IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v246y2015i3p874-885.html
   My bibliography  Save this article

Continuous (s, S) policy with MMPP correlated demand

Author

Listed:
  • Nasr, Walid W.
  • Maddah, Bacel

Abstract

This work considers a continuous inventory replenishment system where demand is stochastic and dependent on the state of the environment. A Markov Modulated Poisson Process (MMPP) is utilized to model the demand process where the corresponding embedded Markov Chain represents the state of the environment. The equations to calculate the system inventory measures and the number of orders per unit time are obtained for a continuous, infinite horizon and dynamically changing (s, S) policy. An efficient optimization heuristic is presented and compared to the commonly used approach of approximating the demand-count process over the lead time with a Normal distribution. An investigation of the MMPP demand process is considered where we quantify the impact of variability in the demand-count process which is due to auto-correlation. Our findings indicate that when demand correlation is high, a dynamic control, where the (s, S) policy changes with state of the environment governing the MMPP, is highly superior to the commonly used “static” heuristics. We propose two dynamic policies of varying computational complexity, and cost efficiency, depending on the class of the product (one for class A, and one for classes B and C), to handle such high-correlation situations.

Suggested Citation

  • Nasr, Walid W. & Maddah, Bacel, 2015. "Continuous (s, S) policy with MMPP correlated demand," European Journal of Operational Research, Elsevier, vol. 246(3), pages 874-885.
    • Handle: RePEc:eee:ejores:v:246:y:2015:i:3:p:874-885
    DOI: 10.1016/j.ejor.2015.05.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715004191
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.05.029?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Nickell, Pamela & Perraudin, William & Varotto, Simone, 2000. "Stability of rating transitions," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 203-227, January.
    3. B S Maddah & M Y Jaber & N E Abboud, 2004. "Periodic review (s, S) inventory model with permissible delay in payments," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(2), pages 147-159, February.
    4. Özkan, Can & Karaesmen, Fikri & Özekici, Süleyman, 2013. "Structural properties of Markov modulated revenue management problems," European Journal of Operational Research, Elsevier, vol. 225(2), pages 324-331.
    5. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
    6. Chung, Chia-Shin & Flynn, James & Kirca, Omer, 2008. "A multi-item newsvendor problem with preseason production and capacitated reactive production," European Journal of Operational Research, Elsevier, vol. 188(3), pages 775-792, August.
    7. Izzet Sahin, 1982. "On the Objective Function Behavior in ( s , S ) Inventory Models," Operations Research, INFORMS, vol. 30(4), pages 709-724, August.
    8. T L Urban, 2000. "Reorder level determination with serially-correlated demand," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 51(6), pages 762-768, June.
    9. Lee, Loo Hay & Chew, Ek Peng, 2005. "A dynamic joint replenishment policy with auto-correlated demand," European Journal of Operational Research, Elsevier, vol. 165(3), pages 729-747, September.
    10. Yu-Sheng Zheng & A. Federgruen, 1991. "Finding Optimal (s, S) Policies Is About As Simple As Evaluating a Single Policy," Operations Research, INFORMS, vol. 39(4), pages 654-665, August.
    11. Frank Youhua Chen & Candace Arai Yano, 2010. "Improving Supply Chain Performance and Managing Risk Under Weather-Related Demand Uncertainty," Management Science, INFORMS, vol. 56(8), pages 1380-1397, August.
    12. Dirk Beyer & Feng Cheng & Suresh P. Sethi & Michael Taksar, 2010. "Markovian Demand Inventory Models," International Series in Operations Research and Management Science, Springer, number 978-0-387-71604-6, December.
    13. Yin, Rui & Rajaram, Kumar, 2007. "Joint pricing and inventory control with a Markovian demand model," European Journal of Operational Research, Elsevier, vol. 182(1), pages 113-126, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Angelos Kourepis & Alexandros Diamantidis & Stylianos Koukoumialos, 2022. "Exact analysis of a push–pull system with multiple non identical retailers, a distribution center and multiple non identical unreliable suppliers with supply disruptions," Operational Research, Springer, vol. 22(5), pages 4801-4827, November.
    2. 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).
    3. Benjamin Avanzi & Greg Taylor & Bernard Wong & Alan Xian, 2020. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," Papers 2003.13888, arXiv.org, revised May 2020.
    4. Walid W. Nasr, 2022. "Inventory systems with stochastic and batch demand: computational approaches," Annals of Operations Research, Springer, vol. 309(1), pages 163-187, February.
    5. Ehsan Ahmadi & Dale T. Masel & Seth Hostetler & Reza Maihami & Iman Ghalehkhondabi, 2020. "A centralized stochastic inventory control model for perishable products considering age-dependent purchase price and lead time," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 231-269, April.
    6. Hallak, Bassam K. & Nasr, Walid W. & Jaber, Mohamad Y., 2021. "Re-ordering policies for inventory systems with recyclable items and stochastic demand – Outsourcing vs. in-house recycling," Omega, Elsevier, vol. 105(C).
    7. Jorge A. Sefair & Oscar Guaje & Andrés L. Medaglia, 2021. "A column-oriented optimization approach for the generation of correlated random vectors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 777-808, September.
    8. Nasr, Walid W. & Elshar, Ibrahim J., 2018. "Continuous inventory control with stochastic and non-stationary Markovian demand," European Journal of Operational Research, Elsevier, vol. 270(1), pages 198-217.
    9. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Xian, Alan, 2021. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," European Journal of Operational Research, Elsevier, vol. 290(1), pages 177-195.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Walid W. Nasr, 2022. "Inventory systems with stochastic and batch demand: computational approaches," Annals of Operations Research, Springer, vol. 309(1), pages 163-187, February.
    2. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
    3. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.
    4. Awi Federgruen & Min Wang, 2015. "Inventory Models with Shelf-Age and Delay-Dependent Inventory Costs," Operations Research, INFORMS, vol. 63(3), pages 701-715, June.
    5. Nasr, Walid W. & Elshar, Ibrahim J., 2018. "Continuous inventory control with stochastic and non-stationary Markovian demand," European Journal of Operational Research, Elsevier, vol. 270(1), pages 198-217.
    6. Alain Bensoussan & Lama Moussawi-Haidar & Metin Çakanyıldırım, 2010. "Inventory control with an order-time constraint: optimality, uniqueness and significance," Annals of Operations Research, Springer, vol. 181(1), pages 603-640, December.
    7. Jinhui Han & Suresh P. Sethi & Chi Chung Siu & Sheung Chi Phillip Yam, 2023. "Co‐op advertising in randomly fluctuating markets," Production and Operations Management, Production and Operations Management Society, vol. 32(6), pages 1617-1635, June.
    8. Arnoud den Boer & Ohad Perry & Bert Zwart, 2018. "Dynamic pricing policies for an inventory model with random windows of opportunities," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(8), pages 660-675, December.
    9. Li, Xiaoming, 2010. "Optimal inventory policies in decentralized supply chains," International Journal of Production Economics, Elsevier, vol. 128(1), pages 303-309, November.
    10. Xiang, Mengyuan & Rossi, Roberto & Martin-Barragan, Belen & Tarim, S. Armagan, 2018. "Computing non-stationary (s, S) policies using mixed integer linear programming," European Journal of Operational Research, Elsevier, vol. 271(2), pages 490-500.
    11. Tovey C. Bachman & Pamela J. Williams & Kristen M. Cheman & Jeffrey Curtis & Robert Carroll, 2016. "PNG: Effective Inventory Control for Items with Highly Variable Demand," Interfaces, INFORMS, vol. 46(1), pages 18-32, February.
    12. Yonit Barron & Dror Hermel, 2017. "Shortage decision policies for a fluid production model with MAP arrivals," International Journal of Production Research, Taylor & Francis Journals, vol. 55(14), pages 3946-3969, July.
    13. Mohebbi, E., 2008. "A note on a production control model for a facility with limited storage capacity in a random environment," European Journal of Operational Research, Elsevier, vol. 190(2), pages 562-570, October.
    14. Xiuli Chao & Xiting Gong & Cong Shi & Chaolin Yang & Huanan Zhang & Sean X. Zhou, 2018. "Approximation Algorithms for Capacitated Perishable Inventory Systems with Positive Lead Times," Management Science, INFORMS, vol. 64(11), pages 5038-5061, November.
    15. Yossi Aviv & Awi Federgruen, 2001. "Design for Postponement: A Comprehensive Characterization of Its Benefits Under Unknown Demand Distributions," Operations Research, INFORMS, vol. 49(4), pages 578-598, August.
    16. D. Beyer & S. P. Sethi & M. Taksar, 1998. "Inventory Models with Markovian Demands and Cost Functions of Polynomial Growth," Journal of Optimization Theory and Applications, Springer, vol. 98(2), pages 281-323, August.
    17. Li Chen & Jing-Sheng Song & Yue Zhang, 2017. "Serial Inventory Systems with Markov-Modulated Demand: Derivative Bounds, Asymptotic Analysis, and Insights," Operations Research, INFORMS, vol. 65(5), pages 1231-1249, October.
    18. Tan, Tarkan & Gullu, Refik & Erkip, Nesim, 2007. "Modelling imperfect advance demand information and analysis of optimal inventory policies," European Journal of Operational Research, Elsevier, vol. 177(2), pages 897-923, March.
    19. Xiaoming Li, 2013. "Managing Dynamic Inventory Systems with Product Returns: A Markov Decision Process," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 577-592, May.
    20. Amar Sapra & Van-Anh Truong & Rachel Q. Zhang, 2010. "How Much Demand Should Be Fulfilled?," Operations Research, INFORMS, vol. 58(3), pages 719-733, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:246:y:2015:i:3:p:874-885. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.