Fully Fuzzy Distribution Planning Problem by Using Interval-Valued Bipolar Trapezoidal Fuzzy Number

Abstract

Distribution planning (DP) is a process in which we study the way to get materials and distribute the product from the delivery point to the consuming point after production planning in the supply chain. The limits of possible creation in a model are stock holding, deferred buying, and transportation costs while thinking about the time value of money. Since uncertainty is an undeniable issue in any evident creation framework, fuzzy sets (FS) have been applied in the proposed mathematical modeling. During the COVID-19 pandemic, to maintain physical distance among humans, used & unused equipment, and daily needs, the researchers kept interval-valued fuzzy numbers (IVFNs) in place of crisp numbers that are much more effective to address uncertainty & hesitation in real-world situations. The cost, consumption, and delivery in distribution planning problems (DPP) are not as effective as crisp numbers in compression of fuzzy numbers (FNs). A realistic numerical model in the form of fully fuzzy DPP (FFDPP) has been introduced to show the practical application of the model. The solution procedure and results show the feasibility and validity of the mathematical model. Here we propose the concept of interval-valued bipolar trapezoidal fuzzy number (IVBTrFN) and its operations in the FFDPP, where fuzzy variables are required to be equal to either 0 or 1. The use of IVBTrFN in place of crisp numbers is more suitable for distributing the necessary equipment, medicines, food products, and other relevant items from one place to another in situations like COVID-19. The solution with the conclusion of FFDPP is introduced to better understand and execute our proposed methodology and results with IVBTrFNs.