Integrating IVFRN-BWM and Goal Programming to Allocate the Order Quantity Considering Discount for Green Supplier

One of the serious supply chain management (SCM) challenges is the effective selection of suppliers and the right allocation of orders to achieve an SCM's suitable financial and technical status. This paper introduced a multi-objective linear programming model to prioritize and weigh suppliers using the modified best–worst method (BWM). The proposed model uses evaluation criteria and used fuzzy variables to determine the right numbers of suppliers as well as order quantity of raw materials each supplier should provide. The model has been made up of four objective functions, and the required constraints have been solved using the goal programming method. The proposed model can take a set of opposing goals into account and prioritize the goals to maximize access to each goal. The uncertain concepts such as fuzzy and rough theories in some criteria enabled the proposed model to use the imprecise information in the best possible manner. This study has solved an example using the proposed model through analytic network process and BWM. Then, the obtained results were compared with our findings for adopting interval-valued fuzzy-rough numbers BWM (IVFRN-BWM) and it was shown that the modified BWM approach generates lower costs and better criteria.