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The Economics and Finance Letters

April 2014, Volume 1, 4, pp 39-48

An Inventory Model with Lost Sale is Time Dependent

Ying-Chieh Chen


Po-Yu Chen

Ying-Chieh Chen 1
Po-Yu Chen 2

  1. Department of Accounting, Ming Chuan University, Taipei, Taiwan 1

  2. Department of Advertising, Ming Chuan University, Taipei, Taiwan 2

Pages: 39-48

DOI: 10.18488/journal.29/2014.1.4/

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In this paper, we shall construct an inventory model with partially backlogged shortage and Poisson demand. In the shortage period, we assume that lost sale is dependent on the length of waiting time. Under these assumptions, we find the optimal planning and shortage periods such that the expected profit per unit time is maximized. Also, we can estimate the optimal expected backordered quantity and the expected order quantity.
Contribution/ Originality



  1. Axsäter, S., 2007. A heuristic for triggering emergency orders in an inventory system. European Journal of Operational Research, 176(2): 880-891.
  2. Bijvank, M. and S.G. Johansen, 2012. Periodic review lost-sales inventory models with compound poisson demand and constant lead times of any length. European Journal of Operational Research, 220(1): 106-114.
  3. Bijvank, M. and I.F.A. Vis, 2011. Lost-sales inventory theory: A review. European Journal of Operational Research, 215(1): 1-13.
  4. Chen, M.S. and Y.C. Chen, 2010. A note on the optimal supply cycle when the whole period is stockout. Asia-Pacific Journal of Operational Research, 27(5): 611-616.
  5. Chen, Y.C., 2003. A probabilistic approach for traditional EOQ model. Journal of Information & Optimization Sciences, 24(2): 249-253.
  6. Chiang, C., 2006. Optimal ordering policed for periodic-review systems with replenishment cycles. European Journal of Operational Research, 170(1): 44-56.
  7. Hogg, R.V. and E.A. Tanis, 1993. Probability and statistical inference. 4th Edn., New York: Macmillan Publishing Company.
  8. Ouyang, L.Y., B.R. Chuang and Y.J. Lin, 2007. Effective investment to reduce lost-sales rate in a periodic review inventory model. OR Spectrum, 29(4): 681-697.
  9. Park, K.S., 1983. Another inventory model with a mixture of backorders and lost sales. Naval Research Logistics Quarterly, 30(3): 397-400.
  10. Rosenberg, D., 1979. A new analysis of a lot-size model with partial backlogging. Naval Research Logistics Quarterly, 26(2): 349-353.
  11. Thangam, A. and R. Uthayakumar, 2008. A two-level supply chain with partial backordering and approximated poisson demand. European Journal of Operational Research, 187(1): 228-242.


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