Sustainable solutions analysis of a bi-objective green inventory routing problem with heterogeneous fleet and different types of fuels

One of the main agents responsible for global warming is greenhouse gases, especially carbon dioxide (CO 2 ) associated with fuel combustion. Most works in the literature address logistics transportation from an economic perspective, giving little attention to the existing trade-off with sustainability. In this work, we develop a bi-objective approach to the inventory routing problem with heterogeneous fleet, where we minimize costs while simultaneously reducing CO 2 emissions. First, we present an explicit vehicular equation developed to calculate CO 2 emissions for different types of vehicles and fuels. We demonstrate that this equation is statistically precise by conducting a study with a database in which machine learning techniques were applied to assess the predictive accuracy of CO 2 emissions. The comparison between the explicit equation and machine learning models proves its efficacy as a suitable approximation for practical applications. Then, we propose an augmented ɛ -constrained method to find the efficient Pareto frontier using a branch-and-cut method. Computational experiments were conducted on 285 instances, of which 125 were adapted from the literature, solving the augmented ɛ -constrained optimally. Result analysis indicates the ability of the approach to trade off between economy and sustainability, where, on average, lexicographic solutions show a 58% reduction in emissions and a 36% increase in costs. We conclude with a managerial analysis providing insights into the proposed approach, highlighting the advantages of using different vehicles and fuels.