Open vehicle routing problem with split deliveries: mathematical formulations and a cutting-plane method

Abstract

This study addresses the open vehicle routing problem with split deliveries, a variant of the classical vehicle routing problem that allows open routes and partitioned deliveries for customers (i.e., multiple vehicles may serve one customer). This approach may be beneficial for companies interested in reducing their logistics and distribution costs. This study is motivated by a company in the pharmaceutical industry, that seeks to explore the possibility of splitting their deliveries to improve quality indicators related to on-time deliveries and customer satisfaction. Two mixed-integer formulations of the problem are proposed. Additionally, a cutting-plane method is designed to improve the optimization performance. Computational experiments were conducted to validate the performance of the formulations. The second formulation effectiveness was confirmed by providing optimal solutions for instances of up to 30 nodes in a reasonable computational time. The incorporation of the cutting-plane method improves performance with a substantial reduction in the GAP. In the case study, this new approach shows its effectiveness in economic terms by providing savings of up to 20% of the current distribution costs.