  This paper is a study of an application-based model in profit-maximizing
multi-vehicle pickup and delivery selection problem (PPDSP). The
graph-theoretic model proposed by existing studies of PPDSP is based on
transport requests to define the corresponding nodes (i.e., each request
corresponds to a pickup node and a delivery node). In practice, however, there
are probably multiple requests coming from or going to an identical location.
Considering the road networks with the integratable nodes as above, we define a
new model based on the integrated nodes for the corresponding PPDSP and propose
a novel mixed-integer formulation. In comparative experiments with the existing
formulation, as the number of integratable nodes increases, our method has a
clear advantage in terms of the number of variables as well as the number of
constraints required in the generated instances, and the accuracy of the
optimized solution obtained within a given time.
