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Determination of safety stocks in a lost sales inventory system with periodic review, positive lead-time, lot-sizing and a target fill rate

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  • van Donselaar, Karel H.
  • Broekmeulen, Rob A.C.M.

Abstract

An approximation for the fill rate, i.e. the percentage of demand being delivered from inventory on hand immediately, is derived for items in a periodic review inventory control system with lost sales. We assume demand is stochastic and discrete, lead-times are positive and replenishments are made in multiples of a given fixed case pack size. Most literature on inventory control systems assumes that unmet demand is backordered. The major reason for this is that the analysis of a general lost sales inventory system is known to be hard. To find an approximation for the fill rate, given a safety stock, we start with existing analytical approximations. By applying linear regression, we slightly modify these existing approximations. The new approximation is tested for a wide set of parameters and performs very well: the average approximation error for the fill rate is only 0.0028 and the standard deviation of the approximation error is 0.0045. Since the approximations are very fast, this result enables inventory controllers dealing with a lost sales inventory system to set safety stocks in accordance with the target service level set by their management in an effective way. The results of our study also show that the assumption that the lost sales system can simply be approximated by a backordering system if the target fill rate is at least 95%, may lead to serious approximation errors. These errors are particularly large when the lead-time is large or demand uncertainty is low and when on average there is at least one replenishment order outstanding.

Suggested Citation

  • van Donselaar, Karel H. & Broekmeulen, Rob A.C.M., 2013. "Determination of safety stocks in a lost sales inventory system with periodic review, positive lead-time, lot-sizing and a target fill rate," International Journal of Production Economics, Elsevier, vol. 143(2), pages 440-448.
    • Handle: RePEc:eee:proeco:v:143:y:2013:i:2:p:440-448
    DOI: 10.1016/j.ijpe.2011.05.020
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    Cited by:

    1. Broekmeulen, Rob A.C.M. & van Donselaar, Karel H., 2019. "Quantifying the potential to improve on food waste, freshness and sales for perishables in supermarkets," International Journal of Production Economics, Elsevier, vol. 209(C), pages 265-273.
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    3. Zolfagharinia, Hossein & Hafezi, Maryam & Farahani, Reza Zanjirani & Fahimnia, Behnam, 2014. "A hybrid two-stock inventory control model for a reverse supply chain," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 67(C), pages 141-161.
    4. Özgün Turgut & Florian Taube & Stefan Minner, 2018. "Data-driven retail inventory management with backroom effect," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 40(4), pages 945-968, October.
    5. 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).
    6. Zied Bahroun & Nidhal Belgacem, 2019. "Determination of dynamic safety stocks for cyclic production schedules," Operations Management Research, Springer, vol. 12(1), pages 62-93, June.
    7. Janssen, Larissa & Diabat, Ali & Sauer, Jürgen & Herrmann, Frank, 2018. "A stochastic micro-periodic age-based inventory replenishment policy for perishable goods," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 445-465.
    8. 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).
    9. Dreyfuss, Michael & Giat, Yahel, 2019. "Allocating spares to maximize the window fill rate in a periodic review inventory system," International Journal of Production Economics, Elsevier, vol. 214(C), pages 151-162.

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