Max min fairness approach for collaborative vehicle routing cost allocation

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 singleobjective 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 inthe cost-benefit balance each company gains over the one obtained through the methods compared.