An emerging question for waste managers is how to determine the best vehicle shredding facility location from a finite set of available alternatives under numerous conflicting criteria as well as high levels of imprecise, vague, and uncertain information. For the first time, we investigate the vehicle shredding facility location problem via the picture fuzzy sets (PFSs), which show a great power in capturing ambiguous, uncertain, and vague information, and mitigating information loss. This paper aims to exploit PFSs and develop a novel picture fuzzy COmbinative Distance-Based ASsessment (CODAS) method for multi-criteria vehicle shredding facility location. The developed method is applied to a real-life case study for locating a new vehicle shredding facility in the Republic of Serbia. The results show that "Bor" is the best alternative among six possible alternative locations. In the decision-making process, four main criteria, such as economical, environmental, social, and technical, and 23 sub-criteria are considered. The robustness of the proposed method is validated by comparing its results with the outcomes of the PFS based TOPSIS, EDAS, TODIM, VIKOR, MABAC, Cross-entropy, Projection, Grey relational projection, and Grey relational analysis methods. The ranking similarity between the proposed picture fuzzy CODAS method and the available state-of-the-art PFS based methods is checked by applying the Spearman's rank correlation coefficient, in which 90% of rankings are matched. The results of the comparative and sensitivity analyses showed that the proposed method generates highly robust outcomes. The formulated picture fuzzy CODAS method can help waste managers to more naturally express their preferences by voting and identify the best facility location. Besides, it can be used to solve any other MCDM problem under the picture fuzzy environment.