehrizi H, Berman O, Sharma S (2015) Optimal joint replenishment and transshipment policies in a multi-period inventory system with lost sales. Oper. Res. 63(2):342–350.LinkGoogle Scholar
  • Adelman D, Mancini AJ (2016) Optimality of quasi-open-loop policies for discounted semi-Markov decision processes. Math. Oper. Res. 41(4):1222–1247.LinkGoogle Scholar
  • Altman E, Stidham S (1995) Optimality of monotonic policies for two-action Markovian decision processes, with applications to control of queues with delayed information. Queueing Systems 21(3–4):267–291.CrossrefGoogle Scholar
  • Altman E, Başar T, Srikant R (1999) Congestion control as a stochastic control problem with action delays. Automatica J. IFAC 35(12):1937–1950.CrossrefGoogle Scholar
  • Arapostathis A, Borkar VS, Fernández-Gaucherand E, Ghosh MK, Marcus SI (1993) Discrete-time controlled Markov processes with average cost criterion: A survey. SIAM J. Control Optim. 31(2):282–344.CrossrefGoogle Scholar
  • Asmussen S (2008) Applied Probability and Queues, vol. 51, 2nd ed. (Springer Science & Business Media, New York).Google Scholar
  • Bander JL, White C (1999) Markov decision processes with noise-corrupted and delayed state observations. J. Oper. Res. Soc. 50(6):660–668.CrossrefGoogle Scholar
  • Bean JC, Birge JR, Mittenthal J, Noon CE (1991) Matchup scheduling with multiple resources, release dates and disruptions. Oper. Res. 39(3):470–483.LinkGoogle Scholar
  • Bensoussan A, Çakanyildirim M, Sethi SP (2007) Optimal ordering policies for inventory problems with dynamic information delays. Production Oper. Management 16(2):241–256.CrossrefGoogle Scholar
  • Bertsekas D (2012) Dynamic Programming and Optimal Control, vol. 1 (Athena Scientific, Belmont, MA).Google Scholar
  • Bu J, Gong X, Yao D (2020) Constant-order policies for lost-sales inventory models with random supply functions: Asymptotics and heuristic. Oper. Res. 68(4):1063–1073.LinkGoogle Scholar
  • Chen B, Shi C (2019) Tailored base-surge policies in dual-sourcing inventory systems with demand learning. Preprint, submitted September 19, https://dx.doi.org/10.2139/ssrn.3456834.Google Scholar
  • Chen X, Simchi-Levi D (2012) Pricing and inventory management. Philips P, Özer Ö, eds. The Oxford Handbook of Pricing Management (Oxford University Press, Oxford), 784–822.Google Scholar
  • Chen X, Hu P, Hu Z (2021) Joint pricing and inventory decisions. Preprint, submitted November 25, https://dx.doi.org/10.2139/ssrn.3971881.Google Scholar
  • Chen X, Pang Z, Pan L (2014) Coordinating inventory control and pricing strategies for perishable products. Oper. Res. 62(2):284–300.LinkGoogle Scholar
  • Chen X, Stolyar AL, Xin L (2023) Asymptotic optimality of constant-order policies in joint pricing and inventory models. Math. Oper. Res. Forthcoming.LinkGoogle Scholar
  • Durrett R (2019) Probability: Theory and Examples, vol. 49 (Cambridge University Press, Cambridge, UK).CrossrefGoogle Scholar
  • Federgruen A, Hordijk A, Tijms HC (1978) A note on simultaneous recurrence conditions on a set of denumerable stochastic matrices. J. Appl. Probab. 15(4):842–847.CrossrefGoogle Scholar
  • Feinberg EA (2016) Optimality conditions for inventory control. Optimization Challenges in Complex, Networked and Risky Systems (INFORMS, Catonsville, MD), 14–45.LinkGoogle Scholar
  • Feinberg EA, Kasyanov PO, Zadoianchuk NV (2012) Average cost Markov decision processes with weakly continuous transition probabilities. Math. Oper. Res. 37(4):591–607.LinkGoogle Scholar
  • Feinberg EA, Kasyanov PO, Zadoianchuk NV (2013) Berge’s theorem for noncompact image sets. J. Math. Anal. Appl. 397(1):255–259.CrossrefGoogle Scholar
  • Feng Q, Shi R (2012) Sourcing from multiple suppliers for price-dependent demands. Production Oper. Management 21(3):547–563.CrossrefGoogle Scholar
  • Gallego G, Van Ryzin G (1997) A multiproduct dynamic pricing problem and its applications to network yield management. Oper. Res. 45(1):24–41.LinkGoogle Scholar
  • Goldberg DA, Reiman MI, Wang Q (2021) A survey of recent progress in the asymptotic analysis of inventory systems. Production Oper. Management 30(6):1718–1750.CrossrefGoogle Scholar
  • Goldberg DA, Katz-Rogozhnikov DA, Lu Y, Sharma M, Squillante MS (2016) Asymptotic optimality of constant-order policies for lost sales inventory models with large lead times. Math. Oper. Res. 41(3):898–913.LinkGoogle Scholar
  • Gong X, Chao X (2013) Optimal control policy for capacitated inventory systems with remanufacturing. Oper. Res. 61(3):603–611.LinkGoogle Scholar
  • Gong X, Chao X, Zheng S (2014) Dynamic pricing and inventory management with dual suppliers of different lead times and disruption risks. Production Oper. Management 23(12):2058–2074.CrossrefGoogle Scholar
  • Hernández-Lerma O (2012) Adaptive Markov Control Processes, vol. 79 (Springer Science & Business Media, New York).Google Scholar
  • Hernández-Lerma O, Montes-de Oca R, Cavazos-Cadena R (1991) Recurrence conditions for Markov decision processes with Borel state space: A survey. Ann. Oper. Res. 28(1):29–46.CrossrefGoogle Scholar
  • Hu X, Duenyas I, Kapuscinski R (2008) Optimal joint inventory and transshipment control under uncertain capacity. Oper. Res. 56(4):881–897.LinkGoogle Scholar
  • Huh WT, Janakiraman G, Nagarajan M (2011) Average cost single-stage inventory models: An analysis using a vanishing discount approach. Oper. Res. 59(1):143–155.LinkGoogle Scholar
  • Katsikopoulos KV, Engelbrecht SE (2003) Markov decision processes with delays and asynchronous cost collection. IEEE Trans. Automatic Control 48(4):568–574.CrossrefGoogle Scholar
  • McKenzie LW (1976) Turnpike theory. Econometrica 44(5):841–865.CrossrefGoogle Scholar
  • Minner S (2003) Multiple-supplier inventory models in supply chain management: A review. Internat. J. Production Econom. 81:265–279.CrossrefGoogle Scholar
  • Pang Z, Chen FY, Feng Y (2012) A note on the structure of joint inventory-pricing control with leadtimes. Oper. Res. 60(3):581–587.LinkGoogle Scholar
  • Reiman MI (2004) A new simple policy for a continuous review lost-sales inventory model. Working paper, Bell Labs, Lucent Technologies, Murray Hill, NJ. Google Scholar
  • Sethi S, Zhang Q, Zhou XY (1992) Hierarchical controls in stochastic manufacturing systems with machines in tandem. Stochastics 41(1–2):89–118.Google Scholar
  • Simchi-Levi D, Chen X, Bramel J (2014) The Logic of Logistics: Theory, Algorithms, and Applications for Logistics Management, 3rd ed. (Springer, New York).CrossrefGoogle Scholar
  • Song X, Zhang H, Xie L (2009) Stochastic linear quadratic regulation for discrete-time linear systems with input delay. Automatica J. IFAC 45(9):2067–2073.CrossrefGoogle Scholar
  • Vakil B, Linton T (2021) Why we’re in the midst of a global semiconductor shortage. Accessed July 29, 2021, https://hbr.org/2021/02/why-were-in-the-midst-of-a-global-semiconductor-shortage.Google Scholar
  • Wang Y, Gilland W, Tomlin B (2010) Mitigating supply risk: Dual sourcing or process improvement? Manufacturing Service Oper. Management 12(3):489–510.LinkGoogle Scholar
  • Xin L (2021) Asymptotic analysis of a remanufacturing system with non-identical lead times. Preprint, submitted February 18, https://dx.doi.org/10.2139/ssrn.3760906.Google Scholar
  • Xin L, Goldberg DA (2016) Optimality gap of constant-order policies decays exponentially in the lead time for lost sales models. Oper. Res. 64(6):1556–1565.LinkGoogle Scholar
  • Xin L, Goldberg DA (2018) Asymptotic optimality of tailored base-surge policies in dual-sourcing inventory systems. Management Sci. 64(1):437–452.LinkGoogle Scholar
  • Zhang H, Duan G, Xie L (2006) Linear quadratic regulation for linear time-varying systems with multiple input delays. Automatica J. IFAC 42(9):1465–1476.CrossrefGoogle Scholar
  • Zhou S, Ding Y, Huh WT, Wan G (2021) Constant job-allowance policies for appointment scheduling: Performance bounds and numerical analysis. Production Oper. Management 30(7):2211–2231.CrossrefGoogle Scholar
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