Journal of Applied Science and Engineering

Published by Tamkang University Press

1.30

Impact Factor

2.10

CiteScore

Hsien-Jen Lin This email address is being protected from spambots. You need JavaScript enabled to view it.1

1Department of Applied Mathematics, Aletheia University, Tamsui, Taiwan 251, R.O.C.


 

Received: November 21, 2011
Accepted: November 12, 2013
Publication Date: December 1, 2013

Download Citation: ||https://doi.org/10.6180/jase.2013.16.4.12  


ABSTRACT


We study a continuous review inventory model which involves controllable lead time, partial backlogging defective items and investment to reduce lost sales rate. Buyer’s order quantity, reorder point, lost sales rate and lead time are taken as decision variables. By framing the model, we observe that a significant amount of savings can be easily achieved to increase the competitive edge. Both normal distribution and distribution free models are discussed sufficiently. Effects of investing in lost sales rate reduction are clearly stated and savings are achieved in a numerical example. We compare the lost sales rate reduction model with fixed lost sales rate model. Also, we give the improvement of the cost performance of the distribution free approach in another numerical example.


Keywords: Inventory, Lost Sales, Defective Items, Lead Time, Minmax Distribution Free Approach


REFERENCES


  1. [1] Montgomery, D. C., Bazaraa, M. S. and Keswani, A. K., “Inventory Models with a Mixture of Backorders and Lost Sales,” Naval Research Logistics, Vol. 20, pp. 255263 (1973). doi: 10.1002/nav.3800200205
  2. [2] Ouyang, L. Y., Yeh, N. C. and Wu, K. S., “Mixture Inventory Model with Backorders and Lost Sales for Variable Lead Time,” Journal of the Operational Research Society, Vol. 47, pp. 829832 (1996). doi: 10.2307/3010290
  3. [3] Ouyang, L. Y. and Wu, K. S., “A Minimax Distribution Free Procedure for Mixed Inventory Model with Variable Lead Time,” International Journal of Production Economics, Vol. 5657, pp. 511516 (1998). doi: 10.1016/S0925-5273(97)00068-6
  4. [4] Moon, I. and Choi, S., “A Note on Lead Time and Distributional Assumptions in Continuous Review Inventory Models,” Computers & Operations Research, Vol. 25, No. 11, pp. 10071012 (1998). doi: 10.1016/ S0305-0548(97)00103-2
  5. [5] Hariga, M. and Ben-Daya, M., “Some Stochastic Inventory Models with Deterministic Variable Lead Time,” European Journal of Operational Research, Vol. 113, pp. 4251 (1999). doi: 10.1016/S0377-2217 (97)00441-4
  6. [6] Ouyang, L. Y., Chen, C. K. and Chang, H. C., “Lead Time and Ordering Cost Reductions in Continuous Review Inventory Systems with Partial Backorders,” Journal of the Operational Research Society, Vol. 50, pp. 12721279 (1999). doi: 10.2307/3010637
  7. [7] Ouyang, L. Y. and Chang, H. C., “The Effects of Investing in Lost Sales Reduction on the Stochastic Inventory Models,” Journal of Information & Optimization Science, Vol. 22, pp. 357368 (2001). doi: 10. 1080/02522667.2001.10699497
  8. [8] Ouyang, L. Y., Chuang, B. R. and Lin, Y. J., “Periodic Review Inventory Models with Controllable Lead Time and Lost Sales Rate Reduction,” Journal of the Chinese Institute of Industrial Engineers, Vol. 22, No. 5, pp. 355368 (2005). doi: 10.1080/101706605095 09305
  9. [9] Ouyang, L. Y., Chuang, B. R. and Lin, Y. J., “Effective Investment to Reduce Lost-Sales Rate in a Periodic Review Inventory Model,” OR Spectrum, Vol. 29, pp. 681697 (2007). doi: 10.1007/s00291-007-0081-8
  10. [10] Rosenblatt, M. J. and Lee, H. L., “Economic Production Cycles with Imperfect Production Processes,” IIE Transactions, Vol. 18, No. 1, pp. 4855 (1986). doi: 10.1080/07408178608975329
  11. [11] Porteus, E. L., “Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction,” Operations Research, Vol. 34, No. 1, pp. 137144 (1986). doi: 10.1287/opre.34.1.137
  12. [12] Paknejad, M. J., Nasri, F. and Affisco, J. F., “Defective Units in a Continuous Review (s, Q) System,” International Journal of Production Research, Vol. 33, pp. 27672777 (1995). doi: 10.1080/00207549508904844
  13. [13] Wu, K. S. and Ouyang, L. Y., “(Q, r, L) Inventory Model with Defective Items,” Computers & Industrial Engineering, Vol. 39, pp. 173185 (2001). doi: 10. 1016/S0360-8352(00)00077-2
  14. [14] Salameh, M. K. and Jaber, M. Y., “Economic Production Quantity Model for Items with Imperfect Quality,” International Journal of Production Economics, Vol. 64, No. 1, pp. 5964 (2000). doi: 10.1016/S0925-5273 (99)00044-4
  15. [15] Ouyang, L. Y. and Chang, H. C., “Impact of Investing in Quality Improvement on (Q, r, L) Model Involving the Imperfect Production Process,” Production Planning & Control, Vol. 11, pp. 598607 (2000). doi: 10.1080/095372800414160
  16. [16] Papachristos, S. and Konstantaras, I., “Economic Ordering Quantity Models for Items with Imperfect Quality,” International Journal of Production Economics, Vol. 100, No. 1, pp. 148154 (2006). doi: 10.1016/j.ijpe.2004.11.004
  17. [17] Eroglu, A. and Ozdemir, G., “An Economic Order Quantity Model with Defective Items and Shortages,” International Journal of Production Economics, Vol. 106, pp. 544549 (2007). doi: 10.1016/j.ijpe.2006. 06.015
  18. [18] Wee, H. H., Yu, J. and Chen, M. C., “Optimal Inventory Model for Items with Imperfect Quality and Shortage Backordering,” Omega, Vol. 35, pp. 711 (2007). doi: 10.1016/j.omega.2005.01.019
  19. [19] Yoo, S. H., Kim, D. and Park, M. S., “Economic Production Quantity Model with Imperfect-Quality Items, Two-Way Imperfect Inspection and Sales Return,” International Journal of Production Economics, Vol 121, pp. 255265 (2009). doi: 10.1016/j.ijpe.2009.05. 008
  20. [20] Annadurai, K. and Uthayakumar, R., “Controlling Setup Cost (Q,r,L) Inventory Model with Defective Items,” Applied Mathematical Modelling, Vol. 34, pp. 14181427 (2010). doi: 10.1016/j.apm.2009.04.010
  21. [21] Sana, S. S., “An Economic Production Lot Size Model in an Imperfect Production System,” European Journal of Operational Research, Vol. 201, pp. 158170 (2010). doi: 10.1016/j.ejor.2009.02.027
  22. [22] Roy, M. S., Sana, S. S. and Chaudhuri, K., “An Economic Order Quantity Model of Imperfect Quality Items with Partial Backlogging,” International Journal of Systems Science, Vol. 42, No. 8, pp. 14091419 (2011). doi: 10.1080/00207720903576498
  23. [23] Lin, Y. J., Ouyang, L. Y. and Dang, Y. F., “A Joint Optimal Ordering and Delivery Policy for an Integrated Supplier-Retailer Inventory Model with Trade Credit and Defective Items,” Applied Mathematics and Computation, Vol. 218, pp. 74987514 (2012). doi: 10. 1016/j.amc.2012.01.016
  24. [24] Lin, H. J., “An Integrated Supply Chain Inventory Model with Imperfect-Quality Items, Controllable Lead Time and Distribution-Free Demand,” Yugoslav Journal of Operations Research, Vol. 23, No. 1, pp. 87 109 (2013). doi: 10.2298/YJOR110506019L
  25. [25] Lin, H. J. and Lin, Y. J., “Supply Chain Coordination with Defective Items and Quantity Discount,” International Journal of Systems Science, pp. 110 (2013). doi:10.1080/00207721.2013.773468
  26. [26] Liao, C. J. and Shyu, C. H., “An Analytical Determination of Lead Time with Normal Demand,” International Journal of Operations & Production Management, Vol. 11, No. 9, pp. 7278 (1991). doi: 10. 1108/EUM0000000001287
  27. [27] Scarf, H., “A Min-Max Solution of an Inventory Problem,” In: Arrow K, Karlin S, Scarf H, editors. The Mathematical Theory of Inventory and Production; Stanford CA: Stanford University Press, pp. 201209 (1958).
  28. [28] Gallego, G. and Moon, I., “The Distribution Free Newsboy Problem: Review and Extensions,” Journal of the Operational Research Society, Vol. 44, No. 8, pp. 825834 (1993). doi: 10.2307/2583894
  29. [29] Hall, R. W., Zero Inventories, Illinois Dow Jones Irwin, Homewood (1983).
  30. [30] Porteus, E. L., “Investing in Reduced Setups in the EOQ Model,” Management Science, Vol. 31, pp. 998 1010 (1985). doi: 10.1287/mnsc.31.8.998
  31. [31] Nasri, F., Affisco, J. F. and Paknejad, M. J., “Setup Cost Reduction in an Inventory Model with FiniteRange Stochastic Lead Times,” International Journal of Production Research, Vol. 28, pp. 199212 (1990). doi: 10.1080/00207549008942693
  32. [32] Shore, H., “General Approximate Solutions for Some Common Inventory Models,” Journal of the Operational Research Society, Vol. 37, pp. 619629 (1986). doi: 10.2307/2582588