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Partial backlogging inventory lot-size models for deteriorating items with fluctuating demand under inflation. (English) Zbl 1144.90004

Summary: The traditional inventory lot-size model is extended to allow not only for general partial backlogging rate but also for inflation. The assumptions of equal cycle length and constant shortage length imposed in the model developed by I. Moon et al. [Eur. J. Oper. Res. 162, No. 3, 773–785 (2005; Zbl 1067.90004)] are also relaxed. For any given number of replenishment cycles the existence of a unique optimal replenishment schedule is proved and further the convexity of the total cost function of the inventory system in the number of replenishments is established. The theoretical results here amend those by H.-L. Yang, J.-T. Teng and M.-S. Chern [Nav. Res. Logist. 48, 144–158 (2001; Zbl 0981.90003)] and provide the solution to those two counterexamples by K. Skouri and S. Papachristos [Nav. Res. Logist. 49, No. 5, 527–529 (2002; Zbl 1013.90005)]. Finally we propose an algorithm to find the solution, and obtain some managerial results by using sensitivity analyses.

MSC:

90B05 Inventory, storage, reservoirs
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