Configuring a Complex Executive System with Nonfixed Parameters

The problem of configuring a complex system is considered. As elements of the system, executors with a link graph that can change over time are considered. Configuration is understood as the process of determining the Executors of a given set of works and organizing their interaction, i.e. formation of the status (set of elements) and/or various structures (relationships) of the system that determine its functioning for the specified purposes. A number of conditions are imposed on communications between Executors. They are caused, firstly, by the physical possibility or impossibility of establishing a connection between each pair of Executors, and secondly, by restrictions on the number of established connections at certain points in time. The established relationships determine the ability to switch the execution of work between the Executors. It is assumed that two types of resources can be used to complete a set of tasks: current production and reserves. The current production resource is the performance of the Executor. At the same time, the desired amount of the general reserve is assigned to each task and allocated to the Executors as a non-renewable resource that increases their productivity. Each task is characterized by a directive interval (fixed parameter) and execution duration, which depends on the amount of reserve allocated to this task (unfixed desired parameter). The problem of determining the system configuration, as well as the distribution of a non-renewable resource between tasks, is solved. This problem is reduced to a multiproduct flow problem, for which necessary and sufficient conditions for the existence of a solution in the form of a system of linear integer relations are obtained.