We consider a single-stage multiproduct manufacturing facility producing several end-products for delivery to customers with a required customer lead-time. The end-products can be split in two classes: few products with high volume demands and a large number of products with low-volume demands. In order to reduce inventory costs, it seems efficient to produce the high-volume products according to an MTS policy and the low volume products according to an MTO policy. The purpose of this paper is to analyze and compare the impact of the scheduling policy on the overall inventory costs, under customer lead-time service level constraints. We consider two policies: the classical FIFO policy and a priority policy (PR) which gives priority to low volume products over high volume products. We show that for some range of parameters, the PR rule can significantly outperform the FIFO rule. In these ranges, the service level constraints are satisfied by the PR rule with much lower inventory costs.