PurposeCybersecurity has received growing attention from academic researchers and industry practitioners as a strategy to accelerate performance gains and social sustainability. Meanwhile, firms are usually prone to cyber-risks that emanate from their supply chain partners especially third-party logistics providers (3PLs). Thus, it is crucial to implement cyber-risks management in 3PLs to achieve social sustainability in supply chains. However, these 3PLs are faced with critical difficulties which tend to hamper the consistent growth of cybersecurity. This paper aims to analyze these critical difficulties.Design/methodology/approachData were sourced from 40 managers in Nigerian 3PLs with the aid of questionnaires. A novel quantitative methodology based on the synergetic combination of interval-valued neutrosophic analytic hierarchy process (IVN-AHP) and multi-objective optimization on the basis of a ratio analysis plus the full multiplicative form (MULTIMOORA) is applied. Sensitivity analysis and comparative analysis with other decision models were conducted.FindingsBarriers were identified from published literature, finalized using experts’ inputs and classified under organizational, institutional and human (cultural values) dimensions. The results highlight the most critical dimension as human followed by organizational and institutional. Also, the results pinpointed indigenous beliefs (e.g. cyber-crime spiritualism), poor humane orientation, unavailable specific tools for managing cyber-risks and skilled workforce shortage as the most critical barriers that show the highest potential to elicit other barriers.Research limitations/implicationsBy illustrating the most significant barriers, this study will assist policy makers and industry practitioners in developing strategies in a coordinated and sequential manner to overcome these barriers and thus, achieve socially sustainable supply chains.Originality/valueThis research pioneers the use of IVN-AHP-MULTIMOORA to analyze cyber-risks management barriers in 3PLs for supply chain social sustainability in a developing nation.