MATHEMATICAL MODELING AND FUZZY $\mathbf{\varepsilon}$ -CONSTRAINT METHOD FOR CLOSED-LOOP MASK SUPPLY CHAIN DESIGN

The outbreak of the deadly coronavirus, which is increasing the number of victims every day, has created many changes in today's world. The use of masks is the most important social tool against this virus. This pandemic has caused a dramatic shortage in the medical supplies needed to treat the virus due to a massive surge in demand as the disease circled the globe during the first half of 2020. Given the importance of rapid and efficient supply of masks in the current situation, it is necessary to study its supply chain in particular. A supply chain is a set of activities including purchase, production, and transportation in order to deliver goods or services to customers. In this research, the design of the closed chain supply chain network for different types of masks is assessed. The studied supply chain includes suppliers, manufacturers, distributors, and retailers in the forward flow and collection centers, separate centers, recycling centers, and disposal centers in the backward flow. In this regard, a bi-objective mathematical model with the objectives of increasing the total profit and reducing the total environmental impact is presented. In this problem, there are some potential locations for collection, recycling, and disposal centers and the model should decide on the location of the established centers as well as the number of produced masks and raw materials. The optimization of this mathematical model was done using fuzzy epsilon-constraint method in GAMS software. The epsilon-constraint method has an advantage that generates Pareto solutions to multi-objective problems. The sample problems are generated using the data of a company in Isfahan, Iran. This company produces 3-layer medical masks and N95 masks, and three raw materials of fabric, mask band, and exhalation valve are used. The results show that maximizing the total profit and minimizing the environmental effects are in contrast to each other, because reducing the environmental impact leads to an increase in total costs and thus, reduction in the organization's profit. Also, increasing demand for mask types increases the profit of the supply chain linearly, but its impact on the chain's environmental impact is completely nonlinear.