Work

Exact and Approximate Linear Models for the Multi-Vehicle Probabilistic Covering Tour Problem

Year: 2026

Type: article

Abstract: The Multi-Vehicle Probabilistic Covering Tour Problem aims at designing the tours of a fleet of vehicles characterized by a limited range that has to distribute goods to some distribution facilities, in order for those goods to subsequently reach the final customers. Each truck distributes directly only to the facilities, and the delivered goods reach the final customers with a given probability. The aim of the problem is to maximize the expected quantity of goods delivered to the final customers. The problem can be modeled as a mixed integer program with a non-linear objective function, as already presented in the literature together with a solving method based on a linear model with an exponential number of constraints. The contributions of the present work are a new model and two new linear approximation models able to provide tight lower and upper bounds for the optimal solution of the original problem. An extensive computational campaign on the instances available in the literature validates the new approaches we propose, providing several improved heuristic solutions and upper bounds with respect to the previous state-of-the-art. Several instances are also closed here for the first time.

Source: Algorithms

DOI: 10.3390/a19080643

Authors: Roberto Montemanni, Derek H. Smith

Institutions: University of Modena and Reggio Emilia, University of South Wales

Language: English

Topic: Vehicle Routing Optimization Methods

Subfield: Industrial and Manufacturing Engineering

Field: Engineering

Domain: Physical Sciences

SDG: Industry, innovation and infrastructure

Open Access status: gold

Estimated APC paid: $1,930