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

Abstract

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