A mixed-integer linear programming formulation for the periodic vehicle routing problem with applica-tion to pathological waste collection

Abstract

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.