×

Lot sizing with random yield and different qualities. (English) Zbl 1205.90038

Summary: This paper considers a production/inventory system where items produced/purchased are of different qualities: Types A and B. Type A items are of perfect quality, and Type B items are of imperfect quality; but not necessarily defective; and have a lower selling price. The percentage of Type A (the yield rate) is assumed to be a random variable with known probability distribution. The electronics industry gives good examples of such situations. We extend the classical single period (newsvendor) and the economic order quantity (EOQ) models by accounting for random supply and for imperfect quality (Type B) items which are assumed to have their own demand and cost structure. We develop mathematical models and prove concavity of the expected profit function for both situations. We also present detailed analysis and numerical results. We focus on comparing the profitability of the novel proposed models with models from the literature (and derivatives of these models) that develop the optimal order quantity based on the properties of Type A items only (and ignore Type B items). We find that accounting for Type B items can significantly improve profitability.

MSC:

90B05 Inventory, storage, reservoirs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Yano, C. A.; Lee, H. L., Lot sizing with random yields: a review, Oper. Res., 43, 311-334 (1995) · Zbl 0832.90031
[2] Banerjee, A., A joint economic-lot size model for purchase and vendor, Decision Sci., 17, 292-311 (1986)
[3] Wright, C. M.; Mehrez, A., An overview of representative research of the relationships between inventory and quality, Omega, 26, 29-47 (1998)
[4] Khouja, M., The single-period (news-vendor) problem: literature review and suggestions for future research, Omega, 27, 537-553 (1999)
[5] Karlin, S., One stage inventory models with uncertainty, (Arrow, K.; Karlin, S.; Scarf, H., Studies in the Mathematical Theory of Inventory and Production (1958), Stanford University Press: Stanford University Press Stanford, CA)
[6] Shih, W., Optimal inventory policies when stockouts result from defective products, Int. J. Prod. Res., 18, 677-685 (1980)
[7] Noori, A. H.; Keller, G., One-period order quantity strategy with uncertain match between the amount received and quantity requisitioned, INFOR, 24, 1-11 (1986) · Zbl 0592.90026
[8] Silver, E. A., Establishing the reorder quantity when the amount received is uncertain, INFOR, 14, 32-39 (1976)
[9] Ehrhardt, R.; Taube, L., An inventory model with random replenishment quantity, Int. J. Prod. Res., 25, 1795-1803 (1987) · Zbl 0629.90029
[10] Gerchak, Y.; Vickson, R. G.; Parlar, M., Periodic review production models with variable yield and uncertain demand, IIE Trans., 20, 44-50 (1988)
[11] Henig, M.; Gerchak, Y., The structure of periodic review policies in the presence of random yield, Oper. Res., 38, 634-643 (1990) · Zbl 0721.90034
[12] Kalro, A. H.; Gohil, M. M., A lot size model with backlogging when the amount received is uncertain, Int. J. Prod. Res., 20, 775-786 (1982)
[13] Mak, K. L., Inventory control of defective product when the demand is partially captive, Int. J. Prod. Res., 23, 533-542 (1985) · Zbl 0579.90019
[14] Porteus, E., Optimal lot sizing, process quality improvement and setup cost reduction, Oper. Res., 34, 137-144 (1986) · Zbl 0591.90043
[15] Rosenblatt, M. J.; Lee, H. L., Economic production cycles with imperfect production processes, IIE Trans., 18, 48-55 (1986)
[16] Freimer, M.; Thomas, D.; Tyworth, J., The value of setup cost reduction and process improvement for the economic production quantity model with defects, Euro. J. Oper. Res., 173, 241-251 (2006) · Zbl 1125.90339
[17] Salameh, M. K.; Jaber, M. Y., Economic production quantity model for items with imperfect quality, Int. J. Prod. Econom., 64, 59-64 (2000)
[18] Goyal, S. K.; Cardenas-Baron, L. E., Note on: economic production quantity model for items with imperfect quality – a practical approach, Int. J. Prod. Econom., 77, 85-87 (2002)
[19] Chang, H. C., An application of fuzzy sets theory to the EOQ model with imperfect quality items, Comput. Oper. Res., 31, 2079-2092 (2004) · Zbl 1100.90500
[20] Huang, C. K., An optimal policy for a single-vendor single-buyer integrated production-inventory problem with process unreliability consideration, Int. J. Prod. Econom., 91, 91-98 (2004)
[21] Maddah, B.; Jaber, M. Y., Economic order quantity for items with imperfect quality: Revisited, Int. J. Prod. Econom., 112, 808-815 (2008)
[22] Papachristos, S.; Konstantaras, I., Economic ordering quantity models for items with imperfect quality, Int. J. Prod. Econom., 100, 148-156 (2006)
[23] Hayek, P. A.; Salameh, M. K., Production lot sizing with the reworking of imperfect quality items produced, Prod. Plann. Control, 12, 584-590 (2001)
[24] Law, A.; Kelton, W., Simulation Modeling and Analysis (1991), McGraw-Hill: McGraw-Hill New York
[25] Ross, S. M., Stochastic Processes (1996), Wiley: Wiley New York, NY · Zbl 0888.60002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.