Vehicle Routing Problem with Vector Profits (VRPVP) with Max-Min Criterion
This work addresses a routing optimization problem for scenarios with multiple stakeholders, such as exploration or tourism, but it is incremental as it extends existing vehicle routing problems with a new profit structure and objective.
The paper tackles the vehicle routing problem with vector profits under a max-min criterion, aiming to maximize the profit sum for the least satisfied stakeholder, and develops a solution approach using linear programming relaxation and column-generation, demonstrating its effectiveness through case studies in planetary surface exploration and Rome tours.
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.