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In most cases, the scheduling problem for the multiprocessor system is NP‐ or strong NP‐hard. For this problem, we have already proposed a practical optimization algorithm DF/IHS (Depth First/Implicit Heuristic Search), which combines the list‐scheduling algorithm and the depth‐first search, for the minimum parallel processing time multiprocessors scheduling problem. This paper presents a result of application of DF/IHS to the minimum total weighted flow time problem, which is used in the optimization of memory utilization. The problem of allocating tasks to m processors is considered with or without precedence constraints among the tasks. It was verified that the DF/IHS can be applied to this kind of problem very effectively, where the optimal or highly accurate approximate solution is obtained for the large‐scale problem with several hundreds of tasks.