Optimal inventory policies for imperfect inventory with price dependent stochastic demand and partially backlogged shortages
DOI:
https://doi.org/10.2298/YJOR101011007BKeywords:
Imperfect inventory, Price-dependent stochastic demand, Random defective units, Partial backloggingAbstract
The paper investigates a single period imperfect inventory model with price dependent stochastic demand and partial backlogging. The backorder rate is a nonlinear non-increasing function of the magnitude of shortage. Two special cases are considered assuming that the percentage of defective items follows a truncated exponential distribution and a normal distribution respectively. The optimal order quantity and the optimal mark up value are determined such that the expected total profit of the system is maximized. Numerical example is given to illustrate the proposed model which is compared with the traditional model of perfect stock. Sensitivity analysis is performed to explain the behavior of the proposed model with respect to the key parameters.References
Abad, P.L., “Optimal price and order size for a reseller under partial backordering”, Computers and Operations Research, 28 (1) (2001) 53-65.
Abad, P., “Optimal pricing and lot-sizing under conditions of perishability, finite production and partial backordering and lost sale”, European Journal of Operational Research, 144(3) (2003), 677-685.
Affisco, J.F., Paknejad, M.J., and Nasri, F., “Quality improvement and setup cost reduction in the joint economic lot size model”, European Journal of Operational Research, 142 (2002) 497-508.
Arcelus, F.J., Kumar, S., and Srinivasan, G., “Risk tolerance and a retailer’s pricing and ordering policies within a newsvendor framework”, Omega, 40(2) (2012) 188-198.
Cachon, “The allocation of inventory risk in a supply chain: Push, pull, and advance – purchase discount contracts”, Management Science, 50(2) (2004) 222-238.
Chang, H.-C., Ho, C.-H., “Exact closed form solutions for optimal inventory model for items with imperfect quality and shortage backordering”, Omega, 38(3-4) (2010) 233-237.
Chang, H.J., and Feng Lin, W., “A partial backlogging inventory model for non-instantaneous deteriorating items with stock-dependent consumption rate under inflation”, Yugoslav Journal of Operations Research, 20(1) (2010) 35-54.
Chang, C.-T., Chen, Y.-Ju., Rutsad, T., and Wu, S.–J., “Inventory models with stock-and price-dependent demand for deteriorating items based on limited shelf space”, 20(1) (2010) 55-69.
Chao, X., Chen, H., and Zheng, S., “Joint replenishment and pricing decisions in inventory systems with stochastically dependent supply capacity”, European Journal of Operational Research, 191 (2008) 142-155.
Cheng, T.C.E., “EPQ with process capability and quality assurance considerations,” Journal of Operational Research Society, 42(8) (1991) 713-720.
Donohue, “Efficient supply contracts for fashion goods with forecast updating and two production modes”, Management Science, 46(11) (2000) 1397-1411.
Geunes, J.P., Ramasesh, R.V., and Hayya, J.C., “Adapting the newsvendor model for infinite horizon inventory systems”, International Journal of Production Economics, 72(3) (2001) 237-250.
Goyal, S.K., Gunasekaran, A., Martikainen, T. and Yli-Olli, P., “Integrating production and quality control policies: A survey”, European Journal of Operational Research, 69 (1993) 1-13.
Hu, J.S., Zheng, H., Xu, R.-Q., Ji, Y.-P., and Guo, C.-Y., “Supply chain co-ordination for fuzzy random newsboy problem with imperfect quality”, International Journal of Approximate Reasoning, 51(7) (2010) 771-784.
Karakul, M., “Joint pricing and procurement of fashion products in the existence of clearance markets”, School of Administrative Studies, York University, 2011 (online).
Keren, B., “The single-period inventory problem: Extension to random yield from the perspective of the supply chain”, Omega, 37(4) (2009) 801-810.
Khouja, M., “Note on the newsboy problem with an emergency supply”, Journal of the Operational Research Society, 47 (12) (1996) 1530-1534.
Khouja, M., “The single-period (news-vendor) problem: Literature review and suggestions for future research”, Omega: International Journal of Management Science, 27 (1999) 537-553.
Liao, Y., Banerjee, A., and Yan, C., “A distribution free newsvendor model with balking and lost sales penalty”, International Journal of Production Economics, 133(1) (2011) 224-227.
Lin, Y.J., “A stochastic periodic review integrated inventory model involving defective items, backorder price discount and variable lead time”, A Quarterly Journal of Operations Research, 8 (3) (2010) 281-297.
Moinzadeh, K., and H.L., Lee, “A continuous review inventory model with constant resupply time and defective items”, Naval Research Logistics, 34 (1987) 457-467.
Nasri, F., Paknejad, M.J., and Affisco, J.F., “Lot size determination in an EOQ model with planned shortage and random defective units,” Proceedings of the Northeast Decision Sciences Institute, Mohegan Sun, CT, 2009, 403-408.
Nasri, F., Paknejad, M.J., and Affisco, J.F., “An EMQ model with planned shortage and random defective units,” Proceedings of the Northeast Decision Sciences Institute, New Orleans, 2009, 10541-10546.
Oberlaender, M., “Dual sourcing of a newsvendor with exponential utility of profit”, International Journal of Production Economics, 133(1) (2011) 370-376.
Paknejad, M.J., Nasri, F., and Affisco, J.F., “Defective units in a continuous review (s, Q) system,” International Journal of Production Research, 33(10)(1995) 2767-2777.
Paknejad, M.J., Nasri, F., and Affisco, J.F., “Flexibility and quality improvement in the EOQ with planned shortage model,” Proceedings of the Northeast Decision Sciences Institute, Pittsburgh, Pennsylvania, 2001, 257-259.
Paknejad, M.J., Nasri, F., and Affisco, J.F., “An EOQ model with two types of shortage and random defective units,” Proceedings of the Northeast Decision Sciences Institute, 2010, 439-444.
Panda, D., Kar, S., Maity, K., and Maity, M., “A single period inventory model with imperfect production and stochastic demand under chance and imprecise constraints”, European Journal of Operational Research, 188(1) (2008) 121-139.
Porteus, E., “Optimal lot sizing, process quality improvement and setup cost reduction”, Operations Research, 34(1) (1986) 137-144.
Qin, Y., Wang, R., Vakharia, A.J., Seref, M.M.H., and Chen, Y., “The newsvendor problem: Review and directions for future research”, European Journal of Operational Research, 213(2)(2011) 361-374.
Rosenblatt, M.J. and Lee, H.L., “Economic production cycles with imperfect production processes”, IIE Transactions, 18(3) (1986) 48-55.
Sahin, E., Buzacott, J., and Dallery, Y., “Analysis of a newsvendor which has errors in inventory data records”, European Journal of Operational Research, 188(2) (2008) 370-389.
Shih, W., “Optimal inventory policies when stock outs result from defective products”, International Journal of Production Research, 18(6) (1980) 677-686.
Tang, O., Musa, S.N., and Li, J., “Dynamic pricing in the newsvendor problem with yield risks”, International Journal of Production Economics, 2011 (online).
Wagner, H.V., Principles of Operations Research, with Applications to Managerial Decisions, PHI Learning Private Limited, New Delhi, 2008.
Wang, C.X., and Webster, S., “The loss-averse newsvendor problem”, Omega, 37(1) (2009) 93-105.
Wee et al., “Optimal inventory model for items with imperfect quality and shortage backordering”, Omega, 35(1) (2007) 7-11.
Weng, Z.K., “Coordinating order quantities between the manufacturer and the buyer: A generalized newsvendor model”, European Journal of Operational Research, 156(2004) 148-161.
Whitin, T.T., “Inventory control and pricing theory”, Management Science, 2 (1955) 61-80.
Yang, S., Shi, C.V., and Zhao, X., “Optimal ordering and pricing decisions for a target oriented newsvendor”, Omega, 39(1) (2011) 110-115.
Zhou, Y-W., and Wang, S.-D., “Manufacturer-buyer co-ordination for newsvendor type products with two ordering opportunities and partial backorders”, European Journal of Operational Research, 198(3) (2009) 958-974.
Downloads
Published
Issue
Section
License
Copyright (c) 2012 YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
