Analysis of a (0, 1) inventory system where demand follows a renewal process Online publication date: Sat, 07-Mar-2015
by Mahmut Parlar
International Journal of Inventory Research (IJIR), Vol. 1, No. 3/4, 2011
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.
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