Further developments on safety stocks in a material requirements planning system applying Laplace transforms and input–output analysis

In a sequence of previous papers, the Laplace transform and Input–Output Analysis have been applied to formulate a theoretical basis for material requirements planning under different levels of generalisation. Searching for the optimal safety stock is one of the extensions of this theory. This paper investigates the safety stock properties in the case that the time interval of demand is Gamma-distributed. The Generalised Leontief inverse plays an effective role in describing the multi-level production–inventory system when the subordinate products are produced according to a lot-for-lot policy.