This document addresses the problem of scheduling and routing a specific number of vehicles to visit a set of customers in specific time windows during a planning horizon. The vehicles have a homogeneous limited capacity and have their starting point and return in a warehouse or initial node, in addition, multiple variants of the classic VRP vehicle routing problem are considered, where computational complexity increases with the increase in the number of customers to visit, as a characteris-tic of an NP-hard problem. The solution method used consists of two connected phases, the first phase makes the allocation through a mixed-integer linear programming model, from which the visit program and its frequency in a determined plan-ning horizon are obtained. In the second phase, the customers are grouped through an unsupervised learning algorithm, the routing is carried out through an Ant Colony Optimization metaheuristic that includes local heu-ristics to make sure com-pliance with the restrictive factors. Finally, we test our algorithm by performance measures using instances of the literature and a comparative model, and we prove the effectiveness of the proposed algorithm.

Pathological waste generated in healthcare facilities poses a significant risk of infectious disease transmission and therefore requires specialized collection, transportation, and disposal systems. Efficient logistical planning is essential for companies responsible for managing this waste in order to reduce operational costs while ensuring adequate health and environmental standards. In this context, this study develops an optimization strategy based on the Periodic Vehicle Routing Problem (PVRP) to support the planning of pathological waste collection and transportation activities. A mixed-integer linear programming model (MILP) is proposed to determine the visit schedule for healthcare centers, assign vehicles to service days, and design vehicle routes that satisfy demand and service frequency requirements over a weekly planning horizon while minimizing total operational costs. The model is validated through a real case study from Argentina, demonstrating its applicability to real-world waste management systems. Additionally, a benchmark case from the literature is solved to evaluate the impact and performance of the proposed approach under a deterministic demand scenario derived from historical data. Finally, the performance of the proposed model is compared with alternative PVRP formulations using several benchmark instances, showing the reliability and consistency of the solutions obtained.