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The object of this research is the modern service and production systems, the specific functioning of which lies in a set of sequential and parallel operations with a random duration. A fundamental peculiarity of such systems is the stochastic nature of the duration of a single operation, which depends not only on the external random factors, but also on the choice of resources, and namely on the operator. This substantiates the parallel solution of the task on making a schedule of mutually dependent operations and the task on assigning the operators. In the conditions of resource and time limits, this task is NP difficult and requires the development of algorithms for developing the solution that is close to optimal in the limited time. For the development of mathematical and algorithmic software to solve this task, the author used the critical path method and PERT method, incident wave method, and methods for solving the assignment tasks. As a result, the author acquired a mathematical model that considers the stochastic nature of the duration of a single operation, which depends not only on random factors, but also on the operators. Based on such model, is formulated the optimization task that allows finding the launch time and the corresponding operators to gain the most profit. Based on the analysis of existing approaches and the specificity of the task at hand, the author proposes the algorithm for solving the task founded on successive refinement of the time characteristics of operations.	

Mathematical model and algorithm for solving the problem of planning the operation of multiphase systems with heterogeneous resources and time limits