We consider a class of scheduling problems of n weighted tasks on M identical, and parallel processors with an objective of minimizing the sum of the tasks weighted flow-times. A priority rule for total weighted flow-time (PRTWF), is then proposed for locally optimal scheduling of tasks with unequal release dates and processing times. Then, an algorithm based on a heuristic and the PRTWF, is worked out to minimize the total weighted flow-time of the given set of tasks on a single server. This algorithm is designed for implementation in a dynamic process of real-time decision-making. It is next extended to tasks scheduling (with unequal release dates and processing times) on parallel servers, while minimizing their total weighted flowtime. A lower bound of solutions is also proposed to evaluate the algorithm, with a complexity in O(n 3) in the off-line scheduling process. The rule is then used in an algorithm of on-line planning and scheduling of maintenance tasks in a large size distributed system with weighted Equipments.