  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.
