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Optimal inventory policies for an economic order quantity model with decreasing cost functions. (English) Zbl 1112.90302
Summary: Three total cost minimization EOQ based inventory problems are modeled and analyzed using geometric programming (GP) techniques. Through GP, optimal solutions for these models are found and sensitivity analysis is performed to investigate the effects of percentage changes in the primal objective function coefficients. The effects on the changes in the optimal order quantity and total cost when different parameters of the problems are changed is also investigated. In addition, a comparative analysis between the total cost minimization models and the basic EOQ model is conducted. By investigating the error in the optimal order quantity and total cost of these models, several interesting economic implications and managerial insights can be observed.

##### MSC:
 90B05 Inventory, storage, reservoirs 90B50 Management decision making, including multiple objectives
##### Keywords:
inventory; geometric programming; EOQ
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##### References:
 [1] Arcelus, F.J.; Srinivasan, G., A ROI-maximizing EOQ model under variable demand and markup rates, Engineering costs and production economics, 9, 113-117, (1985) [2] Arcelus, F.J.; Srinivasan, G., The sensitivity of optimal inventory policies to model assumptions and parameters, Engineering costs and production economics, 15, 291-298, (1988) [3] Beightler, C.S.; Phillips, D.T., Applied geometric programming, (1976), John Wiley and Sons 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 order quantity model with demand-dependent unit cost, European journal of operational research, 40, 252-256, (1989) · Zbl 0665.90017 [6] Cheng, T.C.E., An economic order quantity model with demand-dependent unit production cost and imperfect production processes, IIE transactions, 23, 23-28, (1991) [7] Dinkel, J.J.; Kochenberger, G.A., A note on substitution effects in geometric programming, Management science, 20, 1141-1143, (1974) · Zbl 0303.90038 [8] Duffin, R.J.; Peterson, E.L.; Zener, C., Geometric programming–theory and application, (1976), John Wiley and Sons New York · Zbl 0171.17601 [9] Hillier, S.H.; Lieberman, G.J., Introduction to operations research, (1990), McGraw-Hill San Francisco · Zbl 0155.28202 [10] Hildebrand, F.B., Advanced calculus for applications, (1976), Prentice-Hall Englewood Cliffs, NJ · Zbl 0116.27201 [11] Jung, H.; Klein, C.M., Optimal inventory policies under decreasing cost functions via geometric programming, European journal of operational research, 132, 3, 628-642, (2001) · Zbl 1024.90004 [12] Kochenberger, G.A., Inventory models: optimization by geometric programming, Decision sciences, 2, 193-205, (1971) [13] Ladany, S.; Sternlieb, A., The interaction of economic ordering quantities and marketing policies, AIIE transactions, 6, 35-40, (1974) [14] Lee, W.J., Determining order quantity and selling price by geometric programming: optimal solution, bounds, and sensitivity, Decision sciences, 24, 76-87, (1993) [15] Lee, W.J., Optimal order quantities and prices with storage space and inventory investment limitations, Computers and industrial engineering, 26, 481-488, (1994) [16] Lee, W.J.; Kim, D.S., Optimal and heuristic decision strategies for integrated production and marketing planning, Decision sciences, 24, 1203-1213, (1993) [17] Lee, W.J.; Kim, D.S.; Cabot, A.V., Optimal demand rate, lot sizing, and process reliability improvement decisions, IIE transactions, 28, 941-952, (1996) [18] Worrall, 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)
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