A Branch-and-Bound Algorithm for Determining the Minimal Fleet Size of a Transportation System

The problem of determining a schedule for a traffic system of, e.g., bus or air lines that uses a minimum number of vehicles is treated. The various trips are required to start within given time intervals and have given origins, destinations, and travel times. It is shown that the problem can be formulated as an integer LP problem, but not of the simple network flow type. A rather simple branch-and-bound procedure is devised for its solution, which has been tested with favorable results.