Vehicle Routing Problem with Vector Profits (VRPVP) with Max-Min Criterion

TL;DR

This paper formulates and solves a novel vehicle routing problem where routes are optimized to maximize the minimum stakeholder profit, using linear programming relaxation and column-generation, demonstrated through planetary and city tour case studies.

Contribution

It introduces the VRP with vector profits and max-min criterion, providing a new formulation and solution approach for multi-stakeholder routing problems.

Findings

Effective solution methodology demonstrated on case studies.

Max-min profit optimization improves stakeholder satisfaction.

Applicable to planetary exploration and city tours.

Abstract

This paper introduces a new routing problem referred to as the vehicle routing problem with vector profits. Given a network composed of nodes (depot/sites) and arcs connecting the nodes, the problem determines routes that depart from the depot, visit sites to collect profits, and return to the depot. There are multiple stakeholders interested in the mission and each site is associated with a vector whose k-th element represents the profit value for the k-th stakeholder. The objective of the problem is to maximize the profit sum for the least satisfied stakeholder, i.e., the stakeholder with the smallest total profit value. An approach based on the linear programming relaxation and column-generation to solve this max-min type routing problem was developed. Two cases studies - the planetary surface exploration and the Rome tour cases - were presented to demonstrate the effectiveness of the proposed problem formulation and solution methodology.