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We consider the canonical periodic review lost sales inventory system withpositive lead-times and stochastic i.i.d. demand under the average costcriterion. We introduce a new policy that places orders such that the expectedinventory level at the time of arrival of an order is at a fixed level and callit the Projected Inventory Level (PIL) policy. We prove that this policy has acost-rate superior to the equivalent system where excess demand is back-orderedinstead of lost and is therefore asymptotically optimal as the cost of losing asale approaches infinity under mild distributional assumptions. We further showthat this policy dominates the constant order policy for any finite lead-timeand is therefore asymptotically optimal as the lead-time approaches infinityfor the case of exponentially distributed demand per period. Numerical resultsshow this policy also performs superior relative to other policies.

Projected Inventory Level Policies for Lost Sales Inventory Systems: Asymptotic Optimality in Two Regimes