  We consider the classical discrete time lost-sales model under stationary
continuous demand and linear holding and penalty costs and positive constant
lead time. To date the optimal policy structure is only known implicitly by
solving numerically the Bellman equations. In this paper we derive the first
optimality equation for the lost-sales model. We propose a fixed
non-stockout-probability (FP3) policy, implying that each period the order size
ensures that P3, the probability of no-stockout at the end of the period of
arrival of this order, equals some target value. The FP3-policy can be computed
efficiently and accurately from an exact recursive expression and two-moment
fits to the emerging random variables. We use the lost-sales optimality
equation to compute the optimal FP3-policy. Comparison against the optimal
policy for discrete demand suggests that the fixed P3-policy is
close-to-optimal. An extensive numerical experiment shows that the FP3-policy
outperforms other policies proposed in literature in 97% of all cases. Under
the FP3-policy, the volatility of the replenishment process is much lower than
the volatility of the demand process. This cv-reduction holds a promise for
substantial cost reduction at upstream stages in the supply chain of the
end-item under consideration, compared to the situation with backlogging.
