IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v269y2018i3p909-922.html
   My bibliography  Save this article

Markov-modulated analysis of a spare parts system with random lead times and disruption risks

Author

Listed:
  • Hekimoğlu, Mustafa
  • van der Laan, Ervin
  • Dekker, Rommert

Abstract

Spare parts supply chains are highly dependent on the dynamics of their installed bases. A decreasing number of capital products in use increases the nonstationary supply-side risk especially towards the end-of-life of capital products. This supply-side risk appears to present itself through varying lead times coupled with supply disruptions. To model the nonstationary supply-side risk, we consider an exogenous Markov chain that modulates random lead times and disruption probabilities. Assuming that order crossovers do not occur, we prove the optimality of a state-dependent base stock policy. Later, we conduct an impact study to understand the value of considering stochastic lead times and supply disruption risk in spare parts inventory control. Our results indicate that the coupled effect of random lead times and disruptions can be larger than the summation of individual effects even for moderate lead time variances. Also, the effect of nonstationarity on total cost can be as large as the summation of all risk factors combined. In addition to this managerial insight we present a procedure for supply risk mitigation based on an empirical model and our mathematical model. Experiments on a real business case indicate that the procedure is capable of reducing costs while making the inventory system more prepared for disruptions.

Suggested Citation

  • Hekimoğlu, Mustafa & van der Laan, Ervin & Dekker, Rommert, 2018. "Markov-modulated analysis of a spare parts system with random lead times and disruption risks," European Journal of Operational Research, Elsevier, vol. 269(3), pages 909-922.
    • Handle: RePEc:eee:ejores:v:269:y:2018:i:3:p:909-922
    DOI: 10.1016/j.ejor.2018.02.040
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221718301735
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2018.02.040?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. Robert S. Kaplan, 1970. "A Dynamic Inventory Model with Stochastic Lead Times," Management Science, INFORMS, vol. 16(7), pages 491-507, March.
    2. Parlar, Mahmut & Wang, Yunzeng & Gerchak, Yigal, 1995. "A periodic review inventory model with Markovian supply availability," International Journal of Production Economics, Elsevier, vol. 42(2), pages 131-136, December.
    3. Guillermo Gallego & Haichao Hu, 2004. "Optimal Policies for Production/Inventory Systems with Finite Capacity and Markov-Modulated Demand and Supply Processes," Annals of Operations Research, Springer, vol. 126(1), pages 21-41, February.
    4. Jing-Sheng Song & Paul H. Zipkin, 1996. "Inventory Control with Information About Supply Conditions," Management Science, INFORMS, vol. 42(10), pages 1409-1419, October.
    5. James R. Bradley & Lawrence W. Robinson, 2005. "Improved Base-Stock Approximations for Independent Stochastic Lead Times with Order Crossover," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 319-329, November.
    6. Jing-Sheng Song & Paul Zipkin, 1993. "Inventory Control in a Fluctuating Demand Environment," Operations Research, INFORMS, vol. 41(2), pages 351-370, April.
    7. Jing-Sheng Song, 1994. "The Effect of Leadtime Uncertainty in a Simple Stochastic Inventory Model," Management Science, INFORMS, vol. 40(5), pages 603-613, May.
    8. Volodymyr Babich & Apostolos N. Burnetas & Peter H. Ritchken, 2007. "Competition and Diversification Effects in Supply Chains with Supplier Default Risk," Manufacturing & Service Operations Management, INFORMS, vol. 9(2), pages 123-146, October.
    9. Brian Tomlin, 2006. "On the Value of Mitigation and Contingency Strategies for Managing Supply Chain Disruption Risks," Management Science, INFORMS, vol. 52(5), pages 639-657, May.
    10. Richard Ehrhardt, 1984. "( s , S ) Policies for a Dynamic Inventory Model with Stochastic Lead Times," Operations Research, INFORMS, vol. 32(1), pages 121-132, February.
    11. Steven Nahmias, 1979. "Simple Approximations for a Variety of Dynamic Leadtime Lost-Sales Inventory Models," Operations Research, INFORMS, vol. 27(5), pages 904-924, October.
    12. Arifoglu, Kenan & Özekici, Süleyman, 2010. "Optimal policies for inventory systems with finite capacity and partially observed Markov-modulated demand and supply processes," European Journal of Operational Research, Elsevier, vol. 204(3), pages 421-438, August.
    13. Alp Muharremoglu & John N. Tsitsiklis, 2008. "A Single-Unit Decomposition Approach to Multiechelon Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1089-1103, October.
    14. 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.
    15. Izak Duenyas & John Neale, 1997. "Stochastic scheduling of a batch processing machine with incompatible job families," Annals of Operations Research, Springer, vol. 70(0), pages 191-220, April.
    16. S. Özekici & M. Parlar, 1999. "Inventory models with unreliable suppliersin a random environment," Annals of Operations Research, Springer, vol. 91(0), pages 123-136, January.
    17. Hayya, Jack C. & Bagchi, Uttarayan & Kim, Jeon G. & Sun, Daewon, 2008. "On static stochastic order crossover," International Journal of Production Economics, Elsevier, vol. 114(1), pages 404-413, July.
    18. 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.
    19. Arthur F. Veinott, Jr., 1965. "Optimal Policy for a Multi-Product, Dynamic, Nonstationary Inventory Problem," Management Science, INFORMS, vol. 12(3), pages 206-222, 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. Suresha Kharvi & T. P. M. Pakkala & G. Srinivasan, 2019. "Ordering policies under currency risk sharing agreements: a Markov chain approach," OPSEARCH, Springer;Operational Research Society of India, vol. 56(3), pages 945-964, September.

    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. Ben-Ammar, Oussama & Bettayeb, Belgacem & Dolgui, Alexandre, 2019. "Optimization of multi-period supply planning under stochastic lead times and a dynamic demand," International Journal of Production Economics, Elsevier, vol. 218(C), pages 106-117.
    2. Alp Muharremoglu & Nan Yang, 2010. "Inventory Management with an Exogenous Supply Process," Operations Research, INFORMS, vol. 58(1), pages 111-129, February.
    3. Chen, Junlin & Zhao, Xiaobo & Zhou, Yun, 2012. "A periodic-review inventory system with a capacitated backup supplier for mitigating supply disruptions," European Journal of Operational Research, Elsevier, vol. 219(2), pages 312-323.
    4. Alp Muharremoglu & John N. Tsitsiklis, 2008. "A Single-Unit Decomposition Approach to Multiechelon Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1089-1103, October.
    5. Paul Zipkin, 2008. "On the Structure of Lost-Sales Inventory Models," Operations Research, INFORMS, vol. 56(4), pages 937-944, August.
    6. Hellemans, Tim & Boute, Robert N. & Van Houdt, Benny, 2019. "Analysis of lead time correlation under a base-stock policy," European Journal of Operational Research, Elsevier, vol. 276(2), pages 519-535.
    7. Bendre, Abhijit Bhagwan & Nielsen, Lars Relund, 2013. "Inventory control in a lost-sales setting with information about supply lead times," International Journal of Production Economics, Elsevier, vol. 142(2), pages 324-331.
    8. Hayya, Jack C. & Bagchi, Uttarayan & Kim, Jeon G. & Sun, Daewon, 2008. "On static stochastic order crossover," International Journal of Production Economics, Elsevier, vol. 114(1), pages 404-413, July.
    9. Soroush Saghafian & Mark P. Van Oyen, 2016. "Compensating for Dynamic Supply Disruptions: Backup Flexibility Design," Operations Research, INFORMS, vol. 64(2), pages 390-405, April.
    10. Arifoglu, Kenan & Özekici, Süleyman, 2011. "Inventory management with random supply and imperfect information: A hidden Markov model," International Journal of Production Economics, Elsevier, vol. 134(1), pages 123-137, November.
    11. 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.
    12. Iida, Tetsuo, 2015. "Benefits of leadtime information and of its combination with demand forecast information," International Journal of Production Economics, Elsevier, vol. 163(C), pages 146-156.
    13. Bryan, Nana & Srinivasan, Mandyam M., 2014. "Real-time order tracking for supply systems with multiple transportation stages," European Journal of Operational Research, Elsevier, vol. 236(2), pages 548-560.
    14. Brian M. Lewis & Alan L. Erera & Maciek A. Nowak & White Chelsea C., 2013. "Managing Inventory in Global Supply Chains Facing Port-of-Entry Disruption Risks," Transportation Science, INFORMS, vol. 47(2), pages 162-180, May.
    15. Luo, Sha & Ahiska, S. Sebnem & Fang, Shu-Cherng & King, Russell E. & Warsing, Donald P. & Wu, Shuohao, 2021. "An analysis of optimal ordering policies for a two-supplier system with disruption risk," Omega, Elsevier, vol. 105(C).
    16. E J Lodree Jr & S Taskin, 2008. "An insurance risk management framework for disaster relief and supply chain disruption inventory planning," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 59(5), pages 674-684, May.
    17. Hansen, Ole & Transchel, Sandra & Friedrich, Hanno, 2023. "Replenishment strategies for lost sales inventory systems of perishables under demand and lead time uncertainty," European Journal of Operational Research, Elsevier, vol. 308(2), pages 661-675.
    18. James R. Bradley & Lawrence W. Robinson, 2005. "Improved Base-Stock Approximations for Independent Stochastic Lead Times with Order Crossover," Manufacturing & Service Operations Management, INFORMS, vol. 7(4), pages 319-329, November.
    19. Brian Tomlin, 2009. "Impact of Supply Learning When Suppliers Are Unreliable," Manufacturing & Service Operations Management, INFORMS, vol. 11(2), pages 192-209, August.
    20. Lu Huang & Jing-Sheng Song & Jordan Tong, 2016. "Supply Chain Planning for Random Demand Surges: Reactive Capacity and Safety Stock," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 509-524, October.

    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:269:y:2018:i:3:p:909-922. 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.