This work is motivated by the rapid increasing of the design complexity of many embedded systems. It aims at the proposing of solutions to resolve the hardware contention issues of non-preemptive processing elements shared among tasks and the cost optimization. A software solution based on the starting time management is proposed to interleave task executions on processing elements. Algorithms are proposed to determine the required processing elements of selected types, when there is no knowledge on the releasing time of any task: When task release orders are known a priori, an optimal algorithm is presented if processing elements have the same cost; otherwise, a pseudo-polynomial-time algorithm based on dynamic programming is presented for optimal solutions. The performance of the algorithms is also evaluated for general cases.