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Stochastic Periodic-Review Models with Duration- and Quantity-Dependent Inventory Costs: Properties and Approximations

Tal Avinadav

Department of Management, Bar-Ilan University, Ramat-Gan 52900, Israel

https://doi.org/10.1142/S0217595916500305Cited by:4 (Source: Crossref)

Abstract

In this paper, we formulate a stochastic periodic-review inventory model with lead-time that considers both duration- and quantity-dependent inventory costs, and show that the optimality equation has the same format as the standard newsvendor problem with a modified demand distribution. We suggest (i) an approximation of the optimal order-up-to level, based on discretization of the inventory cost accounting, and (ii) two heuristic formulas, based on the two-moment normal approximation of the modified demand distribution, and on an approximated deterministic model. We evaluate the performances of these formulas using a Brownian motion demand process under different scenarios, and discuss their advantages and disadvantages.

Keywords:

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