Abstract: Studies the problem that a supplier is relatively in an advantageous position but retailers have to decide the quantities to replenish their inventories with various factors taken into account. Assuming that both the allowable stock-out and replenishment intervals are stochastic (independent identically distributed) variables, we give the expected profit function that the replenishment intervals comply with general distribution and the inventory can be controlled effectively by optimizing the replenishment quantity. Then, two particular distribution cases are discussed for replenishment intervals and, by sensitivity analysis, how the replenishment intervals affect retailer s profit is expounded.