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In this paper, a probabilistic continuous review inventory model is developed for deteriorating items. The model is developed under conditions of stochastic demands and no shortages in which both lead time and order quantity are treated as decision variables. We concentrate on lead time as a deterministic variable which is made endogenous through an “expediting factor” , the constant of proportionality between the reduced lead time and ordinary time. For models, we determine the expected cost per unit time then numerical examples are given. Additionally sensitivity analyses are conducted with respect to the various cost parameter ranges and remarks are made for further researches.