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Mathematical Problems in Engineering
Volume 2018, Article ID 6085342, 23 pages
https://doi.org/10.1155/2018/6085342
Research Article

Determining the Optimal Order Quantity with Compound Erlang Demand under (T,Q) Policy

1SHU-UTS SILC Business School, Shanghai University, 20 Chengzhong Road, Jiading District, Shanghai 201899, China
2School of Mathematics and Statistics, UNSW, Sydney, NSW 2052, Australia

Correspondence should be addressed to Aiping Jiang; nc.ude.uhs@427pa

Received 10 March 2018; Revised 25 June 2018; Accepted 12 July 2018; Published 19 August 2018

Academic Editor: Neale R. Smith

Copyright © 2018 Aiping Jiang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. M. Adelson, “The compound Poisson distribution,” Journal of the Operational Research Society, vol. 17, no. 1, pp. 73–75, 1966. View at Google Scholar
  2. J. K. Friend, “Stock control with random opportunities for replenishment,” Journal of the Operational Research Society, vol. 11, no. 3, pp. 130–136, 1960. View at Publisher · View at Google Scholar
  3. F. Hanssmann, Operations Research in Production and Inventory Control, John Wiley and Sons, New York, NY, USA, 1962. View at MathSciNet
  4. J. Xiao, F. L. Lu, and X. Xiao, “Stohastic newsboy inventory control model and its solving on multivariate productd order and pricing,” in Proceedings of the International Conference on Information Computing and Applications, pp. 65–72, 2010.
  5. S. Kébé, N. Sbihi, and B. Penz, “A Lagrangean heuristic for a two-echelon storage capacitated lot-sizing problem,” Journal of Intelligent Manufacturing, vol. 23, no. 6, pp. 2477–2483, 2012. View at Publisher · View at Google Scholar · View at Scopus
  6. P. S. S. Uduman, A. Sulaiman, and R. Sathiyamoorthy, “News boy inventory model with demand satisfying SCBZ property,” Bulletin of Pure and Applied Science, vol. 26, no. 1, pp. 145–150, 2007. View at Google Scholar
  7. D. Fathima, P. S. Sheik Uduman, and S. Srinivasan, “Generalization of newsboy problem with demand distribution satisfying the SCBZ property,” International Journal of Contemporary Mathematical Sciences, vol. 6, no. 37-40, pp. 1989–2000, 2011. View at Google Scholar · View at MathSciNet
  8. D. Fathima and P. S. S. Uduman, “Single period inventory model with stochastic demand and partial backlogging,” International Journal of Management, vol. 24, no. 1, pp. 37–59, 2013. View at Google Scholar
  9. J. Kamburowski, “The distribution-free newsboy problem under the worst-case and best-case scenarios,” European Journal of Operational Research, vol. 237, no. 1, pp. 106–112, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  10. Y.-K. Chen, C.-T. Chen, F.-R. Chiu, and J.-W. Lian, “Applying the bootstrap method to newsvendor model incorporating group buying for optimal price discount and order quantity,” Kybernetes, vol. 46, no. 10, pp. 1692–1705, 2017. View at Publisher · View at Google Scholar · View at Scopus
  11. F. Hnaien, A. Dolgui, and D. D. Wu, “Single-period inventory model for one-level assembly system with stochastic lead times and demand,” International Journal of Production Research, vol. 54, no. 1, pp. 186–203, 2016. View at Publisher · View at Google Scholar · View at Scopus
  12. S. Priyan and R. Uthayakumar, “Two-echelon multi-product multi-constraint product returns inventory model with permissible delay in payments and variable lead time,” Journal of Manufacturing Systems, vol. 36, article no. 304, pp. 244–262, 2015. View at Publisher · View at Google Scholar · View at Scopus
  13. M. Keramatpour, S. T. A. Niaki, and S. H. R. Pasandideh, “A bi-objective two-level newsvendor problem with discount policies and budget constraint,” Computers & Industrial Engineering, vol. 120, pp. 192–205, 2017. View at Google Scholar
  14. S. Axsäter, Inventory Control, Springer, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  15. P. Matheus and L. Gelders, “The (R, Q) inventory policy subject to a compound Poisson demand pattern,” International Journal of Production Economics, vol. 68, no. 3, pp. 307–317, 2000. View at Publisher · View at Google Scholar · View at Scopus
  16. M. Z. Babai, Z. Jemai, and Y. Dallery, “Analysis of order-up-to-level inventory systems with compound Poisson demand,” European Journal of Operational Research, vol. 210, no. 3, pp. 552–558, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. W. T. Dunsmuir and R. D. Snyder, “Control of inventories with intermittent demand,” European Journal of Operational Research, vol. 40, no. 1, pp. 16–21, 1989. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. F. Janssen, R. Heuts, and T. De Kok, “On the (R, s, Q) inventory model when demand is modelled as a compound Bernoulli process,” European Journal of Operational Research, vol. 104, no. 3, pp. 423–436, 1998. View at Publisher · View at Google Scholar · View at Scopus
  19. R. H. Teunter, A. A. Syntetos, and M. Z. Babai, “Determining order-up-to levels under periodic review for compound binomial (intermittent) demand,” European Journal of Operational Research, vol. 203, no. 3, pp. 619–624, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. A. K. Gupta, W.-B. Zeng, and Y. Wu, Probability and Statistical Models. Foundations for Problems in Reliability and Financial Mathematics, Springer Science and Business Media, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  21. M. A. Smith and R. Dekker, “On the (S–1, S) stock model for renewal demand processes: Poisson's poison,” Probability in the Engineering and Informational Sciences, vol. 11, no. 3, pp. 375–386, 1997. View at Publisher · View at Google Scholar · View at MathSciNet
  22. C. Larsen and G. P. Kiesmullerr, “Developing a closed-form cost expression for an (R, s, nQ) policy where the demand process is compound generalized Erlang,” Operations Research Letters, vol. 35, no. 5, pp. 567–572, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  23. C. Larsen and A. Thorstenson, “A comparison between the order and the volume fill rate for a base-stock inventory control system under a compound renewal demand process,” Journal of the Operational Research Society, vol. 59, no. 6, pp. 798–804, 2008. View at Publisher · View at Google Scholar · View at Scopus
  24. C. Larsen and A. Thorstenson, “The order and volume fill rates in inventory control systems,” International Journal of Production Economics, vol. 147, pp. 13–19, 2014. View at Publisher · View at Google Scholar · View at Scopus
  25. S. Saidane, M. Z. Babai, M. S. Aguir, and O. Korbaa, “Spare parts inventory systems under an increasing failure rate demand interval distribution,” in Proceedings of the 41st International Conference on Computers and Industrial Engineering 2011, pp. 214–219, USA, October 2011. View at Scopus
  26. S. Saidane, M. Z. Babai, M. S. Aguir, and O. Korbaa, “On the performance of the base-stock inventory system under a compound Erlang demand distribution,” Computers & Industrial Engineering, vol. 66, no. 3, pp. 548–554, 2013. View at Publisher · View at Google Scholar · View at Scopus
  27. A. A. Syntetos, M. Z. Babai, and S. Luo, “Forecasting of compound erlang demand,” Journal of the Operational Research Society, vol. 66, no. 12, pp. 2061–2074, 2015. View at Publisher · View at Google Scholar · View at Scopus
  28. R. Y. K. Fung, X. Ma, and H. C. W. Lau, “(T, S) policy for coordinated inventory replenishment systems under compound Poisson demands,” Production Planning and Control, vol. 12, no. 6, pp. 575–583, 2001. View at Publisher · View at Google Scholar · View at Scopus
  29. Y. Zhao, “Analysis and evaluation of an assemble-to-order system with batch ordering policy and compound Poisson demand,” European Journal of Operational Research, vol. 198, no. 3, pp. 800–809, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. E. Topan and Z. P. Bayindir, “Multi-item two-echelon spare parts inventory control problem with batch ordering in the central warehouse under compound Poisson demand,” Journal of the Operational Research Society, vol. 63, no. 8, pp. 1143–1152, 2012. View at Publisher · View at Google Scholar · View at Scopus
  31. A. H. C. Eaves and B. G. Kingsman, “Forecasting for the ordering and stock-holding of spare parts,” Journal of the Operational Research Society, vol. 55, no. 4, pp. 431–437, 2004. View at Publisher · View at Google Scholar · View at Scopus
  32. E. A. Trabka and E. W. Marchand, “The mean and variance of intervals between renewals of a type I counter with a censored Poisson input,” Biological Cybernetics, vol. 7, no. 6, pp. 224–227, 1970. View at Google Scholar · View at MathSciNet