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Inventory Management with Partially Observed Nonstationary Demand

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  • Erhan Bayraktar
  • Mike Ludkovski

Abstract

We consider a continuous-time model for inventory management with Markov modulated non-stationary demands. We introduce active learning by assuming that the state of the world is unobserved and must be inferred by the manager. We also assume that demands are observed only when they are completely met. We first derive the explicit filtering equations and pass to an equivalent fully observed impulse control problem in terms of the sufficient statistics, the a posteriori probability process and the current inventory level. We then solve this equivalent formulation and directly characterize an optimal inventory policy. We also describe a computational procedure to calculate the value function and the optimal policy and present two numerical illustrations.

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  • Erhan Bayraktar & Mike Ludkovski, 2012. "Inventory Management with Partially Observed Nonstationary Demand," Papers 1206.6283, arXiv.org.
    • Handle: RePEc:arx:papers:1206.6283
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    1. Arjas, Elja & Haara, Pentti & Norros, Ikka, 1992. "Filtering the histories of a partially observed marked point process," Stochastic Processes and their Applications, Elsevier, vol. 40(2), pages 225-250, March.
    2. Martin A. Lariviere & Evan L. Porteus, 1999. "Stalking Information: Bayesian Inventory Management with Unobserved Lost Sales," Management Science, INFORMS, vol. 45(3), pages 346-363, March.
    3. James T. Treharne & Charles R. Sox, 2002. "Adaptive Inventory Control for Nonstationary Demand and Partial Information," Management Science, INFORMS, vol. 48(5), pages 607-624, May.
    4. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
    5. Bayraktar, Erhan & Ludkovski, Michael, 2009. "Sequential tracking of a hidden Markov chain using point process observations," Stochastic Processes and their Applications, Elsevier, vol. 119(6), pages 1792-1822, June.
    6. Alain Bensoussan & Metin Çakanyıldırım & Suresh P. Sethi, 2007. "A Multiperiod Newsvendor Problem with Partially Observed Demand," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 322-344, May.
    7. A. Bensoussan & M. Çakanyıldırım & J. A. Minjárez-Sosa & A. Royal & S. P. Sethi, 2008. "Inventory Problems with Partially Observed Demands and Lost Sales," Journal of Optimization Theory and Applications, Springer, vol. 136(3), pages 321-340, March.
    8. Suresh P. Sethi & Feng Cheng, 1997. "Optimality of ( s , S ) Policies in Inventory Models with Markovian Demand," Operations Research, INFORMS, vol. 45(6), pages 931-939, December.
    9. William S. Lovejoy, 1990. "Myopic Policies for Some Inventory Models with Uncertain Demand Distributions," Management Science, INFORMS, vol. 36(6), pages 724-738, June.
    10. Katy S. Azoury, 1985. "Bayes Solution to Dynamic Inventory Models Under Unknown Demand Distribution," Management Science, INFORMS, vol. 31(9), pages 1150-1160, September.
    11. Yossi Aviv & Amit Pazgal, 2005. "A Partially Observed Markov Decision Process for Dynamic Pricing," Management Science, INFORMS, vol. 51(9), pages 1400-1416, September.
    12. Dirk Beyer & Suresh P. Sethi, 2005. "Average Cost Optimality in Inventory Models with Markovian Demands and Lost Sales," Springer Books, in: El Kébir Boukas & Roland P. Malhamé (ed.), Analysis, Control and Optimization of Complex Dynamic Systems, chapter 0, pages 3-23, Springer.
    13. D. Beyer & S. P. Sethi, 1997. "Average Cost Optimality in Inventory Models with Markovian Demands," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 497-526, March.
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    Cited by:

    1. Mike Ludkovski, 2022. "Regression Monte Carlo for Impulse Control," Papers 2203.06539, arXiv.org.
    2. Moawia Alghalith, 2012. "A New Stopping Time Model: A Solution to a Free-Boundary Problem," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 265-270, January.
    3. Manafzadeh Dizbin, Nima & Tan, Barış, 2020. "Optimal control of production-inventory systems with correlated demand inter-arrival and processing times," International Journal of Production Economics, Elsevier, vol. 228(C).
    4. Aiden Fisher & David Green & Andrew Metcalfe, 2012. "Modelling of hydrological persistence for hidden state Markov decision processes," Annals of Operations Research, Springer, vol. 199(1), pages 215-224, October.
    5. Roberto Rossi & S. Tarim & Brahim Hnich & Steven Prestwich, 2012. "Constraint programming for stochastic inventory systems under shortage cost," Annals of Operations Research, Springer, vol. 195(1), pages 49-71, May.
    6. Jianqiang Hu & Cheng Zhang & Chenbo Zhu, 2016. "( s , S ) Inventory Systems with Correlated Demands," INFORMS Journal on Computing, INFORMS, vol. 28(4), pages 603-611, November.
    7. Satya S. Malladi & Alan L. Erera & Chelsea C. White, 2023. "Inventory control with modulated demand and a partially observed modulation process," Annals of Operations Research, Springer, vol. 321(1), pages 343-369, February.
    8. Khayyati, Siamak & Tan, Barış, 2020. "Data-driven control of a production system by using marking-dependent threshold policy," International Journal of Production Economics, Elsevier, vol. 226(C).
    9. Ricardo Montoya & Carlos Gonzalez, 2019. "A Hidden Markov Model to Detect On-Shelf Out-of-Stocks Using Point-of-Sale Data," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 932-948, October.
    10. Harun Avci & Kagan Gokbayrak & Emre Nadar, 2020. "Structural Results for Average‐Cost Inventory Models with Markov‐Modulated Demand and Partial Information," Production and Operations Management, Production and Operations Management Society, vol. 29(1), pages 156-173, January.
    11. Alghalith, Moawia, 2013. "The interaction among production, hedging and investment decisions," Economic Modelling, Elsevier, vol. 30(C), pages 193-195.
    12. Park, Hyungjun & Choi, Dong Gu & Min, Daiki, 2023. "Adaptive inventory replenishment using structured reinforcement learning by exploiting a policy structure," International Journal of Production Economics, Elsevier, vol. 266(C).
    13. Pavel V. Gapeev, 2016. "Bayesian Switching Multiple Disorder Problems," Mathematics of Operations Research, INFORMS, vol. 41(3), pages 1108-1124, August.
    14. Stößlein, Martin & Kanet, John Jack & Gorman, Mike & Minner, Stefan, 2014. "Time-phased safety stocks planning and its financial impacts: Empirical evidence based on European econometric data," International Journal of Production Economics, Elsevier, vol. 149(C), pages 47-55.

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