A comparison of cost-sharing models in horizontal cooperative routing

We develop and compare several cost-sharing models for cooperative vehicle routing problems formulated under various objectives and constraints. Our study is motivated by a real-world case involving smallholder farmers in the Province of Quebec. We examine the issues of fairness and stability in cooperative routing, and we show that coalitions served by single routes are sufficient to impose stability conditions. To evaluate equity, we use the Gini coefficient to measure the dispersion of individual savings. Hence we can analyze the trade-offs between fairness and stability. We demonstrate that widely used fairness proxies do not necessarily yield equitable outcomes. We test our methodology on randomly generated instances and on a Quebec-based case study.