Problems and Optimization Algorithms of Schedules of Parallel-Serial Systems with Undefined Service Routes

A new approach to solving the problems to construct optimal operating speed schedules for parallel-serial systems using a two-staged scheme: clustering and subsequent route determination has been presented. Solutions for different types of routing problems with the minimax criterion are special cases of applying the developed tools. Formal definitions of the subproblems clustering and route design in terms of NP-hard discrete programming problems are given. The problem decision approximate algorithm is offered. It is based on the problem decomposition into the subproblem optimum on uniform load on the devices for partitioning a set of jobs into subsets and a sequence of subproblems for optimizing scheduling jobs on devices. Illustrative examples of applying the approach being developed are given. Empirical estimates of the accuracy and software performance have been computed. Speed and accuracy of the developed algorithms have been investigated on randomly generated test examples in wide variety of dimensions. Possible practical application when developing schedules for the implementation of major industrial projects are indicated. Based on this investigation, future research directions are identified.