Max–Min Fairness Approach for Collaborative Vehicle Routing Cost Allocation

Abstract

We consider a collaborative vehicle-routing problem involving two or more companies jointly operating delivery fulfillment. It is known that the collaborative routing improves the delivery efficiency that results in a lower cost, CO₂ emission, and traffic congestions. However, cost allocation is a major challenge in the establishment of collaboration because each company has a set of customers whose locations and demands are different. In this paper, we propose an optimization-based framework for determining the optimal vehicle routing and cost allocation of companies in a collaboration, in an unbiased manner. The proposed method relies on max–min fairness that is a widely accepted concept. We formulated this problem as a multi-objective optimization problem. Thereafter, we reformulated the single-objective problem in which the fairness is considered by maximizing the minimum utility of each company in the collaboration. We quantify the utility by applying a fuzzy membership function based on the gained cost benefit. We present computational results ranging from 10 to 80 customers. In all cases, significant improvements are observed in the cost-benefit balance each company gains over the one obtained through the methods compared.