School bus routing-a column generation approach

The School Bus Routing Problem (SBRP), a generalization of the well‐known Vehicle Routing Problem, involves the routing, planning, and scheduling of public school bus transportation. The problem can be divided into several subproblems, including bus stop selection, assigning students to buses, and determining the bus routes. This work presents an exact branch‐and‐price framework for the SBRP, with a strong emphasis on efficiency issues inherently related to column generation (CG). Experiments are conducted on a set of 128 SBRP instances. Many of these instances are solved optimally; for the remaining instances, strong lower bounds have been derived. Furthermore, better integer solutions were found for a number of instances reported in the literature. Both lower bounds computed on the optimum solution and stabilization added to the CG procedure significantly improved computation times.