IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v271y2018i2d10.1007_s10479-018-2764-8.html
   My bibliography  Save this article

Evaluating shortfall distributions in periodic inventory systems with stochastic endogenous demands and lead-times

Author

Listed:
  • Hernan Caceres

    (Universidad Católica del Norte)

  • Dongchen Yu

    (University at Buffalo)

  • Alexander Nikolaev

    (University at Buffalo)

Abstract

This paper addresses a multi-period production/inventory problem with two suppliers, where demand sizes and supplier lead time are stochastic and correlated. A discrete time, single item inventory system is considered, where inventory levels are reviewed periodically and managed using a base-stock policy. At the end of each period, a replenishment order is placed, which enters a queue at the buffer stage and is consequently forwarded to the first available supplier. We present a mathematical model of this inventory system and determine optimal safety stock levels for it, in closed form, using matrix analytic techniques and the properties of phase type distributions. To account for the effect of order crossovers, which occur whenever replenishment orders do not arrive in the sequence in which they were placed, the inventory shortfall distribution is analyzed. Finally, a set of numerical experiments with a system with two suppliers is presented, where the proposed model is compared to other existing models.

Suggested Citation

  • Hernan Caceres & Dongchen Yu & Alexander Nikolaev, 2018. "Evaluating shortfall distributions in periodic inventory systems with stochastic endogenous demands and lead-times," Annals of Operations Research, Springer, vol. 271(2), pages 405-427, December.
    • Handle: RePEc:spr:annopr:v:271:y:2018:i:2:d:10.1007_s10479-018-2764-8
    DOI: 10.1007/s10479-018-2764-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-018-2764-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-018-2764-8?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. Jing-Sheng Song & David D. Yao, 2002. "Performance Analysis and Optimization of Assemble-to-Order Systems with Random Lead Times," Operations Research, INFORMS, vol. 50(5), pages 889-903, October.
    2. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    3. P. H. Brill & M. J. M. Posner, 1981. "A Two Server Queue with Nonwaiting Customers Receiving Specialized Service," Management Science, INFORMS, vol. 27(8), pages 914-925, August.
    4. Jing-Sheng Song & Paul H. Zipkin, 1996. "The Joint Effect of Leadtime Variance and Lot Size in a Parallel Processing Environment," Management Science, INFORMS, vol. 42(9), pages 1352-1363, September.
    5. Kim, Jeon G. & Chatfield, Dean & Harrison, Terry P. & Hayya, Jack C., 2006. "Quantifying the bullwhip effect in a supply chain with stochastic lead time," European Journal of Operational Research, Elsevier, vol. 173(2), pages 617-636, September.
    6. Chakravarthy, Srinivas R. & Agnihothri, Saligrama R., 2008. "A server backup model with Markovian arrivals and phase type services," European Journal of Operational Research, Elsevier, vol. 184(2), pages 584-609, January.
    7. Paul Glasserman & Sridhar Tayur, 1996. "A simple approximation for a multistage capacitated production‐inventory system," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(1), pages 41-58, February.
    8. Yong-Joo Lee & Paul Zipkin, 1992. "Tandem Queues with Planned Inventories," Operations Research, INFORMS, vol. 40(5), pages 936-947, October.
    9. R.N. Boute & P.J. Colen & S. Creemers & A. Noblesse & B. Van Houdt, 2012. "Matrix-Analytic Methods in Supply Chain Management: Recent Developments," Review of Business and Economic Literature, Intersentia, vol. 57(3), pages 283-302, September.
    10. A. Federgruen & P. Zipkin, 1986. "An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 208-215, May.
    11. Junmin Shi & Michael Katehakis & Benjamin Melamed, 2013. "Martingale methods for pricing inventory penalties under continuous replenishment and compound renewal demands," Annals of Operations Research, Springer, vol. 208(1), pages 593-612, September.
    12. Jing-Sheng Song & Susan H. Xu & Bin Liu, 1999. "Order-Fulfillment Performance Measures in an Assemble-to-Order System with Stochastic Leadtimes," Operations Research, INFORMS, vol. 47(1), pages 131-149, February.
    13. A. Federgruen & P. Zipkin, 1986. "An Inventory Model with Limited Production Capacity and Uncertain Demands I. The Average-Cost Criterion," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 193-207, May.
    14. Robin O. Roundy & John A. Muckstadt, 2000. "Heuristic Computation of Periodic-Review Base Stock Inventory Policies," Management Science, INFORMS, vol. 46(1), pages 104-109, January.
    15. Colin E. Bell, 1980. "Optimal Operation of an M / M /2 Queue with Removable Servers," Operations Research, INFORMS, vol. 28(5), pages 1189-1204, October.
    16. Yingdong Lu & Jing-Sheng Song & David D. Yao, 2003. "Order Fill Rate, Leadtime Variability, and Advance Demand Information in an Assemble-to-Order System," Operations Research, INFORMS, vol. 51(2), pages 292-308, April.
    17. Boute, Robert N. & Disney, Stephen M. & Lambrecht, Marc R. & Houdt, Benny Van, 2014. "Coordinating lead times and safety stocks under autocorrelated demand," European Journal of Operational Research, Elsevier, vol. 232(1), pages 52-63.
    18. Robert N. Boute & Marc R. Lambrecht & Benny Van Houdt, 2007. "Performance evaluation of a production/inventory system with periodic review and endogenous lead times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 462-473, June.
    19. Noblesse, Ann M. & Boute, Robert N. & Lambrecht, Marc R. & Van Houdt, Benny, 2014. "Lot sizing and lead time decisions in production/inventory systems," International Journal of Production Economics, Elsevier, vol. 155(C), pages 351-360.
    20. Lawrence W. Robinson & James R. Bradley & L. Joseph Thomas, 2001. "Consequences of Order Crossover Under Order-Up-To Inventory Policies," Manufacturing & Service Operations Management, INFORMS, vol. 3(3), pages 175-188, September.
    21. Michael H. Veatch & Lawrence M. Wein, 1994. "Optimal Control of a Two-Station Tandem Production/Inventory System," Operations Research, INFORMS, vol. 42(2), pages 337-350, April.
    22. repec:sen:rebelj:v:57:i:3:y:2012:p:19 is not listed on IDEAS
    23. repec:sen:journl:v:57:i:3:y:2012:p:19 is not listed on IDEAS
    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. Barros, Júlio & Cortez, Paulo & Carvalho, M. Sameiro, 2021. "A systematic literature review about dimensioning safety stock under uncertainties and risks in the procurement process," Operations Research Perspectives, Elsevier, vol. 8(C).
    2. Gonçalves, João N.C. & Sameiro Carvalho, M. & Cortez, Paulo, 2020. "Operations research models and methods for safety stock determination: A review," Operations Research Perspectives, Elsevier, vol. 7(C).
    3. Raa, Birger & Aouam, Tarik, 2023. "A shortfall modelling-based solution approach for stochastic cyclic inventory routing," European Journal of Operational Research, Elsevier, vol. 305(2), pages 674-684.

    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. Robert N. Boute & Marc R. Lambrecht & Benny Van Houdt, 2007. "Performance evaluation of a production/inventory system with periodic review and endogenous lead times," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(4), pages 462-473, June.
    2. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2016. "Capacitated Multiechelon Inventory Systems: Policies and Bounds," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 570-584, October.
    3. Rodney P. Parker & Roman Kapuscinski, 2004. "Optimal Policies for a Capacitated Two-Echelon Inventory System," Operations Research, INFORMS, vol. 52(5), pages 739-755, October.
    4. Jing-Sheng Song & David D. Yao, 2002. "Performance Analysis and Optimization of Assemble-to-Order Systems with Random Lead Times," Operations Research, INFORMS, vol. 50(5), pages 889-903, October.
    5. van Houtum, G. J. & Inderfurth, K. & Zijm, W. H. M., 1996. "Materials coordination in stochastic multi-echelon systems," European Journal of Operational Research, Elsevier, vol. 95(1), pages 1-23, November.
    6. Feng Cheng* & Markus Ettl & Yingdong Lu & David D. Yao, 2012. "A Production–Inventory Model for a Push–Pull Manufacturing System with Capacity and Service Level Constraints," Production and Operations Management, Production and Operations Management Society, vol. 21(4), pages 668-681, July.
    7. Erica L. Plambeck, 2008. "Asymptotically Optimal Control for an Assemble-to-Order System with Capacitated Component Production and Fixed Transport Costs," Operations Research, INFORMS, vol. 56(5), pages 1158-1171, October.
    8. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    9. Hoen, K.M.R. & Güllü, R. & van Houtum, G.J. & Vliegen, I.M.H., 2011. "A simple and accurate approximation for the order fill rates in lost-sales Assemble-to-Order systems," International Journal of Production Economics, Elsevier, vol. 133(1), pages 95-104, September.
    10. Sari, Kazim, 2010. "Exploring the impacts of radio frequency identification (RFID) technology on supply chain performance," European Journal of Operational Research, Elsevier, vol. 207(1), pages 174-183, November.
    11. Berling, Peter & Eng-Larsson, Fredrik, 2017. "Environmental implications of transport contract choice - capacity investment and pricing under volume and capacity contracts," European Journal of Operational Research, Elsevier, vol. 261(1), pages 129-142.
    12. Kai Huang, 2014. "Benchmarking non-first-come-first-served component allocation in an assemble-to-order system," Annals of Operations Research, Springer, vol. 223(1), pages 217-237, December.
    13. Rodney P. Parker & Roman Kapuściński, 2011. "Managing a Noncooperative Supply Chain with Limited Capacity," Operations Research, INFORMS, vol. 59(4), pages 866-881, August.
    14. Weidong Chen & Cong Shi & Izak Duenyas, 2020. "Optimal Learning Algorithms for Stochastic Inventory Systems with Random Capacities," Production and Operations Management, Production and Operations Management Society, vol. 29(7), pages 1624-1649, July.
    15. Hossein Abouee-Mehrizi & Opher Baron & Oded Berman, 2014. "Exact Analysis of Capacitated Two-Echelon Inventory Systems with Priorities," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 561-577, October.
    16. Caldentey, René. & Wein, Lawrence M., 1999. "Analysis of decentralized production-inventory system," Working papers WP 4099-99., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    17. Wen Chen & Ying He, 2022. "Dynamic pricing and inventory control with delivery flexibility," Annals of Operations Research, Springer, vol. 317(2), pages 481-508, October.
    18. Yao Zhao & David Simchi-Levi, 2006. "Performance Analysis and Evaluation of Assemble-to-Order Systems with Stochastic Sequential Lead Times," Operations Research, INFORMS, vol. 54(4), pages 706-724, August.
    19. Bo Li & Antonio Arreola‐Risa, 2022. "Minimizing conditional value‐at‐risk under a modified basestock policy," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1822-1838, April.
    20. Woonghee Tim Huh & Ganesh Janakiraman, 2012. "Technical Note---On Optimal Policies for Inventory Systems with Batch Ordering," Operations Research, INFORMS, vol. 60(4), pages 797-802, 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:spr:annopr:v:271:y:2018:i:2:d:10.1007_s10479-018-2764-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.