Technical Note—An Improved Lower Bound to the Minimum Fleet Size Problem

Abstract

We give a formal proof that a procedure similar to that used in the VAMPIRES program to find a starting fleet size is a lower bound on the minimum fleet size problem when deadheading trips are allowed. It is shown that this bound is stronger than the “simultaneous operation” bound used previously by the authors in the URDHC program. The URDHC program is an interactive bus scheduling program which inserts deadheading trips into a timetable in an effort to reduce the required fleet size. The “simultaneous operation” lower bound is equal to the maximum number of trips in a given timetable that are in simultaneous operation over the schedule horizon. The improved lower bound is based on the construction of a temporary timetable in which trips are extended to include potential linkages reflected by deadheading time considerations. One example is given to illustrate the construction of the improved bound. This improved lower bound can be usefully employed in the lower bound termination test of the URDHC program or other procedures for the fleet size reduction problem.