The Problem of Managing Reentrangeable Resources on Network Graphs with Homogeneous Intensity Functions

Abstract: The article considers the problem of optimal distribution of resources allocated for the execution of a certain set of interrelated tasks, according to the criterion of minimizing the execution time of all tasks. In contrast to the traditional consideration of a separable resource, a reentrant resource is considered, i.e. one that can be reused. A formalization of this problem is given in a dynamic statement. For the case of homogeneous linear productivity functions, an analytical solution is given and justified. A demonstration of the non-optimality of some heuristic algorithms is given. A geometric optimality criterion is given for the case of two independent jobs. An example of complete internal resource switching is constructed on its basis.

Keywords: optimization, resource allocation, network schedule, execution intensity functions.