In recent years, the supplier selection problem as one of the important components in sustainable development is considered which this is due to the importance of quality and quantity of the product and sustainability issues. Besides, in this paper, a decision-making tool is provided to solve the sustainable supplier selection and order allocation problem in a multi-period, multi-item, and multi-supplier environment considering quantity discounts and disruption risks. At first, one of the efficient Multiple Criteria Decision Making (MCDM) approaches called Best Worst Method (BWM) is employed to find a global importance weight of each determined criterion and the preference weights of each potential supplier according to these criteria. Then the proposed MILP model attempt to minimize the total costs and maximize the total score of all suppliers in respect to three sustainability aspects. Also, in order to solve the proposed bi-objective mathematical model, a Revised Multi-Choice Goal Programming (RMCGP) method is applied. Additionally, a consistency test is applied to check the quality of expert comments. To investigate the robustness of the approach, the sensitivity analysis is utilized. Also, a real-world case study in the north of Iran is presented to highlight the performance of the proposed model. Finally, the selected suppliers, amount of inventory and shortage, ordered quantity along with other variables are calculated. Also, based on sensitivity analysis, the effect of quantity discounts and disruption risks are revealed. The results approve the efficiency of the proposed approach.