The rapid transition to the digitalization of firms directs companies to speed up their decision-making processes and make technology-based decisions. The increasing environmental concerns and fossil-fuel scarcity force companies to employ new logistical aims, such as reducing fuel consumption and greenhouse gas emission in addition to the traditional cost minimization and profit maximization objectives. Traditional assumptions in fuel consumption calculation have been left not only to reach the objectives of the company and make consistent delivery plans but also to increase the solution quality of real-life problems. From this point of view, this study contributes to the related literature by developing a decision support model for a Travelling Salesman Problem that considers dynamic customer requests and realistic road gradients of the entire road network while calculating fuel consumption from transportation operations. The applicability of the developed model has been shown with a real-life case study in which laboratory samples have been collected and transferred from local family clinics to a central laboratory. Several objective functions are employed to demonstrate the benefits of considering realistic road gradients. The results of the numerical analyses on static and dynamic instances illustrate the benefits of respecting realistic road gradients in fuel consumption and addressing dynamic requests during delivery operations.