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Periodic review lost-sales inventory models with compound Poisson demand and constant lead times of any length

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  • Bijvank, Marco
  • Johansen, Søren Glud

Abstract

In almost all literature on inventory models with lost sales and periodic reviews the lead time is assumed to be either an integer multiple of or less than the review period. In a lot of practical settings such restrictions are not satisfied. We develop new models allowing constant lead times of any length when demand is compound Poisson. Besides an optimal policy, we consider pure and restricted base-stock policies under new lead time and cost circumstances. Based on our numerical results we conclude that the latter policy, which imposes a restriction on the maximum order size, performs almost as well as the optimal policy. We also propose an approximation procedure to determine the base-stock levels for both policies with closed-form expressions.

Suggested Citation

  • Bijvank, Marco & Johansen, Søren Glud, 2012. "Periodic review lost-sales inventory models with compound Poisson demand and constant lead times of any length," European Journal of Operational Research, Elsevier, vol. 220(1), pages 106-114.
    • Handle: RePEc:eee:ejores:v:220:y:2012:i:1:p:106-114
    DOI: 10.1016/j.ejor.2012.01.041
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    References listed on IDEAS

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    1. Brian Downs & Richard Metters & John Semple, 2001. "Managing Inventory with Multiple Products, Lags in Delivery, Resource Constraints, and Lost Sales: A Mathematical Programming Approach," Management Science, INFORMS, vol. 47(3), pages 464-479, March.
    2. Stephen C. Graves, 1996. "A Multiechelon Inventory Model with Fixed Replenishment Intervals," Management Science, INFORMS, vol. 42(1), pages 1-18, January.
    3. F R Johnston & J E Boylan & E A Shale, 2003. "An examination of the size of orders from customers, their characterisation and the implications for inventory control of slow moving items," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 833-837, August.
    4. Woonghee Tim Huh & Ganesh Janakiraman & John A. Muckstadt & Paat Rusmevichientong, 2009. "Asymptotic Optimality of Order-Up-To Policies in Lost Sales Inventory Systems," Management Science, INFORMS, vol. 55(3), pages 404-420, March.
    5. Paul Zipkin, 2008. "On the Structure of Lost-Sales Inventory Models," Operations Research, INFORMS, vol. 56(4), pages 937-944, August.
    6. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    7. Johansen, Soren Glud & Thorstenson, Anders, 1993. "Optimal and approximate (Q, r) inventory policies with lost sales and gamma-distributed lead time," International Journal of Production Economics, Elsevier, vol. 30(1), pages 179-194, July.
    8. Johansen, Soren Glud & Thorstenson, Anders, 1996. "Optimal (r, Q) inventory policies with Poisson demands and lost sales: discounted and undiscounted cases," International Journal of Production Economics, Elsevier, vol. 46(1), pages 359-371, December.
    9. Kaj Rosling, 2002. "Inventory Cost Rate Functions with Nonlinear Shortage Costs," Operations Research, INFORMS, vol. 50(6), pages 1007-1017, December.
    10. Chiang, Chi, 2006. "Optimal ordering policies for periodic-review systems with replenishment cycles," European Journal of Operational Research, Elsevier, vol. 170(1), pages 44-56, April.
    11. Guillermo Gallego & Özalp Özer, 2003. "Optimal Replenishment Policies for Multiechelon Inventory Problems Under Advance Demand Information," Manufacturing & Service Operations Management, INFORMS, vol. 5(2), pages 157-175, February.
    12. Chiang, Chi, 2007. "Optimal ordering policies for periodic-review systems with a refined intra-cycle time scale," European Journal of Operational Research, Elsevier, vol. 177(2), pages 872-881, March.
    13. Paul Zipkin, 2008. "Old and New Methods for Lost-Sales Inventory Systems," Operations Research, INFORMS, vol. 56(5), pages 1256-1263, October.
    14. Mustafa Çagri Gürbüz & Kamran Moinzadeh & Yong-Pin Zhou, 2007. "Coordinated Replenishment Strategies in Inventory/Distribution Systems," Management Science, INFORMS, vol. 53(2), pages 293-307, February.
    15. 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.
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    Cited by:

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    3. Tan, Ken Seng & Wei, Pengyu & Wei, Wei & Zhuang, Sheng Chao, 2020. "Optimal dynamic reinsurance policies under a generalized Denneberg’s absolute deviation principle," European Journal of Operational Research, Elsevier, vol. 282(1), pages 345-362.
    4. Bijvank, Marco & Bhulai, Sandjai & Tim Huh, Woonghee, 2015. "Parametric replenishment policies for inventory systems with lost sales and fixed order cost," European Journal of Operational Research, Elsevier, vol. 241(2), pages 381-390.
    5. Manuel Cardós & Ester Guijarro & Eugenia Babiloni, 2017. "On the estimation of on-hand stocks for base-stock policies and lost sales systems and its impact on service measures," International Journal of Production Research, Taylor & Francis Journals, vol. 55(16), pages 4680-4694, August.
    6. Lin, X. & Basten, R.J.I. & Kranenburg, A.A. & van Houtum, G.J., 2017. "Condition based spare parts supply," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 240-248.
    7. Yanyi Xu & Sang-Phil Kim & Arnab Bisi & Maqbool Dada & Suresh Chand, 2018. "Base-Stock Models for Lost Sales: A Markovian Approach," Purdue University Economics Working Papers 1305, Purdue University, Department of Economics.
    8. Xiaoming Li, 2015. "Optimal Policies and Bounds for Stochastic Inventory Systems with Lost Sales," Journal of Optimization Theory and Applications, Springer, vol. 164(1), pages 359-375, January.
    9. Dimitrova, Dimitrina S. & Ignatov, Zvetan G. & Kaishev, Vladimir K. & Tan, Senren, 2020. "On double-boundary non-crossing probability for a class of compound processes with applications," European Journal of Operational Research, Elsevier, vol. 282(2), pages 602-613.
    10. Kouki, Chaaben & Babai, M. Zied & Jemai, Zied & Minner, Stefan, 2019. "Solution procedures for lost sales base-stock inventory systems with compound Poisson demand," International Journal of Production Economics, Elsevier, vol. 209(C), pages 172-182.
    11. Zhang, Jie & Bai, Lihui & Jin, Tongdan, 2021. "Joint planning for battery swap and supercharging networks with priority service queues," International Journal of Production Economics, Elsevier, vol. 233(C).

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