Mathematical Tool for Choosing the Best Material for Producing Masks

There are specific rules for making professional face masks. These rules establish quality standards for masks that are used by medical professionals. The quality standards are based on the filtering power of bacteria and viruses, fluid resistance, breathability, etc. During periods of pandemic acute respiratory infections, the World Health Organization (WHO) use to recommend that professional masks should be a priority for medical professionals, for people who provide hospital and home medical assistance and for people with comorbidities. For other people, is recommended the use of non-professional masks. This type of mask generally is made from fabric and sold by artisans, or made by users themselves from the material that is within the reach. Unlike professional masks, there is no established norm or standard for the assessment of non-professional masks. Many studies have been carried out in order to measure the filtering efficiency of viruses, bacteria and the breathability of various materials for homemade masks, yet, no conclusions have been made on which type of mask is the best. We use an Operational Research approach to solve the problem of choosing the best mask to be produced from a set of masks made from different materials. We propose a mathematical optimization model which is formulated using the Extended Goal Programming. Computational experiments were conducted to analyze the trade-off between different performance measures of materials in the selection of the best mask. This model serves as a very useful tool to be used in the selection of the type of non-professional mask to be made.