Title: Optimal replenishment in a Brownian Motion EOQ model with hysteretic parameter changes

Authors: Oded Berman, David Perry, Wolfgang Stadje

Addresses: University of Toronto, Joseph L. Rotman School of Management, 105 St. George Street, Toronto, M5S 3E6, Canada. ' Department of Statistics, University of Haifa, Haifa 31909, Israel. ' Department of Mathematics and Computer Science, University of Osnabruck, 49069 Osnabruck, Germany

Abstract: We consider an EOQ model in which the content level is modelled by a Brownian Motion (BM) with state-dependent drift and diffusion parameters. There are either one or two prespecified switchover threshold values (cases 1 and 2) such that the drift and the volatility change whenever the critical threshold is reached (in case 1) or whenever the upper threshold is reached from below or the lower one from above (in case 2). The controller places an order of fixed size every time the content level reaches 0. We derive all the relevant cost functionals for the discounted case with infinite horizon and for the long-run average case. These explicit results are used for finding the optimal replenishment level in the long-run average case.

Keywords: inventory; EOQ models; Brownian motion; hysteretic parameters; state-dependent parameters; cost functional; optimisation; economic order quantity; optimal replenishment.

DOI: 10.1504/IJIR.2008.019205

International Journal of Inventory Research, 2008 Vol.1 No.1, pp.1 - 19

Published online: 02 Jul 2008 *

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