Models of sequential-parallel arrangement of transport operations

The subject of consideration in the research is the problem which belongs to the deterministic theory of schedules. The research presents a model of the problem of drawing up a minimum length expansion. Also, the content and mathematical statements of tasks that are generalizations of this task. The research investigates necessity of formulating and solving generalizations of the problem is dictated by the need for optimization of production processes. In particular, the process of functioning of a flexible automated enterprise, which includes the transport and storage system and parallel operating technological lines, is considered. In this case, technological lines may include conveyors, machining centers, assembly lines, etc. The mathematical model of the problem regarded in the article describes the process of interaction of a transport mechanism with a number of parallel operating lines, on which a certain set of works is performed. There is information about the work assigned to each line. Also the time for each job performance is set. The work is continuous and cannot be broken. Production lines are independent, that is, they function independently of each other. The functions of a vehicle consist in providing lines with means, without which a certain work cannot be started. For its implementation, the transport mechanism at the given time the necessary means delivers from the warehouse to the line and returns to the warehouse, spending the same route time back. Each work cannot begin before the delivery of the resources necessary for its execution. It is necessary to find such a trajectory of the vehicle, which would minimize the time of operation of the whole system. It is shown that the problem can be reduced to the Johnson problem 2 x n.