The assignment problem belongs to the main tasks of combinatorial optimization. This is a special case of the transport problem. Special methods that allow finding the optimal solution from the set of possible ones have been developed for solving the transport problem. The assignment problem is used in transport to optimize the arrangement of the cars along the routes, in the process of distributing the drivers among the cars, and in the process of distributing freights along the production

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... s. This article considers the case when m n  during the search of optimal solutions in the assignment problem of a transport type. The authors offer an algorithm that allows us to build a bus schedule taking into account the current restrictions in the presence of which the passenger traffic is carried out. A theoretical assessment of time complexity of an offered procedure for constructing all optimal solutions to the assignment problem is presented. An example illustrating the operation of the constructed algorithm, which allows finding the whole set of optimal solutions in polynomial time is given. Recommendations on the use of the algorithm in practice are given.