Title: Analysis of a (0, 1) inventory system where demand follows a renewal process

Authors: Mahmut Parlar

Addresses: DeGroote School of Business, McMaster University, 1280 Main St. W., Hamilton, Ontario L8S 4M4, Canada

Abstract: When unit item costs are high and expected demand during leadtime is low, it may be desirable to implement the (0, 1) inventory policy which calls for ordering one unit when the inventory falls to zero. Under this policy, when demand arrivals constitute a renewal process it may also be desirable to delay the order release (but expedite the orders occurring during the delay period). This paper examines the (0, 1) model by focussing on its probabilistic properties. We first present explicit expressions for, 1) the probability distribution of the expedited orders; 2) the interval over which inventory is positive. Using these results, we introduce a (service-level type) chance-constraint on the number of expedited orders and determine the optimal and finite order delay. We also consider a case where the cost of expediting an order may be difficult to estimate and compute its implied value. More general models that allow non-monotone renewal density and random leadtimes are also presented and analysed.

Keywords: stochastic inventory; 0-1 order policy; renewal process; implied cost; probability distribution; order delay; modelling; renewal density; random leadtimes.

DOI: 10.1504/IJIR.2011.045385

International Journal of Inventory Research, 2011 Vol.1 No.3/4, pp.262 - 287

Published online: 07 Mar 2015 *

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