Picture Fuzzy Decision-Making Approach for Sustainable Last-Mile Delivery

In light of the increasing importance of last-mile delivery (LMD) and the associated high costs, air pollution, and logistical challenges, research on sustainable LMD is highly trending and dynamic. The selection of sustainable LMD mode is an emerging problem for decision-makers in the logistics industry. The key question is how to determine the best LMD mode from a set of alternatives under numerous criteria with ambiguous, vague, and uncertain sustainability-related information. This paper aims to provide an advanced decision-making approach for sustainable LMD. Firstly, 20 sustainable LMD mode evaluation criteria are identified. Secondly, picture fuzzy sets (PFSs) are exploited to help decision-makers to more naturally express their preferences by voting. Thirdly, a hybrid picture fuzzy criteria weighting method based on the Direct rating and R-norm entropy is developed to compute the importance of evaluation criteria. Fourthly, a novel picture fuzzy Combined Compromise Solution method is formulated to rank alternative LMD modes. Fifthly, the presented picture fuzzy approach for sustainable LMD is implemented in the real-life decision-making context. The results show that “e-cargo bike” is the best alternative in the Pardubice context. The comparative analysis with three state-of-the-art PFS-based MCDM methods approved the high reliability of the provided approach. The sensitivity analyses of the trade-off parameter and balancing factor confirmed the high robustness of the presented approach. The introduced approach can help decision-makers in the logistics industry to elucidate sustainable LMD mode. It can solve not only the highlighted problem but also other MCDM problems under the picture fuzzy environment.