A branch-and-price algorithm for a routing and scheduling problem from economic and environmental perspectives

This paper addresses a routing and scheduling problem from two different perspectives: economic environmental. From perspective, we aim to optimize the vehicle plan reduce operating cost, but environmental speed decisions carbon emissions. research can provide decision plans under these perspectives, comparison of results perspectives will be very meaningful helpful logistics decision-makers. We formulate using mixed-integer programming (MIP) models with objectives. However, this is challenging, medium-sized instances already difficult for MIP solver. In order solve it larger scale instances, propose an exact branch-and-price (BAP) algorithm. The BAP algorithm relies on efficiently solving pricing sub-problem design tailored labeling algorithms it. Extensive computational experiments demonstrate effectiveness proposed algorithm, comparing formulation solved by CPLEX time limit 2 h.