Locomotive assignment graph model for freight traffic on linear section of railway. The problem of finding a maximal independent schedule coverage

The paper is devoted to the formal statement and solution of a problem arising when assigning the locomotives for freight transportation realization in accordance with preset schedule. The goal is to determine whether the number of locomotives is sufficient at a specified initial allocation of them to perform all transport operations. The solution is presented in the form of an algorithm that builds the coverage of the schedule: the complete one, if it exists, or else the partial one being the maximal independent. The theorem is proved on one-to-one correspondence between the existence of the complete coverage and the sufficiency of the number of locomotives.