IJE TRANSACTIONS B: Applications Vol. 35, No. 02, (February 2022) Please cite this article as: H. Nozari, R. Tavakkoli-Moghaddam, J. Gharemani-Nahr, A Neutrosophic Fuzzy Programming Method to Solve a Multi- Depot Vehicle Routing Model under Uncertainty during the COVID-19 Pandemic, International Journal of Engineering, Transactions B: Applications Vol. 35, No. 02, (2022) International Journal of Engineering Journal Homepage: www.ije.ir A Neutrosophic Fuzzy Programming Method to Solve a Multi-Depot Vehicle Routing Model under Uncertainty during the COVID-19 Pandemic H. Nozari 1 , R. Tavakkoli-Moghaddam 1,* , J. Gharemani-Nahr 2 1 School of Industrial Engineering, College of Engineering, University of Tehran, Tehran, Iran 2 Faculty member of Academic Center for Education, Culture and Research, Tabriz, Iran PAPER INFO Paper history: Received 15 September 2021 Received in revised form 20 October 2021 Accepted 23 October 2021 Keywords: Multi-depot vehicle routing Robust fuzzy method Neutrosophic fuzzy programming COVID-19 pandemic ABSTRACT The worldwide prevalence of coronavirus disease (COVID-19) and the severe problems in the distribution of medical equipment have led to the modeling of multi-depot vehicle routing under uncertainty in the COVID-19 pandemic. The primary purpose of the proposed model is to locate warehouses and production centers and route vehicles for the distribution of medical goods to hospitals. A robust fuzzy method controls uncertain parameters, such as demand, transmission, and distribution costs. The effect of uncertainty using a neutrosophic fuzzy programming method shows that by increasing demand, the volume of medical goods exchanges and the number of vehicles used to distribute goods increase. This leads to an increase in the total cost of the problem and the amount of greenhouse gas (GHG) emissions. The results also show that using more vehicles reduces staff fatigue to distribute medical products and reduces the prevalence of the COVID-19 pandemic. In the most important sensitivity analysis of the problem on the capacity of the vehicle, it was determined that by increasing the capacity of the vehicle, fewer vehicles are used, and as a result, the cost and amount of greenhouse gas emissions are reduced. On the other hand, this has led to a decrease in the prevalence of the COVID- 19 virus. doi: 10.5829/ije.2022.35.02b.12 1. INTRODUCTION 1 Logistics is a recognized science as a value-added activity for companies and their products and services by coordinating activities, such as materials management and management, optimizing resource use, minimizing costs, and maximizing service levels. In traditional systems, traffic flows are provided from one category of the supply chain to another. More flexible systems allow for relocation at one level, divide inventory between wholesalers and thus inventory, and manage costs without changing the level of service [1]. Logistics systems are emerging as an essential tool for competition and efficiency for companies to maintain sustainable business and achieve global scale [2]. Their primary purpose is to coordinate activities (e.g., transportation, order processing, warehousing, inventory management, and maintenance) designated as inventory management. *Corresponding Author Email: tavakoli@ut.ac.ir (R. Tavakkoli- Moghaddam). Along with the level of services, the total logistical cost of these activities has become one of the most important economic indicators for the efficiency of a supply chain [3]. In 2014, logistics costs accounted for 11.2% of Brazilian companies’ revenues. Vehicle routing and inventory management are essential for logistics systems that directly impact design costs [4]. Dantzig and Ramser [5] first proposed the problem of vehicle routing in 1959. This is a combination of the two issues of the traveling salesman (unlimited consideration of vehicle capacity) and the packing of boxes (zero consideration of freight costs on the ridges), trying to optimally design a set of routes for the transport fleet in such a way that a certain number of customers to be served and has different side restrictions [6]. The variety of this problem is so great that it is challenging and time- consuming to classify them and express the various states in which it occurs. Since its inception in the 1960s, many