Traveling Salesman Problem (TSP) is a generic name that includes diverse practical models. Motivated by applications, a new model of TSP is examined -- a synthesis of classical TSP and classical Transportation Problem. Algorithms based on Integer Programming cutting-plane methods and Branch and Bound Techniques are obvious. Mathematics Subject Classification 2000: 91A05, 91A06, 91A10, 91A44, 90C05, 90C31, 90C90. Keywords and phrases: Traveling Salesman Problem with Transportation and Fixed Additional Payments (TSPT), TSP, algorithm, computational complexity.