Several factors, such as rapid industrial development, rising population, growing waste disposal, and exponential depletion of natural resources, have become a global challenge and call for a multifaceted approach to environmental protection. Rising consumers' awareness of environmental issues and the evolving ecological legislation puts pressure on businesses to adopt green practices in product design, manufacturing, distribution, and end-of-life disposition. Looking at these challenges, reverse logistics (RL) also known as reverse operations has become the most investigated theme in Supply Chain Management (SCM). Incorporating reverse logistics into the supply chain is not a simple task. Outsourcing reverse operations to the third-party reverse logistics service provider (3PRLSP) is an important strategic decision by many companies. This helps them to achieve a competitive advantage by reducing costs and improving quality processes and services. To this aim, this paper proposes a novel hybrid framework for selecting a 3PRLSP for the electronic industry. The first stage includes the preliminary screening of 3PRLSPs based on the method of effectiveness and compliance (E&C). In the second phase, graph theory and matrix approach (GTMA) is employed to choose the best 3PRLSP for outsourcing the reverse operations. The application of the proposed method is validated through a case-study based approach with reference to the Indian consumer electronic company. The data for the study was collected from experienced experts in senior managerial positions in the industry. The study findings revealed that the three dimensions of sustainability- economic, environmental and social, are vital in selecting 3PRLSP. •Proposed a novel hybrid framework for selection of third-party reverse logistics service provider (3PRLSP).•Method of effectiveness and compliance (E&C) was adopted for screening of 3PRLSPs.•Graph theory and matrix approach (GTMA) was employed for final selection of 3PRLSP.•The model's effectiveness was confirmed by applying it in the Indian consumer electronic industry.