Picture fuzzy WASPAS method for selecting last-mile delivery mode: a case study of Belgrade

BACKGROUND: Last-mile delivery (LMD) is becoming more and more demanding due to an increasing number of users and traffic problems in cities. Besides, medical crises (like the COVID-19 outbreak) and air pollution represent additional motives for the transition from traditional to socially and environmentally sustainable LMD mode. An emerging problem for companies in the postal and logistics industry is how to determine the best LMD mode in a multi-criteria setting under uncertainty. METHOD: For the first time, an extension of the Weighted Aggregated Sum Product ASsessment (WASPAS) method under the picture fuzzy environment is presented to solve the LMD mode selection problem. The introduced picture fuzzy set (PFS) based multi-criteria decision-making (MCDM) method can be highly beneficial to managers who are in charge of LMD since it can take into account the neutral/refusal information and efficiently deal with high levels of imprecise, vague, and uncertain information. The comparative analysis with the existing state-of-the-art PFS-based MCDM methods approved the high reliability of the proposed picture fuzzy WASPAS method. Its high robustness and consistency are also confirmed. The presented method can be used to improve LMD in urban areas worldwide. Besides, it can be applied to solve other emerging MCDM problems in an uncertain environment. FINDINGS: A real-life case study of Belgrade is presented to fully illustrate the potentials and applicability of the picture fuzzy WASPAS method. The results show that postomates are the best mode for LMD in Belgrade, followed by cargo bicycles, drones, traditional delivery, autonomous vehicles, and tube transport. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1186/s12544-021-00501-6.