Methods for the optimal resource allocation in the problems of scheduling of tasks described with concave dynamic model

In some models of tasks used in the scheduling theory an additional continuously divisible resource is needed to process the task. One of such models, the dynamic one, is considered in the paper. Such model often appears in the real-life situations. Up to date, it was successfully used in many different fields, e.g. scheduling of tasks in the multiple computer systems, the forging process in the steel plants and refuelling of the fleet of boats in a given critical time. In most applications this model is also concave. For such case two phases are distinguished in the methodology of the solution construction. In the fist phase tasks are distributed among the processors and in the second one the resource is (optimally) allotted to the tasks. The second phase is computationally very expensive. Moreover, the methods of the optimal resource allocation proposed so far, although theoretically impeccable, are difficult and in some cases even impossible to apply. Thus in the paper, based on a recent theoretical results we propose a new method of the resource allocation: efficient and easily applicable. This method is compared in the computational experiment to other methods.