The probabilistic order level inventory model with lead time when shortages are permitted is developed whe supplier allows some credit periodT ^* for setting the accounts for the purchase quantity. The scheduling periodT is known. Mathematical models are derived for both the cases: i)T ^*≤T and ii)T ^*>T. Expressions are derived for average expected total cost of the system and for obtaining optimum order levelZ=Z ₀ under each case.