The Team Orienteering Problem with Service Times and Mandatory & Incompatible Nodes

TL;DR

This paper introduces a new variant of the Team Orienteering Problem that incorporates service times and node constraints, providing novel formulations and an efficient algorithm that outperform existing solvers on benchmark instances.

Contribution

The authors propose two mathematical formulations and a Cutting-Plane Algorithm for TOP-ST-MIN, addressing its NP-completeness and improving solution efficiency over standard methods.

Findings

CPA outperforms CPLEX on new benchmark instances

The problem is NP-complete even for feasibility

The algorithm is competitive with state-of-the-art methods

Abstract

The Team Orienteering Problem with Service Times and Mandatory & Incompatible Nodes (TOP-ST-MIN) is a variant of the classic Team Orienteering Problem (TOP), which includes three novel features that stem from two real-world problems previously studied by the authors. We prove that even finding a feasible solution is NP-complete. Two versions of this variant are considered in our study. For such versions, we proposed two alternative mathematical formulations, a mixed and a compact formulations. Based on the compact formulation, we developed a Cutting-Plane Algorithm (CPA) exploiting five families of valid inequalities. Extensive computational experiments showed that the CPA outperforms CPLEX in solving the new benchmark instances, generated in such a way to evaluate the impact of the three novel features that characterise the problem. The CPA is also competitive for the TOP since it is able to solve almost the same number of instances as the state-of-art algorithms.