×

Inventory model of deteriorated items with a constraint: a geometric programming approach. (English) Zbl 1125.90005

Summary: An inventory model for deteriorating items is built-up with limited storage space. Here, demand rate for the items is finite, items deteriorate at constant rates and are replenished instantaneously. Following EOQ model, the problem is formulated with and without truncation on the deterioration term and ultimately is converted to the minimization of a signomial expression with a posynomial constraint. It is solved by modified geometric programming (MGP) method and non-linear programming (NLP) method. The problem is supported by numerical examples. The results from two versions of the model (with and without truncation) and two methods (i.e. MGP and NLP) are compared.

MSC:

90B05 Inventory, storage, reservoirs
90C30 Nonlinear programming
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abou-El-Ata, M. O.; Kotb, K. A.M., Multi-item EOQ inventory model with varying holding cost under two restrictions: A geometric programming approach, Production Planning and Control, 8, 608-611 (1997)
[2] Arrow, K.; Karlin, J.; Scarf, H., Studies in the Mathematical Theory of Inventory and Production (1958), Stanford University Press: Stanford University Press Stanford, CA · Zbl 0079.36003
[3] Bazara, M. S.; Sherali, H. D.; Shetty, C. M., Nonlinear Programming Theory and Application (1993), John Wiley and Sons Inc.: John Wiley and Sons Inc. New York
[4] Cheng, T. C.E., An economic production quantity model with flexibility and reliability considerations, European Journal of Operational Research, 39, 174-179 (1989) · Zbl 0672.90039
[5] Cheng, T. C.E., An economic production quantity model with demand-dependent unit cost, European Journal of Operational Research, 40, 252-256 (1989) · Zbl 0665.90017
[6] Duffin, R. J.; Peterson, E. L.; Zener, C., Geometric Programming-Theory and Application (1967), John Wiley: John Wiley New York · Zbl 0171.17601
[7] Ghare, P. N.; Schrader, G. F., A model for exponentially decaying inventories, Journal of Industrial Engineering, 15, 238-243 (1963)
[8] Goyal, K.; Giri, B. C., Recent trends in modeling of deteriorating inventory, European Journal of Operational Research, 134, 1-16 (2001) · Zbl 0978.90004
[9] Hadley, G.; Whitin, T. M., Analysis of Inventory Systems (1958), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ · Zbl 0176.50004
[10] Hariri, A. M.A.; Abou-El-Ata, M. O., Multi-item production lot-size inventory model with varying order cost under a restriction: A geometric programming approach, Production Planning and Control, 8, 179-182 (1997)
[11] Harris, F., Operations and Cost (Factory Management Sciences) (1915), A.W. Shaw Co.: A.W. Shaw Co. Chicago, pp. 48-52
[12] Jung, H.; Klein, C. M., Optimal inventory policies under decreasing cost functions via geometric programming, European Journal of Operational Research, 132, 628-642 (2001) · Zbl 1024.90004
[13] Kotchenberger, G. A., Inventory models: Optimization by geometric programming, Decision Sciences, 2, 193-205 (1971)
[14] Naddor, E., Inventory Systems (1966), John Wiley: John Wiley New York
[15] Raafat, F., Survey of literature on continuously on deteriorating inventory model, Journal of Operational Research Society, 42, 27-37 (1991) · Zbl 0718.90025
[16] Roy, T. K.; Maiti, M., Multi-objective models of deteriorating items with some constraints in a fuzzy environment, Computers and Operations Research, 25, 1085-1095 (1998) · Zbl 1042.90511
[17] Shaky, A. I.; Abou-El-Ata, M. O., Constrained production lot-size model with trade credit policy: ‘A comparison geometric programming approach via Lagrange’, Production Planning and Control, 12, 654-659 (2001)
[18] Worral, B. M.; Hall, M. A., The analysis of an inventory control model using posynomial geometric programming, International Journal of Production Research, 20, 657-667 (1982)
[19] Zener, C. M., Engineering Design by Geometric Programming (1971), John Wiley & Sons: John Wiley & Sons New York
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.