With the momentous competition on gaining performance objectives and also increasing sustainability regulations rising from the social awareness, selection of the right suppliers meeting both targets within a strategic dimension is highly critical. Indeed, aligning the performance measures with the sustainability goals - representing the social responsibility of corporate - is considered a building block in today's environment. This paper presents a strategic triple-period supplier selection approach based on the consecutive phases of introduction, growth and maturity of a product supplied to the market. Toward this, we utilize a modified sandcone policy indicating the distinctive and also cumulative significances of the competitive priorities in the different periods. Meanwhile, minimum achievement levels are determined for both sustainability and performance measures by a governmental institution and a single manufacturer, respectively. Further, aiming at meeting both cumulative improvement and sustainable alignment, a multi-stage screening algorithm is utilized to evaluate and select suppliers at each period. This innovative solving methodology provides a mechanism where the final supplier is selected based on its current and former performances. The evaluation results show that the use of the cited heuristic method can help decision-makers to conduct preferable strategic relationships with the suppliers having a stable and satisfying performance.