Team orienteering problem with nonidentical agents and balanced score

In this work, we study a variant of the team orienteering problem motivated by a real-world situation faced by a Mexican telecommunications company. The problem consists of the daily assignment and scheduling of service orders to crews, aiming to balance their wages, and considering the compatibility between service orders and crews. We present a mixed-integer linear formulation with two different metrics to achieve balanced scores and two valid inequalities leveraging the structure of the problem. Afterward, we propose a practical adaptive multi-start heuristic that integrates the learning mechanism of a reactive Greedy Randomized Adaptive Search Procedure. We test the performance of the models and the proposed algorithm on a benchmark of instances adapted from the literature and in a case study based on real data. The results confirm the effectiveness of the proposed algorithm to support the decision-making process.