zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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.

90B05Inventory, storage, reservoirs
Full Text: DOI
[1] Yano, C. A.; Lee, H. L.: Lot sizing with random yields: a review, Oper. res. 43, 311-334 (1995) · Zbl 0832.90031 · doi:10.1287/opre.43.2.311
[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, Studies in the mathematical theory of inventory and production (1958) · Zbl 0079.36003
[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 · doi:10.1287/opre.38.4.634
[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 · doi:10.1080/00207548508904726
[14] Porteus, E.: Optimal lot sizing, process quality improvement and setup cost reduction, Oper. res. 34, 137-144 (1986) · Zbl 0591.90043 · doi:10.1287/opre.34.1.137
[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 · doi:10.1016/j.ejor.2004.11.024
[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) · Zbl 1128.90302
[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) · Zbl 0489.65007
[25] Ross, S. M.: Stochastic processes, (1996) · Zbl 0888.60002