Abstract
Most traditional inventory models assume that the lead time is prescribed (either deterministic or stochastic) and thus is not subject to control. We consider an inventory model in which the lead time can be controlled. It is assumed that the demand follows a Poisson distribution and the crashing cost for reduced lead time is proportional to the length of time being crashed. The objective is to determine the optimal lead lime and re-order point pair in order to minimize the expected total cost which is composed of the expected carrying cost, the expected shortage cost and the crashing cost.
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