Optimization of the Structure and Execution Modes of Intersecting Operation Sets

A collection of intersecting packages of operations is executed successively and all operations of each current package are executed in parallel. The intensities of execution of operations to be defined remain invariable for all packages that include these operations. A family of nonintersecting non-unit subsets of the initial set of operations is given. Each of these subsets is considered as a potential block of operations. All operations of such block can be executed with common intensity (in aggregated manner) or completely disaggregated (each operation with its own intensity). Cost and time expenses for execution of operations depend on their volumes and intensities. Additional expenses for execution of operation package are proportional to the duration of this package. The proportionality factor is a sum of coefficient related to aggregate implementation of all blocks in the package and additional coefficients for each such disaggregate block. On the other hand disaggregation allows to reduce the expenses for operations execution by selecting optimal intensities of its operations. The problem is to determine an option to aggregate the operations of the potential blocks or not and to define the intensities of all operations minimizing the total cost under constraint on the total collection duration. The methods for two special cases of the problem are proposed.