Optimization of logistics operations: a mathematical model for the Periodic Vehicle Routing Problem

Abstract

This work addresses a logistics problem faced by a company dedicated to the collection of a single product. The company has a limited and heterogeneous fleet of vehicles, and its customers have known demand and visit frequency within a given planning horizon. The problem is formulated as a Periodic Vehicle Routing Problem (PVRP), and a mixed-integer linear programming (MILP) model is proposed for its resolution, which simultaneously determines the assignment of customers and vehicles to each day, as well as the daily routing. The objective is to minimize the total transportation cost over the planning horizon, subject to capacity constraints, maximum route duration, and frequency requirements. The model is evaluated using real data provided by a pathological waste collection company, analyzing its computational performance and reporting the main results obtained. These results demonstrate the potential of optimization methods to improve operational efficiency and decision-making in real-world logistics contexts.