Maximum matching for multi-capacitated fleet backhaul management

Supply chain efficiency is one of the keys to success for many companies. A critical link in the supply chain is transportation, which needs to be well managed to ensure timeliness, reliability, and minimum cost implications. A potentially costly problem is empty backhauling, which occurs when a cargo truck runs empty on the return trip. To achieve efficient backhaul management, companies need to foster collaboration with other entities to reduce empty load routing. Successful collaborations lead to reduced transportation costs and potentially higher profitability for both entities involved. Given that the objective is to minimize the transportation cost for both sides, the initial aim of our study is to write a model to maximize the matching of delivery trucks and cargoes. Potential constraints to matching include types of trucks and cargoes, cost of shipping and deliveries, time availability of each truck and cargo, and the loading and unloading times of the cargoes. Solutions of the mathematical model are found using the branch and bound technique.