IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v251y2016i2p495-508.html
   My bibliography  Save this article

Clearing control policies for MAP inventory process with lost sales

Author

Listed:
  • Barron, Yonit

Abstract

We consider a production/clearing process in a random environment where a single machine produces a certain product into a buffer continuously. The demands arrive according to a Markov Additive Process (MAP) governed by a continuous-time Markov chain, and their sizes are independent and have phase-type distributions depending on the type of arrival. Since negative inventory is not allowed, the demand may be partially satisfied. The production process switches between predetermined rates that depend on the state of the environment. In addition, the system is totally cleared at stationary renewal times and starts anew at level zero immediately. Several clearing policies are considered: clearing at random times, clearing at crossings of a specified level, and a combination of the above policies. We assume the total cost includes a fixed clearing cost, a variable cost for the cleared amount, a holding cost, and a lost demand cost. By applying regenerative theory, we use tools from the exit-time theorem for fluid processes and martingales to obtain cost functionals under both the discounted and average criteria. Finally, illustrative examples and a comparative study are provided.

Suggested Citation

  • Barron, Yonit, 2016. "Clearing control policies for MAP inventory process with lost sales," European Journal of Operational Research, Elsevier, vol. 251(2), pages 495-508.
    • Handle: RePEc:eee:ejores:v:251:y:2016:i:2:p:495-508
    DOI: 10.1016/j.ejor.2015.12.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715011674
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.12.028?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. V. Ramaswami, 2006. "Passage Times in Fluid Models with Application to Risk Processes," Methodology and Computing in Applied Probability, Springer, vol. 8(4), pages 497-515, December.
    2. Nigel Bean & Małgorzata O’Reilly, 2008. "Performance measures of a multi-layer Markovian fluid model," Annals of Operations Research, Springer, vol. 160(1), pages 99-120, April.
    3. Shaler Stidham, 1977. "Cost Models for Stochastic Clearing Systems," Operations Research, INFORMS, vol. 25(1), pages 100-127, February.
    4. A. Gómez-Corral, 2005. "On a finite-buffer bulk-service queue with disasters," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(1), pages 57-84, March.
    5. Edward Ignall & Peter Kolesar, 1972. "Operating Characteristics of a Simple Shuttle under Local Dispatching Rules," Operations Research, INFORMS, vol. 20(6), pages 1077-1088, December.
    6. Serfozo, Richard & Stidham, Shaler, 1978. "Semi-stationary clearing processes," Stochastic Processes and their Applications, Elsevier, vol. 6(2), pages 165-178, January.
    7. Jing-Sheng Song & Paul H. Zipkin, 1996. "Managing Inventory with the Prospect of Obsolescence," Operations Research, INFORMS, vol. 44(1), pages 215-222, February.
    8. Pinçe, Çerag & Gürler, Ülkü & Berk, Emre, 2008. "A continuous review replenishment-disposal policy for an inventory system with autonomous supply and fixed disposal costs," European Journal of Operational Research, Elsevier, vol. 190(2), pages 421-442, October.
    9. Shen, Yuelin & Willems, Sean P., 2014. "Modeling sourcing strategies to mitigate part obsolescence," European Journal of Operational Research, Elsevier, vol. 236(2), pages 522-533.
    10. Song, Yuyue & Lau, Hoong Chuin, 2004. "A periodic-review inventory model with application to the continuous-review obsolescence problem," European Journal of Operational Research, Elsevier, vol. 159(1), pages 110-120, November.
    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. Yonit Barron & Opher Baron, 2020. "The residual time approach for (Q, r) model under perishability, general lead times, and lost sales," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(3), pages 601-648, December.
    2. 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.
    3. Hédi Nabli & Itidel Abdallah, 2023. "Stochastic Fluid Models with Upward Jumps and Phase Transitions," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-26, March.

    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. Yonit Barron, 2016. "Performance analysis of a reflected fluid production/inventory model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 1-31, February.
    2. Yonit Barron, 2016. "Performance analysis of a reflected fluid production/inventory model," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 83(1), pages 1-31, February.
    3. Artalejo, J. R., 2000. "G-networks: A versatile approach for work removal in queueing networks," European Journal of Operational Research, Elsevier, vol. 126(2), pages 233-249, October.
    4. van Jaarsveld, Willem & Dekker, Rommert, 2011. "Estimating obsolescence risk from demand data to enhance inventory control--A case study," International Journal of Production Economics, Elsevier, vol. 133(1), pages 423-431, September.
    5. Antonis Economou & Athanasia Manou, 2013. "Equilibrium balking strategies for a clearing queueing system in alternating environment," Annals of Operations Research, Springer, vol. 208(1), pages 489-514, September.
    6. Wang, Jinting & Liu, Bin & Li, Jianghua, 2008. "Transient analysis of an M/G/1 retrial queue subject to disasters and server failures," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1118-1132, September.
    7. Opher Baron & Oded Berman & David Perry, 2010. "Continuous review inventory models for perishable items ordered in batches," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 72(2), pages 217-247, October.
    8. Royi Jacobovic & Offer Kella, 2019. "Asymptotic independence of regenerative processes with a special dependence structure," Queueing Systems: Theory and Applications, Springer, vol. 93(1), pages 139-152, October.
    9. Perry, David & Stadje, Wolfgang, 2000. "Risk analysis for a stochastic cash management model with two types of customers," Insurance: Mathematics and Economics, Elsevier, vol. 26(1), pages 25-36, February.
    10. Oded Berman & Mahmut Parlar & David Perry & M. J. M. Posner, 2005. "Production/Clearing Models Under Continuous and Sporadic Reviews," Methodology and Computing in Applied Probability, Springer, vol. 7(2), pages 203-224, June.
    11. Mehmet Akif Yazici & Nail Akar, 2017. "The finite/infinite horizon ruin problem with multi-threshold premiums: a Markov fluid queue approach," Annals of Operations Research, Springer, vol. 252(1), pages 85-99, May.
    12. Lagodimos, A.G. & Christou, I.T. & Skouri, K., 2012. "Computing globally optimal (s,S,T) inventory policies," Omega, Elsevier, vol. 40(5), pages 660-671.
    13. Tamjidzad, Shahrzad & Mirmohammadi, S. Hamid, 2015. "An optimal (r, Q) policy in a stochastic inventory system with all-units quantity discount and limited sharable resource," European Journal of Operational Research, Elsevier, vol. 247(1), pages 93-100.
    14. Alamri, Adel A. & Syntetos, Aris A., 2018. "Beyond LIFO and FIFO: Exploring an Allocation-In-Fraction-Out (AIFO) policy in a two-warehouse inventory model," International Journal of Production Economics, Elsevier, vol. 206(C), pages 33-45.
    15. P. Escalona & F. Ordóñez & I. Kauak, 2017. "Critical level rationing in inventory systems with continuously distributed demand," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(1), pages 273-301, January.
    16. 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.
    17. Yossi Aviv, 2003. "A Time-Series Framework for Supply-Chain Inventory Management," Operations Research, INFORMS, vol. 51(2), pages 210-227, April.
    18. Cattani, Kyle D. & Souza, Gilvan C., 2003. "Good buy? Delaying end-of-life purchases," European Journal of Operational Research, Elsevier, vol. 146(1), pages 216-228, April.
    19. Yonit Barron & David Perry & Wolfgang Stadje, 2016. "A make-to-stock production/inventory model with MAP arrivals and phase-type demands," Annals of Operations Research, Springer, vol. 241(1), pages 373-409, June.
    20. Charles J. Corbett, 2001. "Stochastic Inventory Systems in a Supply Chain with Asymmetric Information: Cycle Stocks, Safety Stocks, and Consignment Stock," Operations Research, INFORMS, vol. 49(4), pages 487-500, August.

    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:251:y:2016:i:2:p:495-508. 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.