A generalized travelling salesman problem and its applications

The paper is concerned with the problem of developing a salesman's itinerary with minimal total losses due to travel expenses for going to the point $j$ from the point $i$ and due to completion of service in the point $i$ at time $T_i$. The constraints on the itinerary imply that certain points should be serviced before a deadline. The problem has numerous applications in the sheduling theory, maintenance arrangements and routing the shipments. Properties of these problems are revealed and branch-and-bound solution algorithms are proposed.