The result of the work is the developed algorithms used in solving transport mode problems (choice problems and traveling salesman problems). Algorithm 1 is designed to construct orthogonal cyclic permutations. A modification of the Hungarian method (algorithm 2) allows one to determine a system of different representatives of subsets of a finite set, to determine a set of orthogonal permutations. Algorithm 2 can use elements of randomness in the construction of orthogonal permutations and, as it turned out, Latin squares and, thereby, regulate the uniformity of the probability of each digit falling into each cell of the Latin square, which improves the quality of its application.