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Most continuous time inventory models which allow for the stochastic nature of demands usually include a delivery lag. This disguises a close link between deterministic and stochastic formulations of the inventory problem. By assuming that there is no delivery lag a stochastic version of the classical economic lot size model is developed. It yields the traditional square root formula where the constant demand term is replaced by mean demand.
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Ralph D. Snyder (1973) studied this question.
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