A case study of the profit-maximizing multi-vehicle pickup and delivery selection problem for the road networks with the integratable nodes

TL;DR

This paper introduces a new model for profit-maximizing multi-vehicle pickup and delivery problems that accounts for integratable nodes in road networks, improving efficiency and solution accuracy over existing models.

Contribution

It proposes a novel mixed-integer formulation for PPDSP considering integratable nodes, enhancing computational efficiency and solution quality compared to traditional models.

Findings

The new model reduces the number of variables and constraints as integratable nodes increase.

The proposed method achieves higher solution accuracy within the same time frame.

Experimental results demonstrate clear advantages over existing formulations.

Abstract

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.