The Vehicle Routing Problem (VRP) is a well-known optimization problem in which we aim traditionally to minimize transportation costs while satisfying customer demands. In fact, most logistics companies use a heterogeneous fleet with varying capacities and costs, presenting a more complex variant known as Rich VRP (RVRP). In this paper, we present a mathematical formulation of the RVRP, considering both hard time windows and dynamically changing requests to be as close as possible to real-life logistics scenarios. To solve this challenging problem, we propose a Hybrid Genetic Algorithm (HGA). The experimental study highlights the out-performance of our proposal when evaluated alongside other algorithms on the same benchmark problems. Additionally, we conduct a sensitivity analysis to illustrate how resilient the algorithm is when problem parameters are altered.