The efficient processing of database applications by computing systems with multi-tiered persistent storage devices needs specialized algorithms to generate optimal persistent storage management plans. A correct allocation and deallocation of multi-tiered persistent storage may significantly impact the overall performance of data processing in such systems. This paper describes the new algorithms, that create persistent storage allocation plans for data processing on multi-tiered persistent storage devices. This work is based on the pipelined data processing model, and it applies a formalism of extended Petri nets to describe the data flows between the tiers of persistent storage devices. The algorithms presented in the paper perform linearization of the extended Petri nets and generate the optimal persistent storage allocation plans. The paper describes the experiments conducted to validate the generate data allocation plans for multi-tiered persistent storage devices and prove the improvements in performance compared with random data allocation plans.