Minimizing the Total Weighted Flow-time of Jobs with Set-up Times and Unequal Release Dates: Application to Minimizing Maintenance Operations Cost

Abstract : An efficient heuristic is proposed in this paper for solving the minimization problem of total weighted flow-time of n tasks or jobs while scheduling the tasks on parallel machines. The heuristic considers tasks with unequal release dates and set-up times characterized by the task sequences. For solving this problem, we designed an appropriate priority rule that locally optimizes task scheduling and minimizes their weighted flow-time. The Priority Rule for Total Weighted Flow-time with Set-ups Times (PRTWFST) is then used to design a real-time algorithm of tasks scheduling and allocation, with a complexity of O(n3). The algorithm is implemented for the scheduling and allocation of preventive maintenance tasks of a distributed system. Results of computational experimentation testify to the efficiency of the algorithm.