###### Abstract  
At this time the effectiveness of the COVID-19 vaccines has been proven, and it is crucial to carry out the complete vaccination of the population. Therefore, it is imperative to optimize the vaccine distribution fleets. This paper discusses the optimization of distribution routes for the Pfizer vaccine in Portugal in terms of transportation time, total costs, and CO\({}_{2}\) emissions. To this end, the Vehicle Routing Problem with Time Windows (VRPTW) model with a vehicle capacity restriction was used. The VRPTW model was tested for two scenarios. The first scenario allowed the driver to work overtime (585 min). The second scenario considered that the driver works 8 h (480 min). The results are presented to compare and justify the proposed method with large significance placed in terms of safety concerns, economic savings, environmental protection, and energy consumption. This paper aims to contribute to the healthcare system by optimizing the COVID-19 vaccine distribution routes and minimizing this process's carbon footprint. vehicle routing problem with time windows; capacity; COVID-19; decision support system; case study +
Footnote †: journal: Applied system  
definition  
on how to define the problem, as well as identify the current solutions to the problem. Therefore, the literature review and theoretical foundations justify the choice of methodology used in this case study. Then, the case study (scenarios to be tested) and the methodology used are presented. Afterwards, the results are presented and discussed. Finally, some limitations and proposals for future works on this matter are detailed and a conclusion is made. When it comes to optimizing vaccine distribution routes, there are several constraints to consider; two of the most crucial being maximum time (due to the fragile state of the vaccines, the deteriorating nature of the vaccine compound, and the storage conditions of the transport unit) and capacity [3; 4; 5]. Therefore, the case study must present a model that considers the present constraints and provides an optimized route. Another relevant aspect that this problem must address is the human impact on the environment, given that transport is a source of greenhouse gas emissions [6]. Logistical processes are not just strongly linked to environmental consequences; they also represent a large part of an organization's costs, forcing the implementation of mechanisms that allow for a minimization of those costs [6; 7]. The strategy to optimize vehicle routes is used in transportation networks to minimize the cost of operation and increase consideration for sustainability. Thus, using the VPRTW model, it is possible to reduce the emission of Carbon Dioxide (CO\({}_{2}\)), reducing environmental impact [6]. The Vehicle Routing Problem with Time Windows (VRPTW) consists of finding the least costly routes that stills ensures each point is visited within a predetermined time window. Thus, considering that each vehicle cannot exceed its capacity, it must start and end a route at a given depot [8]. However, for this study's problem, as already mentioned, the most crucial constraints are time and capacity--not cost--given the short life span during which vaccines can be transported and not lose their effectiveness. Therefore, the problem that this paper focuses on is determining a method to optimize Pfizer vaccine distribution routes in Central Portugal, considering that the proposed solution must consider constraints such as time, vehicle capacity, and logistical environmental consequences. Thus, some other constraints and lines of thought must be considered. Several aspects must be considered to optimize the number of vehicles: the maximum capacity of each vehicle in terms of maximum weight it can carry and the maximum number of Pfizer vaccine bottles it can transport. the demand of each vaccination center and its location must also be considered, in order to calculate the distance in terms of time and minimize it.