Алгоритм поиска времени завершения сложного проекта

The article discusses the problem of minimizing the construction time of a complex system, which consists of the set of subsystems. Such problems arise in manufacturing, construction, management, computer science and other fields. Building a system requires consistent construction of its subsystems, which include numerous elements. These elements are supplied to the system’s entrance at specific moments of time. The technological route of each element and each subsystem consisting of a given number of elements, as well as the processing time of each element and subsystem are known. Construction of a complex system is represented as a network graph, which determines its construction sequence. The network graph in this case is a tree of arcs, the root of which is the completion of a complex system’s construction. With a given times of system elements supply and of their compounding into subsystem, the minimum time of system’s construction is equal to the critical path of network graph. To find the critical path it is necessary to determine the completion time of each subsystem. This time depends on availability time of all elements of subsystems required for its assembly. Time critical path can be reduced by removing the idling in the areas of subsystems assembly. Minimization of idling periods provides a critical path of minimum length. There are such timings of complex system element’s arrival at the entrance of network graph for which the total idle periods of elements and subsystems at each point of the assembly will be minimal. Determining such moments of arriving at system’s entrance requires starting from the end of the network graph. Reducing the completion time of system’s assembly entails a reduction in the time of its elements arrival. This reduction leads to a decrease in the arrival time of the subsystem’s elements on the previous point of assembly. Such passage from end to beginning of the network graph, changing times of subsystems’ elements arrival allows minimizing idle periods before the assembly of subsystems at each region. This is achieved by determining the optimum arrive timings of elements at the entrance of network graph. After the performed changes the critical path must be recalculated and only if its value is not changed, the minimum construction time of complex system will be found. To implement the computing algorithm of minimization of a complex system’s construction time, a computer program is developed and the numerical experiments that confirm the effectiveness of the algorithm are performed.