For the lost sales inventory system we distinguish two different replenishment strategies. The simplest strategy is the classical ‘fixed reorder level’ replenishment rule: every period the inventory position in the system is raised up to a fixed quantity S. For this simple strategy we derive and test heuristics for the determination of the reorder level, given a target service level. Next we demonstrate that it may be more efficient in a lost sales system to use a different replenishment strategy. This alternative replenishment strategy however is more complex. Therefore a comparison is made between the two replenishment strategies in a lost sales environment, to get an indication of the price which has to be paid here for simplicity.